

                             Students' QuickField (TM)

                          Finite Element Analysis System

                                    Version 3.4

                                   User's Guide



 Copyright (C) Tera Analysis Company, 1995.
 All Rights Reserved.

 The information  contained in  this document is  subject to  change without
 notice.

 Tera Analysis Co.
 P.O. Box 571086,
 Tarzana, CA 91357

 E-mail:   terainfo@tera-analysis.com
 URL:      http://www.tera-analysis.com
 Tel:      818 831 9662
 Fax:      805 493 2172

 QuickField is a trademark of Tera Analysis Company.
 DXF is a trademark of Autodesk, Inc.
 IBM PC/AT and PC-DOS are trademarks of International Business Machines
 Corporation.
 Microsoft and MS-DOS are registered trademarks, and Windows and Microsoft
 Word are trademarks, of Microsoft Corporation.
 Adobe, Adobe Illustrator, and PostScript are registered trademarks of Adobe
 Systems, Inc.


  All other brand and product names are trademarks or registered trademarks
                         of their respective owners.



                              Table Of Contents


 1. Getting Started

 2. Required Hardware Configuration
    2.1 QuickField Installation
    2.2 Starting QuickField
    2.3 Quitting QuickField

 3. Introductory Guide
    3.1 Basic Organization of QuickField
    3.2 Overview of Analysis Capabilities
      3.2.1 Magnetostatic Analysis
      3.2.2 Harmonic Magnetic Field
      3.2.3 Electrostatic Analysis
      3.2.4 Current Flow Analysis
      3.2.5 Thermal Analysis
      3.2.6 Stress Analysis

 4. Basic Skills
    4.1 Terminology
    4.2 Working with Menus
    4.3 Working with Dialog Boxes
      4.3.1 Command Buttons
      4.3.2 Text Boxes
      4.3.3 List Boxes
      4.3.4 Drop-Down List Boxes
      4.3.5 Option Buttons
      4.3.6 Check Boxes
    4.4 Selecting Geometric Objects
    4.5 Using Rubber Band Rectangle

 5. Problem Description
    5.1 Structure of Problem Database
    5.2 Creating a New Problem
    5.3 Establishing Coupling Links
    5.4 Choosing Length Units
    5.5 Cartesian vs. Polar Coordinates

 6. Model Geometry Definition
    6.1 Terminology
    6.2 How to Create a Model
      6.2.1 Starting and Quitting the Model Editor
      6.2.2 Objects Selection
      6.2.3 Geometry Description
      6.2.4 Copying and Moving Geometric Objects
      6.2.5 Labeling Vertices, Edges and Blocks
      6.2.6 Building the Mesh
      6.2.7 Zooming
      6.2.8 Obtaining Model Information
    6.3 Additional Options
      6.3.1 Saving Model
      6.3.2 Opening Model File
      6.3.3 DXF File Import
      6.3.4 Discretization Visibility Options
      6.3.5 Attraction Distance Parameter

 7. Problem Parameters Description
    7.1 Creating a New Label
    7.2 Editing Label Data
      7.2.1 Editing Data in Magnetostatics
      7.2.2 Editing Data in Harmonic Magnetics
      7.2.3 Editing Data in Electrostatics
      7.2.4 Editing Data with Current Flow Problems
      7.2.5 Editing Data with Heat Transfer Problems
      7.2.6 Editing Data with Stress Analysis Problems
      7.2.7 Editing the Curves
    7.3 Copying, Renaming and Deleting Labels
    7.4 Merging and Copying Data Files

 8. Solving the Problem

 9. Analyzing Solution
    9.1 Starting and Quitting the Postprocessor
    9.2 Building the Field Picture on the Screen
      9.2.1 Interpreted Quantities
      9.2.2 Field Presentation Methods
      9.2.3 Field Picture Constructing
      9.2.4 Zooming
    9.3 Access to Local Field Data
    9.4 X-Y Plots
      9.4.1 Editing Contours
      9.4.2 X-Y Plot Control
      9.4.3 Zooming the X-Y Plot
    9.5 Calculating Integrals
    9.6 Saving Prepared Results to Files
      9.6.1 Saving the Screen Picture
      9.6.2 Exporting Local Values to the Table File
      9.6.3 Exporting Field Values along the Contour to the Table File
      9.6.4 Fast Printing the Results
    9.7 Additional Options
      9.7.1 Saving the Postprocessor State
      9.7.2 Controlling Legend Display
      9.7.3 Changing Color Scheme

 10. Examples
    10.1 Magnetic Problems
      10.1.1 MAGN1: Nonlinear Permanent Magnet
      10.1.2 MAGN2: Solenoid Actuator
      10.1.3 MAGN3: Ferromagnetic C-Magnet
    10.2 Time-Harmonic Magnetics Problem
      10.2.1 HMAGN1: Slot Embedded Conductor
      10.2.2 HMAGN2: Symmetric Double Line of Conductors
    10.3 Electrostatic Problems
      10.3.1 ELEC1: Microstrip Transmission Line
      10.3.2 ELEC2: Two Conductor Transmission Line
    10.4 Heat Transfer Problems
      10.4.1 HEAT1: Slot of an Electric Machine
      10.4.2 HEAT2: Cylinder with Temperature Dependent Conductivity
    10.5 Stress Analysis Problems
      10.5.1 STRES1: Perforated Plate
    10.6 Coupled Problems
      10.6.1 COUPL1: Stress Distribution in a Long Solenoid
      10.6.2 COUPL2: Cylinder Subject to Temperature and Pressure
      10.6.3 COUPL3: Temperature Distribution in an Electric Wire


                              About This Manual



 What Is QuickField?


 Welcome  to QuickField  Finite Elements  Analysis System.  QuickField is  a
 PC-oriented interactive environment for electromagnetic, thermal and stress
 analysis. Standard analysis types include:

 * Electrostatics.
 * Linear and nonlinear magnetostatics.
 * Harmonic magnetics (involving eddy current analysis).
 * Linear and nonlinear heat transfer and diffusion.
 * Linear stress analysis.
 * Coupled problems.


 During  a  15-minute  session, you  can  describe  the  problem  (geometry,
 material properties,  sources and other  conditions), obtain  solution with
 high accuracy and analyze field details looking through full color picture.
 With  QuickField, complicated  field  problems can  be  solved  on your  PC
 instead of large mainframes or workstations.


 How to Use this Manual


 This manual has nine chapters:

 Chapter 1, "Getting Started", describes first steps of using QuickField. In
 this chapter, you will learn how to install and start the package.

 Chapter 2,  "Introductory Guide",  briefly  describes  the organization  of
 QuickField and gives an overview of analysis capabilities.

 Chapter 3,  "Basic   Skills",  tells  you   about  working   patterns  with
 QuickField.
 Chapter 4, "Problem Description", explains how to specify the analysis type
 and general problem features.

 Chapter 5, "Model  Geometry Definition", explains how  to describe geometry
 of the model,  build the mesh, and define material  properties and boundary
 conditions.

 Chapter 6, "Problem Parameters  Description", introduces non-geometric data
 file organization, and the way to attach this file to the model.

 Chapter 7, "Solving  the Problem",  tells you  how to  start the  solver to
 obtain analysis results.

 Chapter 8, "Analyzing  Solution", introduces QuickField  Postprocessor, its
 features and capabilities.

 Chapter 9, "Examples", contains description of some example problems, which
 can be analyzed using QuickField.


 Conventions


 In this manual we use CAPITAL LETTERS to  specify the names of keys on your
 keyboard. For  example, ENTER, ESC,  or ALT. Four  arrows on  the keyboard,
 collectively named the DIRECTION keys, are  named for the direction the key
 points: UP ARROW, DOWN ARROW, RIGHT ARROW, and LEFT ARROW.

 A plus sign  (+) between key names means  to hold down the  first key while
 you press the second key. A comma (,)  between key names means to press the
 keys one after the other.

 "Text in quotation marks" is used for QuickField menu and dialog options.


                              1. Getting Started



                      2. Required Hardware Configuration




           Computer:           A 286 or higher Intel processor based
                               IBM PC compatible.

           Coprocessor:        Intel 287 or higher math coprocessor.

           Memory:             640K.

           Display:            EGA, VGA color or LCD monochrome.

           Mouse:              Microsoft mouse or 100% compatible with
                               Microsoft mouse driver, version 8.00 or
                               above.

           Operating System:   MS-DOS, or PC-DOS (Rev. 3.3 or above).


           2.1 QuickField Installation


 Distribtuion kit of  QuickField 3.4 (Students' QuickField)  consist of four
 archive files:QFLD34-1.ZIP, QFLD34-2.ZIP, QFLD34-3.ZIP, QFLD34-4.ZIP
 After unzipping  (don't forget  -d switch  to restore  directory structure)
 QuickField directory should contain:

 six ASCII files:
 *    FILE_ID.DIZ    - descriptor;
 *    README.TXT     - primary information;
 *    MANUAL.TXT     - system documentation;
 *    REG_FORM.TXT   - registration form;
 *    VENDOR.TXT     - information for shareware distributors;
 *    FAQ.TXT        - frequently asked questions about QuickField.

 and two subdirectories:
 *    BIN       - contains all the files needed to run QuickField;
 *    EXAMPLES  - contains example problems.

 The BIN  directory contains  all the  necessary to  run the  package. These
 files are  to be  copied to  the special  directory on  the hard  disk, for
 example, C:\QF\BIN. For your convenience, we  recommend to include the name
 of this directory to DOS PATH environment variable.

 The  EXAMPLES  directory   contains  a  number  of   problems  solved  with
 QuickField. We suggest you to look through the examples in the area of your
 interest, before you start with your own problems.

 To operate with large amount of  data, QuickField creates temporary file in
 the current  working directory.  You can specify  alternate place  for this
 file by  assigning path  of the preferred  directory to  QFTEMP environment
 variable,  e.g., to  store temporary  files in  the C:\TEMP  directory, you
 could include SET QFTEMP=C:\TEMP line in your AUTOEXEC.BAT.

 QuickField can  use the extended  memory of PC.  This feature  is available
 through the XMS driver, e.g., HIMEM.SYS distributed with MS-DOS 5.0 and 6.x
 and Microsoft Windows 3.x.

      Note. QuickField  uses part  of the extended  memory that  is not
      occupied by  RAM disks,  disk caching  systems or  other resident
      programs.

 The BIN directory  of QuickField distribution kit contains  four files with
 .CFG extension. These files contain optional color tables:

 SCREENC.CFG    color table for VGA and EGA color monitors;

 SCREENL.CFG    color table for LCD monitor of Laptop;

 SCREENG.CFG    gray scale  color table, can  be used when  obtaining screen
                hard copy on a monochrome printer;

 SCREEN.CFG     default color table, the same as SCREENC.CFG.

 You can change the default by replacing SCREEN.CFG on your hard disk with a
 copy of the color table you prefer.

 Installation under Windows

 If you are not  planning to run QuickField under Windows,  you can skip the
 rest of this section.

 The  installation under  Windows 3.x  is done  after completion  the normal
 installation procedure. While in Program Manager,  select the program group
 you  want to  add  QuickField to,  or  create a  new  program group  called
 QuickField. From the  File menu of Program Manager, choose  New. In the New
 Program Item  dialog box, select the  Program Item option, and  then choose
 the OK  button.. In Program Item  Properties dialog box.,  type "QuickField
 3.4" in  Description line. Choose the  Browse button, and in  Browse dialog
 box, select the  QFIELD.PIF file from the QuickField  BIN directory. Choose
 the OK button  to return to Program Item Properties  dialog box. Choose the
 Change Icon  button. Choose  OK button  to get to  Change Icon  dialog box.
 Choose  the Browse  button and  select  the QFIELD.ICO  file  from the  BIN
 directory. Choose  the OK button three  times to complete  the installation
 process.

 Now you can start QuickField under Windows by double clicking its icon.

 Additional Configuration Options

 QuickField can  use the extended  memory of PC.  This feature  is available
 through the XMS driver, e.g., HIMEM.SYS  included in MS-DOS 5.0 and 6.x and
 in Microsoft Windows 3.x. See Chapter -2 for  details how additional memory
 can improve performance.

     Note.  QuickField uses  part of  the  extended memory  that is  not
     occupied  by RAM  disks,  disk caching  systems  or other  resident
     programs.


 If you do not have extended memory QuickField creates temporary file in the
 current working directory.You can specify alternate  place for this file by
 assigning path of  the preferred directory to  QFTEMP environment variable,
 e.g., to store temporary files in  the C:\TEMP directory, you could include
 SET QFTEMP=C:\TEMP line in your AUTOEXEC.BAT.

 The BIN  directory of QuickField contains  four files with  .CFG extension.
 These files represent optional color schemes:

 SCREENC.CFG    color scheme for VGA and EGA color monitors;

 SCREENL.CFG    color scheme for a monochrome LCD monitor of Laptop;

 SCREENG.CFG    gray scale color  scheme, can be used  when obtaining screen
                hard copy on a monochrome printer;

 SCREEN.CFG     default color scheme, the same as SCREENC.CFG.

 You can change the default by replacing SCREEN.CFG on your hard disk with a
 copy of the color scheme you prefer.


           2.2 Starting QuickField


 To start  QuickField, go  to the  directory you devoted  for this  work and
 enter  QFIELD at  your system  prompt.  The command  line  may include  the
 problem file name. If  it does not, the name is  taken from QFIELD.INI file
 of the previous session. If QFIELD.INI  is absent in the current directory,
 or does not contain the problem file  name, QuickField will ask you for the
 name of the problem to work with.


           2.3 Quitting QuickField


 To exit from QuickField to operating system environment, choose "Exit" from
 the "File" menu (ALT+F, X), or press ALT+F4.


                            3. Introductory Guide



 This chapter  briefly describes  the basic  organization of  the QuickField
 program. It presents an overview of the available capabilities.

 The aim of this chapter is to  get you started with modeling in QuickField.
 If you are new  to the QuickField, we strongly recommend  you to study this
 chapter.  If  you haven't  yet  installed  QuickField,  please do  so.  For
 information on installing QuickField see Getting Started


           3.1 Basic Organization of QuickField


 QuickField is a  menu driven system, when you just  get into QuickField you
 see the  main menus which  are located in  a horizontal bar  on top  of the
 screen. The four  main menus are "File", "Edit",  "Results", and "Options".
 Here, we  briefly describe the functions  of these menus and  some of their
 corresponding submenus.

 "File"  menu contains  all  the tools  for  choosing  and manipulating  the
 database files. For example, you can choose a new problem name or select an
 old  problem  in  any  existing  directory.  The  detailed  description  of
 operations on problem files is given in Problem Description.

 Edit menu  contains all  the submenus  and tools  for creating  the problem
 model and defining all the necessary parameters. It consists of four parts,
 "Problem", "Geometry", "Data", and "Library Data".

 "Problem" provides  you with a dialog  box to describe the  general problem
 parameters,   such    as   the   type   of    analysis   ("Electrostatics",
 "Magnetostatics", "Heat  transfer" and etc.) or  the model type  (planar or
 axisymmetric).  The detailed  description of  how to  do this  is given  in
 Problem Description.

 "Geometry", takes you to another graphic  interface to define the geometry,
 the part  labels and the mesh  for your model. The  detailed description of
 the geometric modeler is given in Model Geometry Definition.

 "Data" provides  you with  dialog boxes  to assign  the values  of material
 properties, loadings and boundary conditions for different part labels, and
 "Library Data" allows  you to edit the existing data  library. The detailed
 description of how  to specify properties and boundary  conditions is given
 in Chapter 6.

 The "Results"  menu contains  all the  tools for  solving your  problem and
 analyzing  the results.  It  consists of  two  parts,  "Solve Problem"  and
 "Analyze".  After completing  the  model and  assigning  all the  necessary
 parameters, you can choose "Solve Problem"  to obtain the solution for your
 problem. "Analyze"  takes you  to a special  graphic interface  for graphic
 display of  the results  and other  postprocessing functions.  The detailed
 description of how to get and explore  the results of the analysis is given
 in Chapter 7 and Chapter 8.

 Using  the above  features, QuickField  helps  you build  and analyze  your
 design problems very quickly. In analyzing  a problem, the typical sequence
 of phases that you go through  with QuickField is depicted in the flowchart
 below:

    +--------------------------+
    ! Choose a problem name    !
    !                          !
    !         File: New        !
    +--------------------------+
                !
                !
    +--------------------------+
    ! Specify the problem type !
    !                          !
    !      Edit: Problem       !
    +--------------------------+
                !
                !
    +--------------------------+
    ! Define the geometry,     !
    ! part labels and          !
    ! mesh for your model      !
    !                          !
    !      Edit: Geometry      !
    +--------------------------+
                !
                !
    +--------------------------+
    ! Provide the data for the !
    ! materials, loads,        !
    ! boundary conditions      !
    !                          !
    !         File: New        !
    +--------------------------+
                !
                !
    +--------------------------+
    ! Obtain the solution      !
    !                          !
    ! Results: Solve Problem   !
    +--------------------------+
                !
                !
    +--------------------------+
    ! Review the results and   !
    ! obtain the postprocessing!
    ! parameters               !
    !                          !
    !    Results: Analyze      !
    +--------------------------+



           3.2 Overview of Analysis Capabilities


 This section provides you with the  basic information on different analysis
 capabilities.

       3.2.1 Magnetostatic Analysis

 Magnetic analysis is  used to design or analyze variety  of devices such as
 solenoids, electric  motors, magnetic shields, permanent  magnets, magnetic
 disk  drives,  and  so  forth. Generally  the  quantities  of  interest  in
 magnetostatic analysis are magnetic flux  density, field intensity, forces,
 torques, inductance, and flux linkage.

 QuickField can perform linear and nonlinear  magnetostatic analysis for 2-D
 and  axisymmetric  models. The  program  is  based  on a  vector  potential
 formulation. Following options are available for magnetic analysis:

 MATERIAL PROPERTIES: air, orthotropic materials with constant permeability,
 ferromagnets,  current  carrying  conductors, and  permanent  magnets.  B-H
 curves for ferromagnets can easily be  defined through an interactive curve
 editor, see the "Editing the Curves" section in Chapter 6.
 LOADING  SOURCES: current  density, uniform  external  field and  permanent
 magnets.

 BOUNDARY  CONDITIONS: Prescribed  potential  values (Dirichlet  condition),
 prescribed values for tangential flux density (Neumann condition), constant
 potential  constraint for  zero normal  flux conditions  on the  surface of
 superconductor.

 POSTPROCESSING RESULTS: magnetic potential,  flux density, field intensity,
 forces,   torques,  magnetic   energy,  flux   linkage,  self   and  mutual
 inductances.

 SPECIAL FEATURES:  A postprocessing calculator is  available for evaluating
 user defined  integrals on given curves  and surfaces. The  magnetic forces
 can be  used for stress analysis  on any existing  part (magneto-structural
 coupling).

       3.2.2 Harmonic Magnetic Field

 Harmonic  magnetic analysis  is used  to analyze  magnetic field  caused by
 alternating  currents  and,  vise  versa,   electric  currents  induced  by
 alternating magnetic field (eddy currents). This kind of analysis is useful
 with different inductor devices, solenoids, electric  motors, and so forth.
 Generally  the quantities  of interest  in harmonic  magnetic analysis  are
 electric current (and its source and induced component), voltage, generated
 Joule  heat,  magnetic  flux density,  field  intensity,  forces,  torques,
 impedance and inductance.

 Following options are available for harmonic magnetic analysis:

 MATERIAL PROPERTIES: air, orthotropic materials with constant permeability,
 current carrying conductors with known current or voltage.

 LOADING SOURCES: voltage, total current,  current density, uniform external
 field.

 BOUNDARY  CONDITIONS: Prescribed  potential  values (Dirichlet  condition),
 prescribed values for tangential flux density (Neumann condition), constant
 potential  constraint for  zero normal  flux conditions  on the  surface of
 superconductor.

 POSTPROCESSING RESULTS: magnetic potential,  current density, voltage, flux
 density,  field intensity,  forces, torques,  Joule heat,  magnetic energy,
 impedances, self and mutual inductances.

 SPECIAL FEATURES:  A postprocessing calculator is  available for evaluating
 user defined  integrals on given curves  and surfaces. The  magnetic forces
 can be  used for stress analysis  on any existing  part (magneto-structural
 coupling);  and power  losses  can  be used  as  heat  sources for  thermal
 analysis (electro-thermal coupling).

       3.2.3 Electrostatic Analysis

 Electrostatic analysis is  used to design or analyze  variety of capacitive
 systems  such as  fuses, transmission  lines  and so  forth. Generally  the
 quantities  of interest  in electrostatic  analysis are  voltages, electric
 fields, capacitances, and electric forces.

 QuickField  can   perform  linear  electrostatic   analysis  for   2-D  and
 axisymmetric models. The program is based  on Poisson's equation. Following
 options are available for electrostatic analysis:

 MATERIAL PROPERTIES: air, orthotropic materials with constant permittivity.

 LOADING SOURCES: Voltages, and electric charge density.
 BOUNDARY  CONDITIONS: Prescribed  potential  values (Voltages),  prescribed
 values for normal derivatives (surface charges), and prescribed constraints
 for constant potential boundaries with given total charges.

 POSTPROCESSING RESULTS:  voltages, electric  fields, gradients  of electric
 field, flux  densities (electric displacements), surface  charges, self and
 mutual capacitances, forces, torques, and electric energy.

 SPECIAL FEATURES:  A postprocessing calculator is  available for evaluating
 user defined  integrals on given  curves and surfaces.  Floating conductors
 with unknown voltages  and given charges can be  modeled. The electrostatic
 forces can  be used for stresses  on any existing  part (electro-structural
 coupling).

       3.2.4 Current Flow Analysis

 Current flow  analysis is  used to analyze  variety of  conductive systems.
 Generally the quantities of interest in current flow analysis are voltages,
 current densities, electric power losses (Joule heat).

 QuickField  can   perform  linear  current   flow  analysis  for   2-D  and
 axisymmetric models. The program is based  on Poisson's equation. Following
 options are available for current flow analysis:

 MATERIAL PROPERTIES: orthotropic materials with constant resistivity.

 LOADING SOURCES: Voltages, electric current density.

 BOUNDARY  CONDITIONS: Prescribed  potential  values (Voltages),  prescribed
 values for  normal derivatives (surface current  densities), and prescribed
 constraints for constant potential boundaries.

 POSTPROCESSING  RESULTS:  voltages,  current  densities,  electric  fields,
 electric current through a surface, and power losses.

 SPECIAL FEATURES:  A postprocessing calculator is  available for evaluating
 user defined  integrals on  given curves and  surfaces. The  electric power
 losses can  be used as heat  sources for thermal  analysis (electro-thermal
 coupling).

       3.2.5 Thermal Analysis

 Thermal  analysis plays  an  important role  in  design  of many  different
 mechanical and electrical systems. Generally the  quantities of interest in
 thermal analysis are temperature distribution,  thermal gradients, and heat
 losses.

 QuickField can  perform linear and nonlinear  thermal analysis for  2-D and
 axisymmetric models. The program is based  on heat conduction equation with
 convection  and  radiation  boundary   conditions.  Following  options  are
 available for thermal analysis:

 MATERIAL   PROPERTIES:   orthotropic   materials  with   constant   thermal
 conductivity, isotropic temperature dependent conductivities.

 LOADING SOURCES: constant and temperature  dependent volume heat densities,
 convective and radiative sources, Joule heat  sources imported from current
 flow analysis.

 BOUNDARY   CONDITIONS:  Prescribed   temperatures,  boundary   heat  flows,
 convection, radiation, and prescribed  constraints for constant temperature
 boundaries.

 POSTPROCESSING   RESULTS:  temperatures,   thermal  gradients,   heat  flux
 densities, and total heat losses or gains on a given part.
 SPECIAL FEATURES:  A postprocessing calculator is  available for evaluating
 user  defined integrals  on given  curves and  surfaces. Plate  models with
 varying thicknesses can be used for  thermal analysis. The temperatures can
 be used for thermal stress analysis (thermo-structural coupling).

       3.2.6 Stress Analysis

 Stress  analysis  plays an  important  role  in  design of  many  different
 mechanical and electrical components. Generally  the quantities of interest
 in stress analysis  are displacements, strains and  different components of
 stresses.

 QuickField can perform  linear stress analysis for 2-D  plane stress, plane
 strain, and axisymmetric  models. The program is based  on Navier equations
 of elasticity. Following options are available for stress analysis:

 MATERIAL PROPERTIES: isotropic and orthotropic materials.

 LOADING  SOURCES:  concentrated  loads,   body  forces,  pressure,  thermal
 strains, and  imported electric  or magnetic  forces from  electrostatic or
 magnetostatic analysis.

 BOUNDARY CONDITIONS: prescribed displacements, elastic spring supports.

 POSTPROCESSING   RESULTS:  displacements,   stress  components,   principal
 stresses, von Mises stress, Tresca,  Mohr-Coulomb, Drucker-Prager, and Hill
 criteria.


                               4. Basic Skills


 This  chapter describes  the working  environment  that you  will use  with
 QuickField.

 QuickField is a  menu driven system. The meaning of  the selected menu item
 is explained by the prompt message occupying the bottom line of the screen.
 The same line is used for other messages.

 In most  context the  ESC key  may be used  to cancel  or to  interrupt the
 current action. The right mouse button  is completely equivalent to the ESC
 key. The left mouse button is used to click objects.


           4.1 Terminology


 The following  terms are used  to describe your  actions when  working with
 QuickField.

 Choose  - To use a mouse or key combination  to pick an item that begins an
           action.  For example,  choosing a  menu item  usually causes  the
           execution of QuickField command.

 Click   - To press  the mouse  button while  the tip  of the  mouse pointer
           rests on the item of choice.

 Double-click   -    To click the mouse button twice in rapid succession.

 Select  - To mark  an item by highlighting  it with key combinations  or by
           clicking it with a mouse. Selecting does not initiate an action.


           4.2 Working with Menus

 To choose a  menu item click it with a  mouse. You can also use  the UP and
 DOWN ARROW keys to select the item you  want; then press ENTER. If the item
 name has an underlined letter, you can type it to choose the menu item with
 one step. To select an item on the horizontal menu bar press its underlined
 letter while holding down the ALT key.

 Pressing the  ESC key  or clicking  the right mouse  button returns  to the
 previous menu level. If you press ESC while in main menu, you will be asked
 about exiting to DOS.


           4.3 Working with Dialog Boxes


 QuickField  uses dialog  boxes  to get  information  from  you and  provide
 information  to   you.  For  example,  when   QuickField  needs  additional
 information to carry  out a command you have chosen,  a dialog box requests
 the  information. You  complete the  dialog  box by  providing the  missing
 information.  Whenever you  see an  ellipsis  (...) after  a menu  command,
 another menu or a dialog box follows.

 For  example, when  you  choose "Open"  from  the  "File" menu,  QuickField
 displays a dialog box asking for the name of the file you want to open.

 Most dialog  boxes contain  options, each  asking for  a different  kind of
 information. After you  supply all the requested information,  you choose a
 command button to carry out the command.

 Often  you  need  to move  around  within  a  dialog  box to  make  several
 selections. The current option is marked by a highlight or dotted rectangle
 (or both) around the name of the option  or button. To move within a dialog
 box:

 * Click the option you want to move to.
 * Press  TAB to  move forward  (generally  from left  to right  and top  to
   bottom) or SHIFT+TAB to move in opposite direction.
 * Use the DIRECTION keys to move in desired direction.
 * Or, while you hold ALT, you can  type the underlined letter in the option
   name or group name.


 The options that are unavailable for some reason are dimmed.

 The next  few sections describe different  dialog boxes and  the procedures
 for selecting options.

       4.3.1 Command Buttons

 Command buttons  initiate an immediate action.  One command button  in each
 dialog  box carries  out  the command  you  choose,  using the  information
 supplied  in the  dialog box.  This  button is  usually  named "OK".  Other
 command  buttons let  you  cancel the  command  or  choose from  additional
 options.

 Command buttons  marked with an ellipsis  (...) open another dialog  box so
 you  can provide  more  information. The  currently  selected, or  default,
 button has  a highlighted  green name  or, in a  monochrome mode,  a darker
 border  than the  other buttons.  You  can choose  the  selected button  by
 pressing ENTER.

 You  can close  the dialog  box without  completing a  command by  choosing
 "Cancel" button.
 To choose a command button:

 * Click it.
 * Move to the command button you want. A dotted rectangle around the button
   text marks the  selected button. Press the SPACEBAR (or  ENTER) to choose
   the button.
 * Or, while you hold ALT, you can  type the underlined letter in the button
   name.


 Some dialog boxes are so small that do not contain any command button. Such
 dialog boxes are  usually located at the right-hand side  of the screen and
 have gray  background. In spite of  missing the "OK" command  button, it is
 still possible to  use a mouse to  carry out the command  you choose. Click
 the dialog box background anywhere outside  options. The effect will be the
 same as if using the "OK" command button.

       4.3.2 Text Boxes

 A text box is a rectangle into which you type information.

 When you move to an empty text box, a  text cursor appears at the left side
 of the box. The text you type starts at the cursor position.

 If the box already contains text  when you move to it, all  the text in the
 box is  automatically selected and any  text you type replaces  it. Or, you
 can  erase the  existing text  by pressing  DEL. To  discard the  selection
 simply move the cursor to the point where  you want to enter or erase text.
 Use LEFT and RIGHT ARROW, HOME or END keys to move the cursor.

 The text exceeding the length of the text box is scrolled automatically.

       4.3.3 List Boxes

 The list box shows a column of available choices. If there are more choices
 than can fit in the list box, a scroll bar  is provided so that you can use
 your mouse to move up and down quickly through the list.

 To scroll one line click one of the  scroll arrows. To scroll one window up
 or down  click the gray  background of  the scroll bar  above or  below the
 white rectangle.

 When the required item  is already visible in the list  box, you can select
 it by  clicking it  with a  mouse. You  also can  double-click the  item to
 choose it and complete the command at once.

 To select  an item using a  keyboard press UP or  DOWN ARROW key  until you
 reach  your choice.  You also  can use  PAGE UP and  PAGE DOWN to  move one
 window a time, and HOME or END to move to the  first or to the last item of
 the list.  Or, type the first  letter of the  item you want,  the highlight
 will be moved to the first item that starts from that letter.

       4.3.4 Drop-Down List Boxes

 A  drop-down list  box appears  initially  as a  rectangular  box with  the
 current choice (default) displayed in the box. The arrow in a square box at
 the right  opens into a list  of available choices  when you select  it. If
 there are more choices than can fit in the drop-down list box, a scroll bar
 is provided.

 A selected  drop-down list box  can be opened  without a mouse  by pressing
 ALT+DOWN ARROW. An opened  drop-down list box is closed when  you select an
 item in it, select other option in the dialog box, or press ALT+DOWN ARROW.

       4.3.5 Option Buttons

 Option  buttons appear  in dialog  boxes as  a list  of mutually  exclusive
 items. From the list you can select only  one option a time. You can change
 a selection by selecting a different button.

 The selected option button contains a black dot.

 To select an option button:

 * Click it.
 * Press TAB to move into the option  group you want; then use the DIRECTION
   keys to select the option button you want.
 * Or, if the  option name contains an underlined letter,  you can hold down
   ALT and  press the underlined letter  from anywhere in the  dialog box to
   select an option button.

  In dialog boxes  where all options are represented by  option buttons, you
 can double-click an option button to  choose it and complete the command at
 once.

       4.3.6 Check Boxes

 Check boxes  offer a list  of options you  can switch on  and off.  You can
 select as  many or as  few check  box options as  are appropriate.  When an
 option in  a check box is  selected, it contains  X. Otherwise, the  box is
 empty.

 To select or clear a check box option:

 * Click the empty check box you want  to select. Click a selected box again
   to clear the selection.
 * Press TAB to  move to the empty check  box you want to  select. Press the
   SPACEBAR to enter an X. Press the SPACEBAR again if you want to clear the
   selection.
 * Or, if  the check-box name  has an underlined  letter, hold down  ALT and
   press the  underlined letter  for each  check box you  want to  select or
   clear.


           4.4 Selecting Geometric Objects


 When editing  the model geometry or  analyzing the results you  may need to
 enter  the coordinates  of a  point.  The plus  sign cursor  (+) arises  to
 indicate the  point locating  mode. This  cursor can be  moved by  mouse or
 using the  DIRECTION keys. The HOME,  END, PAGE DOWN and PAGE UP  keys move
 the cursor in four diagonal directions. You can control the keyboard cursor
 step by  the MINUS and  PLUS keys. The  MINUS key approximately  halves the
 cursor step,  the PLUS key increases  it back. You  also can get  very fine
 cursor movement by holding down CTRL while pressing the DIRECTION keys.

 To select a  point of the model move  the cursor to the  position of choice
 and click left mouse button or press the  ENTER key. ESC or the right mouse
 button  cancels  the  operation.  If  you  prefer  numerical  form  of  the
 coordinates input  press TAB and you  will get a  dialog box with  two text
 boxes  for  coordinates  typing.  Press  ENTER  or  click  the  dialog  box
 background to complete the dialog and carry out the command.

 When  working  with  the  model  you  often need  to  select  some  of  its
 constituent  geometric objects.  The picking  mode is  indicated by  the X-
 shaped cursor. You  can move this cursor  the same way as  while locating a
 point. To pick a massive object like a block place the center of the cursor
 on that object and click  the left mouse button or press  the ENTER key. To
 pick a vertex or an edge it is not necessary to point cursor exactly on the
 object. The selected object is always the closest to the cursor.


           4.5 Using Rubber Band Rectangle


 The rubber band rectangle  is used to zoom-in to a  rectangular part of the
 model or of  an X-Y plot. The chosen  part is enlarged to  occupy the whole
 available  screen area.  The rubber  band rectangle  is controlled  using a
 mouse or the  DIRECTION keys. First, choose the position  of the lower left
 hand corner, then of the upper right hand one.


                            5. Problem Description



           5.1 Structure of Problem Database


 A special  database is built for  each problem solved with  QuickField. The
 core of  the database is the  problem description, which is  stored in file
 with the extension .PBM. The problem description contains the basics of the
 problem: its subject, plane, precision class,  etc., and also references to
 all other files, which constitute the problem database. These files are the
 model file,  with standard extension .MOD",  and physical data  files, with
 extension .DES, .DCF, .DMS, .DHE, .DHT,  or .DSA", depending on the subject
 of the problem.

 The problem  description may refer  to one or  two files of  physical data.
 Both files have  the same format, and differ only  in purpose. Usually, the
 first  data file  contains specific  data  concerning the  problem, as  the
 second  file is  a library  of  standard material  properties and  boundary
 conditions, which are common for a whole class of problems.

 Depending on  the problem  type, you  may share  a single  model file  or a
 single data file between several similar problems.

 While solving  the problem,  QuickField creates one  more filesthe  file of
 results with the extension .RES. This file  always has the same name as the
 problem description file, and is stored in the same directory.


           5.2 Creating a New Problem


 To create a new  problem, choose "New" in the "Files"  menu (ALT+F, N), and
 then enter the name of the new problem. While created, new problem inherits
 settings  of  the  preceding problem.  To  change  these  settings,  choose
 "Problem" in the "Edit" menu (ALT+E, P). The dialog box appears, containing
 problem description options. Here you can pick the problem type, model type
 (2D planar or axisymmetric), precision level, and etc.

 To  exit from  problem description  editing,  choose "OK".  You can  cancel
 editing by  choosing "Cancel"  button, or pressing  ESC, or  clicking right
 mouse button.

 Choosing the "Browse" button  allows you to select a file  from the list of
 files and directories when defining the  model or data filename. The button
 acts on that type of file, which is currently selected.

 Once the file is chosen, you can  instantly open it for editing by choosing
 the "Open" button.  It acts upon the currently selected  file. For example,
 if you have selected geometry file,  by choosing "Open", you would get into
 the Model Editor.


           5.3 Establishing Coupling Links


 The stress analysis and heat transfer  problems can incorporate data, which
 come from  other analysis types. The  data types are:  electrostatic and/or
 magnetic forces  and temperature field for  the stress analysis,  and power
 losses generated by the current flow for the heat transfer.

 To establish a  link between the problem that imports  data and the problem
 that originates them  choose "Imported Data" button  in problem description
 dialog box. The following dialog box will appear.

 To add a data link:

 1. Select the type of the data in the "Data Type" pull-down list box;
 2. Type a name of  the source problem in the "Problem"  text box, or choose
    "Browse"  button  to  make  the selection  from  the  list  of  existing
    problems;
 3. And, choose "Add" button to add the link to the list of data sources.


 To add a data link:

 1. Select the type of the data in the "Data Type" pull-down list box;
 2. Type a name of  the source problem in the "Problem"  text box, or choose
    "Browse"  button  to  make  the selection  from  the  list  of  existing
    problems;
 3. And, choose "Add" button to add the link to the list of data sources.


 To change a data link:

 1. Select the link of choice in the "Data Sources" list box;
 2. Change the source problem name as necessary;
 3. And,  choose "Update"  button to  update the  link in  the list  of data
    sources.


 To delete a link:

 1. Select the link of choice in the "Data Sources" list box;
 2. And, choose  "Delete" button to  delete the link  from the list  of data
    sources, or use "Delete All" button to delete all data links at once.


 The links to the imported  data are considered to be a  part of the problem
 description. The changes made in them are preserved only if you choose "OK"
 when completing  the problem description editing.  And, vice versa,  if you
 would choose "Cancel"  button or press ESC, the changes  made in data links
 will be discarded along with other changes in problem description.


           5.4 Choosing Length Units


 QuickField allows  you to use various  units for coordinates  when creating
 model's geometry.  You can use  microns, millimeters,  centimeters, meters,
 kilometers, inches, feet, or miles. To  set the units of preference, choose
 "Length Units" from the "Options" menu (ALT+O, U).
 Chosen units are  associated with each particular problem,  which gives you
 freedom to  use different  units for different  problems. Usually  units of
 length are  chosen before creating  the model geometry.  It is  possible to
 change units of length later, but it does not affect physical dimensions of
 the model. So,  if you create your geometry  as a square with  1 m side and
 then  switch to  centimeters, you  will  get a  square  measured 100 cm  by
 100 cm, which is the same as it was  before. To actually change size of the
 model you should rather use "Scaling" option of the "Move Selected" command
 of the Model Editor.

 The  choice of  length  units  does not  affect  units  for other  physical
 parameters, which always  use standard SI units. E.g.,  the current density
 is always measured  in A/m2 and never in A/mm2.  The only physical quantity
 that is measured  in chosen units of length, is  the displacement vector in
 stress analysis problems.


           5.5 Cartesian vs. Polar Coordinates


 Problem geometry as well as material properties and boundary conditions can
 be  defined in  Cartesian or  polar coordinate  systems. There  are several
 places in QuickField where you can  make choice between Cartesian and polar
 coordinate  systems. Using  "Coordinates" option  from  the "Options"  menu
 (ALT+O, C) you can  define the default coordinate system  associated with a
 problem. The same option  is also available in the Model  Editor and in the
 Postprocessor. Definition  of orthotropic  material properties,  some loads
 and boundary conditions depends on the choice of the coordinate system. You
 can choose Cartesian  or polar coordinate system for   each element of data
 individually  and   independently  from   the  default   coordinate  system
 associated with the  problem. This choice is available in  the dialog boxes
 of the Data Editor.


                         6. Model Geometry Definition


 This chapter describes how to define  the model geometry and build the mesh
 using QuickField preprocessing utility-the Model Editor.


           6.1 Terminology


 Vertex, edge, and  block are three basic types of  geometric objects, which
 the Model Editor operates with.

 Vertex is  a point on  the plane  with coordinates defined  by the  user or
 calculated automatically as intersection of the  edges. For each vertex you
 can define  the mesh spacing  value and the  label. The mesh  spacing value
 defines approximate distance between mesh nodes  in the neighborhood of the
 vertex. The label is used, for example, to describe a line source or load.

 Edge is a line segment or a  circular arc connecting two vertices. It can't
 intersect any other  edge of the region. If an  edge being created contains
 an  existing vertex,  two  adjacent edges  are  created.  New vertices  are
 automatically created in all points where  new edge intersects the existing
 ones and  all intersected edges are  split by these vertices.  Edges can be
 labeled, for example, to specify the boundary conditions.

 Block is a  continuous subregion with its boundary consisting  of edges and
 possibly isolated vertices.  A block may contain holes which  can be formed
 by chains of edges or by isolated vertices. Each block has to be labeled to
 describe material properties. Labels of the  blocks are also used to define
 distributed field sources.  Unlabeled block is not  included in calculation
 of field even it is covered by the mesh. The mesh is created block by block
 automatically or according to the mesh spacing value defined for particular
 vertices.

 The Label is a string of up  to 16 characters length, which establishes the
 correspondence between geometrical  parts of the model  and physical values
 assigned  to  them. Any  printable  characters  including letters,  digits,
 punctuation marks, space  character are permitted, except  for asterisk (*)
 and  question  mark (?)  characters.  The  label  cannot begin  with  space
 character; trailing spaces are ignored. Labels are case-sensitive.

 The  Mesh Spacing  value defines  an  approximate element  size around  the
 vertex.  The mesh  spacing  parameter is  associated  with  the vertex  and
 measured in the current units of  length. By setting mesh spacing values in
 some vertices you  can control the mesh density and  therefore the accuracy
 of the solution.


           6.2 How to Create a Model


 Model development consists of three stages:

 * Geometry description;
 * Definition of properties, field sources and boundary conditions;
 * Mesh generation.


 To  describe  model geometry  you  define  vertices  and edges  which  form
 boundaries of all subregions having different  physical properties. You can
 create  vertices and  edges; move,  copy and  delete any  geometric objects
 using the selection mechanism or one by one.

 You  define  properties,  sources  and  boundary  conditions  by  means  of
 assigning labels to geometrical objects.

 There are  two options available for  creating the finite element  mesh for
 your model:

 * Fully automated method which generates a smooth mesh with a density based
   on region's dimensions and sizes of geometrical details. This option does
   not require any information from the user.
 * The second method allows you to choose the mesh density. In this case you
   need to define the spacing values at few vertices of your choice. Spacing
   values for other  vertices are calculated automatically to  make the mesh
   distribution smooth.


       6.2.1 Starting and Quitting the Model Editor

 To start the Model Editor, choose "Geometry" from "Edit" menu (ALT+E, G) or
 while editing the problem description select  the model filename and choose
 "Edit" button.

 The  Model  Editor  uses interactive  graphics.  Two  graphic  windows  are
 displayed on screen permanently. The small  window presents general view of
 the problem  region, while  the large  one provides  a more  detailed view.
 Below the  graphic windows  is a  prompt line. Upper  right screen  area is
 normally occupied by the  menu or a dialog box used  for editing values and
 labels.

 The Model Editor has hierarchical structure of menus. Pressing ESC or right
 mouse button causes returning to preceding menu level or quitting the Model
 Editor in the main menu.
 To quit  the Model Editor  select "Exit"  from the main  menu or  press ESC
 while in the main menu. You will be prompted to save the model.

       6.2.2 Objects Selection

 The Model  Editor provides  possibility to make  some group  operation upon
 several objects  at once if those  have been previously selected.  To enter
 select  mode,   choose  "Select"   and  then   one  of     "Select Blocks",
 "Select Edges" or "Select Vertices" in a dialog box that will appear.

 While in select mode pick an object  to select or unselect it. All selected
 objects are highlighted  on the screen. To leave the  select mode press ESC
 or  right mouse  button.  Objects of  different  types  cannot be  selected
 simultaneously.

 "Unselect All" cancels all previous selections.

       6.2.3 Geometry Description

 Whenever a new model is created, the default window is set to correspond to
 a unit  square. For  planar models the  horizontal and  vertical directions
 correspond to X and Y axes, and. for axisymmetric models they correspond to
 Z and  R axes,  respectively. It  is convenient to  assign the  window with
 region's dimensions and  create the outward boundary of the  model at once,
 and then describe  the details. To change default  window dimensions choose
 "Keyboard" from  "Zoom" submenu.  The default  window dimensions  are saved
 with the model to be restored in later editing sessions.

 To build  the geometry of  your problem go  to "Model" submenu.  First, you
 need  to create  the vertices  using the  "Add Vertex" command.  Locate the
 required positions with  the cursor or press TAB to  enter coordinates from
 the  keyboard. New  vertex appears  in the  window. Then  you can  continue
 creating vertices or return to "Model"  menu by pressing ESC or right mouse
 button.

 If at  least two vertices are  defined in the  region you can  connect them
 with an edge. To do  this, choose "Add Edge" and type in  the angle size in
 degrees for a new edge. Zero  value corresponds to a line segment. Positive
 value  defines an  arc directed  from the  first vertex  to the  second one
 counter-clockwise, or clockwise if negative. After defining the angle size,
 pick the vertices  to be connected by the edge  in corresponding order. New
 edge appears in the window. Picking vertex by vertex you can create several
 edges of the same angle size. To break the chain and start a new one, press
 ESC. To return to menu press ESC twice.

       6.2.4 Copying and Moving Geometric Objects

 Repeated geometry  elements can be easily  created by means of  copying any
 set  of objects  to new  location, using  geometric transformations  listed
 below. To make a copy:

 1. Select any  number of objects  (vertices, edges or  blocks) you  want to
    copy, choosing "Select" from the menu.
 2. Choose  "Copy Selected".  The  dialog box  appears,  asking for  copying
    parameters.
 3. Select  transformation, enter  its  parameters and  choose  OK. The  new
    objects will appear  on screen and the program will  be waiting for your
    confirmation,  so you  could be  sure  that you  entered the  parameters
    correctly.
 4. Choose "Create" to confirm copying. New objects will be `implanted' into
    the model, and selection will move to the last copy.


 The  copy operation  affects all  explicitly set  features of  the selected
 objects, including labels and spacing values. Only the mesh is not copied.

     Caution.  Use  copy operation  with  care,  because improperly  set
     transformation  parameters may  cause creating  new objects  in the
     wrong places. Such improper objects may interfere with the existing
     objects and  generate a lot  of useless intersection  points, which
     will be hard to remove later.

 You can also move selected objects  to other location with the restriction,
 that region topology will not change, and no new intersection or coinciding
 will arise. To move selected objects, choose "Move Selected" from the menu.
 The dialog box which appears is very similar to "Copy Selected" dialog box.

 Geometric transformations available with move and copy operations are:

 Displacement   -    parallel  displacement is  applied to  selected objects
           for specified  displacement vector. With copy  operation, several
           copies can be asked for, it  means that copying operation will be
           performed several times, each time being  applied to the previous
           result. Parameters needed are displacement vector components.

 Rotation- selected objects are  rotated around the specified  point for the
           specified angle. With copy operation, several copies can be asked
           for, it  means that copying  operation will be  performed several
           times, each time being applied to the previous result. Parameters
           needed are center  of rotation coordinates and  angle measured in
           degrees.

 Symmetry- selected  objects are  mirrored; symmetry  line  is specified  by
           coordinates  of  any  point  on it  and  the  angle  between  the
           horizontal axis and the symmetry line. Positive value of an angle
           means   counter-clockwise  direction.   This  transformation   is
           available for copy operation only.

 Scaling - selected objects are dilated (constricted) by means of homothetic
           transformation.  Parameters needed  are center  of homothety  and
           scaling  factor.  This  transformation   is  available  for  move
           operation only.

 You can remove auxiliary or incorrectly  defined vertices, edges and blocks
 by  choosing "Delete  Selected", "Delete Vertex"  or "Delete Edge".  If the
 vertex being  removed contacts exactly two  edges, which can be  treated as
 single  edge  when eliminating  that  vertex,  those are  joined  together.
 Otherwise confirmation will be asked to delete all the connected edges.

       6.2.5 Labeling Vertices, Edges and Blocks

 The  correspondence   between  geometrical   objects  and   their  physical
 properties,  such as  material properties,  boundary  conditions, or  field
 sources is established by the use  of labels. All operation with assigning,
 editing and checking the labels is done in the "Label" menu.

 To  assign   a  label,  choose   one  of  "Label Block",   "Label Edge"  or
 "Label Vertex",  and then  pick the  entity which  you need  to label.  The
 dialog box will appear, which allows you to type in the label from keyboard
 or to select one from the previously defined labels in the model or in data
 files assigned to the problem. After you define the label, you can continue
 picking the objects or return to the menu by pressing ESC key.

 You may assign the same labels to several entities of similar type at once.
 To do  so, first select those  objects by using "Select"  command (for more
 details see  the section on  Object Selections) and  then label  them using
 "Label Selected".

 To check labels assignment or to  select objects possessing the same label,
 use "Find Label".  The dialog box will  appear, which allows you  to select
 the type of object, and  contains the full list of labels  as appear in the
 model  for the  given object  type. Picking  some label  in the  list would
 select all the objects associated with that label.

       6.2.6 Building the Mesh

 After creating the geometry of the model or its parts, you can proceed with
 building the  finite element  mesh. With  the Model  Editor you  can easily
 build a  nonuniform mesh for  a highly complex  geometry. You may  choose a
 fine mesh  in some regions and  very coarse in others,  since the geometric
 decomposition technique  would produce  a smooth  transition from  large to
 small element  sizes. Generally, the  mesh has to  be fine where  the field
 changes  most  rapidly  (high  gradient), and  also  where  you  need  high
 precision.

 If the  geometry is  rather simple,  or a  draft precision  for preliminary
 design analysis is satisfactory, it is suggested to use the fully automatic
 mode to create the mesh. With this option, once you built your geometry you
 would  simply choose  "Build Mesh"  and a  suitable  mesh is  automatically
 created without any information on the mesh size.

 You also have the option to  pick the mesh density if you  choose to do so.
 The mesh density  is controlled by spacing values in  vertices. The spacing
 value defines approximate  distance between mesh nodes  around that vertex.
 You never  need to define  the spacing in  all model's vertices.  To obtain
 uniform mesh  you can  set the  spacing in  any one  vertex. This  value is
 spread among all other vertices automatically.  If you need the non-uniform
 mesh, define  spacing values only in  those vertices where you  need finest
 and roughest  mesh. The  spacing values  are automatically  interpolated to
 other vertices to smooth the mesh density distribution. The group selection
 mechanism allows to assign the value to several vertices at once.

 After defining spacing values, you can  proceed with the mesh building. The
 mesh is built block by block. You may choose to build the mesh in one block
 or in selected blocks or in entire region at once.

 Changing the  density of a  pre-built mesh (e.g.  if solution  results show
 that you need more precision somewhere in the region) obey some rules:

 * When you  change the spacing  value in some  vertex, the mesh  is removed
   automatically in those blocks which are connected to that vertex.
 * The mesh that  is not removed, freezes spacing values  along its boundary
   from recalculation  as if those values  were defined manually; so  if you
   need major  changes in  the mesh  density, first remove  the mesh  in the
   whole region.


 All operation with  spacing values and the mesh is  performed in the "Mesh"
 submenu. To define the spacing, choose  "Set Spacing", then pick the vertex
 and type  in the spacing  value. Then  you can alter  spacing at  any other
 vertex or  return to  menu by  pressing ESC. If  there are  some previously
 selected vertices, the spacing  values are set for all of  them at once. If
 some edges  are selected, the spacing  values are set for  all the vertices
 located  on them.  The same  way, if  there are  some selected  blocks, the
 spacing values are set for all  the vertices located on their boundaries or
 inside them.

 To build the mesh, choose "Build Mesh"  and select an option. "Delete Mesh"
 removes mesh in some blocks or in the entire region.

 If the  spacing visibility  switch is on  ("Show Spacing" in  the "Options"
 menu), the explicitly set spacing values  are shown as small circles around
 the vertices. You  can see the mesh building process  if "Show Mesh" toggle
 in the "Options" menu is on.

       6.2.7 Zooming

 There are  two graphic windows on  the screen while editing  the model. The
 small  window always  displays the  general view  of the  model. The  large
 window is used to present a more detailed picture of the whole model or its
 selected  parts.  "Zoom"  menu provides  several  options  to  control  the
 displays in each graphic window.

 "Keyboard"  allows  you  to  type in  dimensions  of  the  visible  region.
 Specified region is displayed in both windows and becomes the default. This
 is a normal way to extend the default visible region. Limits of the visible
 region can be automatically adjusted to  preserve equal horizontal (X or Z)
 and vertical (Y or R) scales.

 "Natural" sets  minimum visible  region large enough  to contain  the whole
 model.  Resulting region  is  displayed in  both  windows  and becomes  the
 default.

 "Default" sets visible region dimensions to  the default values. The region
 visible in the large window becomes the same as in the small one.

 "Large Window" controls the  dimensions of the visible  region using rubber
 band  rectangle in  the large  window. The  rubber rectangle  is controlled
 using mouse or  cursor keys. First, choose position of  the lower left hand
 corner, then of the upper right hand one.

 "Small Window"  does the  same, but  rubber band  rectangle appears  in the
 small window. This  mode is recommended when whole or  part of the required
 region lies outside the large window.

       6.2.8 Obtaining Model Information

 You can get detailed information on the current model using "Info" submenu.
 In this  submenu choose  the object  type (vertices,  edges or  blocks) and
 complete information corresponding  to that type will  be displayed (amount
 of objects, presence of labels, mesh parameters, etc.). Then you can pick a
 specific object within  that group to get more  local information. Pressing
 ESC returns  to the menu.  This mode is  used to get  total number  of mesh
 nodes, to check labels, to examine the mesh spacing values and so on.


           6.3 Additional Options


       6.3.1 Saving Model

 The "Save"  command of "File" menu  saves the model to  disk. The "Save As"
 does the same  but lets you change the name  of output file. It  is wise to
 save model not only when editing  is over, but regularly during the session
 to avoid troubles due to errors or power failure.

     Note. When the "Save As" command changes  name of the model file it
     automatically  updates  reference  to the  model  file  in  problem
     description.


       6.3.2 Opening Model File

 To create new empty model choose "New" in the "File" menu. To open existing
 model file choose "Open" in the same menu, and then type or select the file
 name. If  the active  model was  changed you  will be  prompted to  save it
 before transition to the new one.
 With "Open", you  can import old geometry model files  created with the 1.x
 or 2.x  versions of QuickField and  having ".TRI" extension. To  do so, you
 need only to specify ".TRI" extension when selecting the file.

     Note. While  loading old-formatted model, all  numerical labels are
     transferred to literal form automatically.


       6.3.3 DXF File Import

 You can import  model geometry or its fragments from  the DXF file produced
 by any major CAD  system. To do so, choose "Import DXF"  in the "File" menu
 and  then  type  or  select  required file  name.  The  visible  region  is
 automatically  extended if  needed  to assure  visibility  of all  imported
 geometric objects. If the model is not  empty when reading the DXF file, it
 is recommended to  save the current model state before  the operation. This
 will give  you a  chance to  return to  the initial  stage if  the imported
 objects incidentally overlap the existing part of model.

       6.3.4 Discretization Visibility Options

 There are  four switches  "Show Mesh", "Show Domain",  "Show Breaking", and
 "Show Spacing" which affect the discretization  visibility level. These are
 accessible through "Options" menu. When all  these switches are off, region
 is  displayed  without  discretization. This  mode  is  useful  for  region
 geometry  description and  label  setting. If  the  "Show Spacing" mode  is
 switched on,  all explicitly set spacing  values are shown as  circles with
 the appropriate radii.

 When "Show Breaking" switch is on, the size of the elements along the edges
 is  shown  as  tic marks  on  the  edges.  It  is convenient  to  use  both
 "Show Spacing" and "Show Breaking" when specifying the mesh spacing values.
 "Show Mesh" lets you see the complete  triangular mesh. Turn it on to check
 the mesh  building process. "Show Domain" without  "Show Mesh" displays the
 domains due to geometric decomposition process.

 The state of these switches is remembered between sessions.

       6.3.5 Attraction Distance Parameter

 To  avoid small  unrecognizable inaccuracies  in  geometry definition,  new
 vertices or  edges cannot be created  very close to the  existing ones. The
 creation of  new geometric objects  is controlled by  the e  parameter also
 called the attraction distance.

 The following rules concern creating new vertices and edges.

 * Creating a new vertex is prohibited  within 2*epsilon-neighborhood of the
   existing one.
 * A  new edge  cannot be  added if  it  joins the  same vertices  as of  an
   existing edge and the maximum gap between them does not exceed epsilon.
 * If the  distance between a vertex  to add and some  edge is less  than or
   equal  epsilon, the  vertex is  attracted  by the  edge and  the edge  is
   automatically split into pair of new edges to incorporate the vertex. The
   same is true when new edge is added, but in this case the new edge may be
   attracted by existing vertex.


 The default value  of epsilon is 0.5  per cent of the  visible region size.
 You  can set  different  value by  choosing  "Epsilon"  in "Options"  menu.
 Decreasing epsilon  would allow you  to describe very  fine details  of the
 model. But the most convenient way to get the same result is to zoom in the
 window.
                      7. Problem Parameters Description


 To solve  the problem  it is  needed to  describe the  material properties,
 field sources and  boundary conditions. These parameters are  stored in the
 property  description file.  The correspondence  between  records of  these
 files and  subdomains or  boundaries of  the region  is established  by the
 labels assigned to  geometrical objects during editing  the model. Labeling
 blocks,  edges  and vertices  is  described  in Chapter 5  "Model  Geometry
 Definition".

 Physical values  for a  problem may  be defined  in one  or two  data files
 attached to  the problem. Both files  have the same format  and distinguish
 only in purpose. The first  file is the basic data file  of the problem and
 is assumed to contain the data specific  to that problem. The second is the
 library  file,  that  contains  common  material  properties  and  standard
 boundary conditions for a class of problems.

 To edit the basic data file, choose "Data" in the "Edit" menu (ALT+E, D) to
 edit the library  file, choose  "Library" (ALT+E, L.)  The alternate method
 to start editing data is to select the name of one of the data files and to
 choose the "Open" button while editing the problem description.

 When entering  data file editing mode,  the dialog box  appears, containing
 three lists of labels, which correspond to blocks, edges and vertices.

 Option buttons  above the list boxes,  allow you to choose  the label group
 type. Once you pick a label  from the available lists, it gets highlighted.
 In this  case it appears  also in the  text box below  the list  boxes. The
 label in the  text box is the  current label, so all  the immediate actions
 are done to this label.

 The labels with no specified data  are marked with asterisks. Labels of the
 blocks which are  excluded from consideration (i.e.,  having empty material
 properties,) are marked with double exclamation mark.

 Options for editing  the data file could be divided  into three groups. The
 first group considers  actions on creating new labels and  editing data for
 existing  ones. Operations  on copying,  renaming and  deleting a  data set
 associated  with the  label belong  to the  second group.  The third  group
 includes  saving the  data file  under another  name and  merging two  data
 files.

 To exit from data file editing,  choose the "Close" command button or press
 the ESC key. You will be prompted to save the changes to file.


           7.1 Creating a New Label


 To create a new label:

 1. Choose appropriate type of geometric objectsblock, edge or vertex;
 2. Type the name of the  label in the text box titled  "Label". You may use
    the INS key in addition to usual methods to move to the text box. If the
    label's name  already exists in  the list, but  is marked  with asterisk
    (which means that  the data for the  label is not defined  yet) you need
    not type the  name, but simply select  it in the list  using keyboard or
    mouse;
 3. Choose "Add" button or press ENTER to start editing the data.


 After  you define  the data,  new  label appears  in the  list of  existing
 labels. If data editing was canceled, new label is not created.


           7.2 Editing Label Data


 To edit the  data associated with some label, select  that label and choose
 "Edit" button or  press ENTER. The dialog box appears,  its view depends on
 the class  of current problem and  on the type of  geometrical object which
 the label corresponds to.

 To finish label data editing, choose  "OK" button. Choosing "Cancel" button
 will end the editing and discards all changes to the values.

       7.2.1 Editing Data in Magnetostatics

 With problems of magnetostatics, block label data contain two components of
 magnetic  permeability  tensor,  the current  density,  and  for  permanent
 magnets also magnitude and direction of coercive force.

 With  nonlinear materials,  you  need to  define  the magnetization  curve,
 instead of magnetic permeability. In this case check the "Nonlinear" box to
 get into the B-H curve editor. If a B-H curve had already been defined, the
 dialog box  would contain a "B-H Curve"  button which can be  chosen to get
 into  the curve  editor. Editing  the magnetization  curve is  discussed in
 "Editing the Curves" section later in this chapter.

 When  creating  data  for  a  new   label,  the  text  boxes  for  magnetic
 permeability components contain None" instead of numbers. The word None" in
 these boxes  or absence of value  means that the  block with such  label is
 excluded.  If you  want to  define the  material properties  (and therefore
 include the block into consideration), simply type in the value of magnetic
 permeability, which will replace the highlighted None".

 If you need to define two components different from each other, first check
 the "Anisotropic" box.

 The  data for  the edge  label  allow to  assign one  of possible  boundary
 conditions. Select the type of condition and then type in the values.

 The vertex in the problem of magnetostatics may have known potential or the
 concentrated current may flow through the  vertex. Check one of the options
 and then enter a value.

       7.2.2 Editing Data in Harmonic Magnetics

 With  problems  of  harmonic  magnetics,  block   label  data  contain  two
 components of  magnetic permeability tensor, electric  conductivity and one
 of three possible field sources: source  current density, voltage, or total
 current.

 When  creating  data  for  a  new   label,  the  text  boxes  for  magnetic
 permeability components contain None" instead of numbers. The word None" in
 these boxes  or absence of value  means that the  block with such  label is
 excluded.  If you  want to  define the  material properties  (and therefore
 include the block into consideration), simply type in the value of magnetic
 permeability, which will replace the highlighted None".

 If you need to define two components different from each other, first check
 the "Anisotropic" box.

 The  method  of applying  sources  is  different  for conductors  and  non-
 conductive areas. In  first case, you may switch between  voltage and total
 current,  as in  second case  voltage  is inaccessible  and  you can  apply
 current density or total current only.

     Note.  It is  assumed that  total current  specified for  some data
     label is a summary current in all blocks carrying that label.

 With harmonic problems,  you always specify amplitude, or  peak, values for
 all alternating quantities.

 The  data for  the edge  label  allow to  assign one  of possible  boundary
 conditions. Select the type of condition and then type in the values.

 The vertex in the problem of harmonic magnetics may have known potential or
 the concentrated  current may  flow through  the vertex.  Check one  of the
 options and then enter a value.

       7.2.3 Editing Data in Electrostatics

 Block  label data  for  electrostatics problem  contain  two components  of
 electric permittivity and possibly distributed charge density.

 When  creating  data  for  a  new   label,  the  text  boxes  for  electric
 permittivity components contain None" instead of numbers. The word None" in
 these boxes  or absence of value  means that the  block with such  label is
 excluded.  If you  want to  define the  material properties  (and therefore
 include the block into consideration), simply type in the value of electric
 permittivity, which will replace the highlighted None".

 If you need to define two components different from each other, first check
 the "Anisotropic" box.

 The data for  the edge label allow  to assign one of  the possible boundary
 conditions. Select the type of condition and then type in the values.

 The vertex  in the problem  of electrostatics may  have known  potential or
 concentrated charge. Check one of these options and then enter a value.

       7.2.4 Editing Data with Current Flow Problems

 Block label data for the problem  of current flow contain two components of
 electric resistivity.

 When creating data for a new label, the text boxes for electric resistivity
 components contain None" instead of numbers.  The word None" in these boxes
 or absence of value means that the block containing such label is excluded.
 If you  want to define the  material properties (and therefore  include the
 block  into   consideration),  simply  type   in  the  value   of  electric
 resistivity, which will replace the highlighted None".

 If you need to define two  different components of resistivity, first check
 the "Anisotropic" box.

 The data for  the edge label allow  you to assign one  of possible boundary
 conditions. Select the type of condition and then type in the values.

 The  vertex in  the problem  of current  flow may  have known  potential or
 external current. Check one of these options and then enter a value.

       7.2.5 Editing Data with Heat Transfer Problems

 The data  for block  label contain two  components of  thermal conductivity
 tensor and, possibly, the volume power of heat source.

 To describe  the thermal conductivity as  a function of  temperature, check
 the  "Nonlinear"  box  and  the  temperature   curve  editor  for  defining
 "lambda = f(T)" will be  displayed. Curve editing is  discussed in "Editing
 the Curves" section later in this chapter.

 Also the volume  power of heat source  could be described as  a function of
 temperature. To do  so, check the "Function of Temperature"  box related to
 the heat  source field. Editing the  dependencies is described  in "Editing
 the Curves".

 When creating new label, the text boxes for thermal conductivity components
 contain None" instead of numbers. The  word None" in these boxes or absence
 of value  means that the  block containing such  label is excluded.  If you
 want to  define the  material properties (and  therefore include  the block
 into  consideration), simply  type in  the value  of thermal  conductivity,
 which will replace the highlighted None".

 If you  need to  define two different  components of  thermal conductivity,
 first check the "Anisotropic" box.

 The data  for edge label allow  you to describe boundary  conditions. Check
 the condition  which you need,  and then type  in the parameters.  The heat
 flux, convection, and radiation can be  combined together, which means that
 the heat flow through the surface is compounded from several components.

 The  vertex  in  heat  transfer problem  may  have  known  temperature,  or
 represent a  line heat source. Check  one of these options,  and then enter
 the numeric parameter.

       7.2.6 Editing Data with Stress Analysis Problems

 When editing  the data for  the block label  with stress  analysis problem,
 there are  two sets of  properties to be  edited simultaneously.  To switch
 from one  set to another, use  option buttons at the  top of dialog  box or
 press PAGE UP or PAGE DOWN keys.

 When creating  new label, the text  boxes for Young's moduli  contain None"
 instead of numbers. The word None" in these boxes or absence of value means
 that the block containing such label is excluded. If you want to define the
 material properties  (and therefore include the  block into consideration),
 simply type  in the value  of the Young's  modulus, which will  replace the
 highlighted None".

 The "Anisotropic" boxes, which applied to elastic moduli or coefficients of
 thermal expansion, allow you to describe anisotropic properties in each set
 independently.

 The data for thermal loading are defined slightly different way for thermo-
 structural coupled and non coupled problems:

 * With an uncoupled problem, you define  the temperature difference between
   strained and  strainfree states, which is  assumed to be  constant within
   all blocks with the corresponding label.
 * With thermo-structural  coupling, you need  to define the  temperature of
   strain free state  for each block subjected to thermal loading.


 The values of allowable stresses do not affect the solution. Those are only
 used in postprocessing stage to calculate the Mohr-Coulomb, Drucker-Prager,
 and Hill  criteria. You don't need  to define allowable stresses,  if these
 criteria are of no interest to you.

 The data  defined for an  edge label may  include constraints along  one or
 both coordinate axes and the surface  forces are described either as normal
 pressure or  by their Cartesian or  polar coordinate system  components. To
 apply fixed displacement along an axis,  check the appropriate box and then
 enter a value of displacement.

 The vertex label data may define rigid or elastic support along one or both
 coordinate  axes,  or  concentrated  external   force.  To  describe  rigid
 constraint along some  axis, check the appropriate box, and  then enter the
 value of fixed displacement.

       7.2.7 Editing the Curves

 Curve  functions,  which  describe some  field  dependent  parameters,  are
 implemented as tables  containing two columns: an argument  and a function,
 e.g., magnetic field intensity and flux  density or temperature and thermal
 conductivity. Editing the table is supported with graphical presentation of
 the dependency, which is interpolated with cubic spline between the entered
 points. The solver uses just the same curve as you see on your screen.

 To add  the new point  to the dependency,  type in two  values (B and  H in
 shown example) and press ENTER key  or choose "Add" button. If the argument
 of  a new  point coincides  with the  argument of  existing one,  new point
 replaces the old one.

 To remove the point,  select it in the table and  choose "Delete" button or
 press the DEL key.

 You may  control the scaling of  the graph with use  of "Zoom In"  or "Zoom
 Out" buttons.

 To exit  from editing the curve,  choose "Close" button or  press ESC. Note
 that  subsequent canceling  of  label  data editing  with  ESC  key or  the
 "Cancel" button will discard all changes including the curve editing.


           7.3 Copying, Renaming and Deleting Labels


 In order to  copy or rename a label (to  be precise, a data  set related to
 the label),  select the  label in  the list and  choose "Copy"  or "Rename"
 button. A  new name  is entered  in a  dialog box,  which appears  when you
 choose the button.

 To remove a label, select it and choose "Delete" or press DEL.


           7.4 Merging and Copying Data Files


 "Merge" command button  allows you to expand the contents  of the data file
 being edited with the labels contained in some other data file for the same
 type of problem. The labels with coinciding names will not be replaced.


                            8. Solving the Problem


 This  chapter describes,  how to  solve the  prepared problem,  and methods
 QuickField uses to solve.

 Several conditions  have to be  met to solve  a problem. The  problem type,
 plane, required precision and other parameters  have to be specified in the
 problem description  file. The  model geometry  file must  contain complete
 model with mesh and labels. Each label referred  by the model file is to be
 defined in the problem's private or library data file.

 To obtain the  problem solution, choose "Solve Problem"  from the "Results"
 menu  (ALT+R, S).  You may  skip this  action and  directly proceed  to the
 analysis results by choosing "Analyze" from  the "Results" menu (ALT+R, A).
 If the problem has not been solved yet, or its results are out of date, the
 solver will be invoked automatically.

 Special bar  indicator lets you see  the progress of the  solution process.
 Linear problems  are solved  by using  a powerful  preconditioned conjugate
 gradients method. The preconditioning based  on the geometric decomposition
 technique  guaranties a  very high  speed  and close  to linear  dependence
 between number of nodes and the resulting solution time. Nonlinear problems
 are solved using the Newton-Raphson method.  The Jacobian matrix arising at
 each step of  the Newton-Raphson method is  inverted the same way  as it is
 done for linear problems.


                            9. Analyzing Solution


 This  chapter  explains the  procedures  for  detailed examination  of  the
 results  using the  QuickField  postprocessing  utility. The  Postprocessor
 provides various ways of results presentation:

 * field pictures,
 * local field values,
 * integral quantities,
 * X-Y plots.


 Field pictures and X-Y plots can be saved in vector-formatted files for use
 with any word-processing or desktop publishing  utility. Local field values
 and sequences  of points from X-Y  plots can be  stored in table  files for
 subsequent use by spreadsheet or user-written programs.


           9.1 Starting and Quitting the Postprocessor


 To examine  the results, choose "Analyze"  from the "Results"  menu (ALT+R,
 A).

 Screen layout when working with the Postprocessor is very similar to one of
 the Model  Editor. There are two  graphic windows displayed on  the screen.
 The small one presents general view of the model, while the large one shows
 detailed field  picture or an X-Y  plot. The message  bar is at  the screen
 bottom edge. Upper  right screen area is normally occupied  by menu, legend
 box, or a temporary window used to display text information.

 To quit  the Postprocessor select "Exit"  from its main menu,  or press ESC
 while in the main menu.


           9.2 Building the Field Picture on the Screen


       9.2.1 Interpreted Quantities

 The  set  of  the  physical  quantities  which  can  be  displayed  by  the
 Postprocessor depends on the problem type.

       9.2.1.1 For the electrostatic problem these quantities are:

 * scalar electric potential (voltage) U;
 * vector of electric field intensity E = - grad(U);
 * tensor of gradient of electric field  G = grad(E);
 * vector of electrostatic induction D = epsilon * E;
 * electric permittivity e (or its largest component in anisotropic media);
 * electrostatic field energy density w = (E*D)/2.

       9.2.1.2 For the magnetostatic problem:

 * vector magnetic  potential A in  plane-parallel problem or  flux function
   Phi = 2*PI*rA in axisymmetric case;
 * vector of magnetic flux density B = curl (A);
 * vector of magnetic field intensity H = (1/mu)*B;
 * magnetic permeability mu (its largest component in anisotropic media);
 * magnetic field energy density:

      w = (B*H)/2              s in linear media,

      w = Integral(H*dB)       s in ferromagnetic media.

       9.2.1.3 For the problem of harmonic magnetics:

 * complex amplitude  of vector  magnetic potential A  (flux function  rA in
   axisymmetric case);
 * complex amplitude of voltage U applied to the conductor;
 * complex amplitude of total current density j = j0 + jeddy, source current
   density j0 and eddy current density jeddy = -I*omega*g*A.

   All these complex quantities may be shown in form of momentary, root mean
   square (RMS) or peak value in time dimension.

   E.g., complex quantity z = z0*exp(i*(omega*t + phiz)) my be shown as:
    * momentary value at given phase  phi0 = omega*t0

      z = Re (z0*exp(i*(phi0+phiz)) = z0*cos(phi0+phiz);

    * peak value z0;
    * RMS value

      z = sqrt(2)/2 * z0.

 * Complex vector of the magnetic flux density B = curl (A)
 * complex vector of magnetic field intensity  H = (1/mu)*B, where mu is the
   magnetic permeability tensor.

   Complex vectors may be shown in form of momentary, RMS or peak magnitude.
 * Time average and peak Joule heat density Q = (1/g)*j*j;
 * time average and peak magnetic field energy density w = (B*H)/2;
 * time average Poynting vector (local power flow) S = [E, H] (cross product
   E and H);
 * time average Lorentz force density vector F = [j, B];
 * magnetic permeability mu (its largest component in anisotropic media);
 * electric conductivity g.


       9.2.1.4 For the problem of current flow:

 * scalar electric potential U;
 * vector of electric field intensity E = - grad(U);
 * vector of current density j = (1/ro)xE;
 * electric resistivity ro (its largest component in anisotropic media);
 * ohmic losses per volume unit w = (j*E)/2.


       9.2.1.5 For heat transfer problem:

 * temperature T;
 * vector of heat flow F = -lambda * grad(T);
 * thermal conductivity lambda (its largest component in anisotropic media).

       9.2.1.6 For stress analysis problem:

 * displacement vector delta;
 * strain tensor epsilon and its principal values;
 * stress tensor sigma and its principal values;
 * von Mises stress (stored energy of deformation criterion)
 * Tresca criterion (maximum shear)
 * Mohr-Coulomb criterion
 * Drucker-Prager criterion
 * Hill failure index for orthotropic materials

   The  Hill failure  index is  calculated only  for those  materials, where
   allowable  stresses  were defined  (while  editing  the block  data,  see
   "Problem Parameters Description").  If any pair of  allowable stresses is
   not given, the  corresponding term is dropped while  calculating the Hill
   Index.

       9.2.2 Field Presentation Methods

 Several methods are available for displaying the field picture:

 * Color map for distribution of a  chosen scalar quantity. The color map is
   accompanied by the  legend showing the correspondence  between colors and
   numerical values.

   You  can adjust  the color  scale by  changing the  range limits  for the
   chosen quantity.

 * Field lines. Those  are isotherms for temperature fields,  lines of equal
   potential in electrostatics and flux lines for magnetostatic problems.

   You  can  manipulate  the  picture  by   changing  the  distance  between
   neighboring lines. This distance is measured in units of chosen quantity.

 * Vectors-family of  line segments showing  magnitude and direction  of the
   vector  quantity. The  base point  of  each vector  is marked  by a  dot.
   Vectors are drawn in the nodes of the regular rectangular grid.

   You can change  the grid cell size  and the scaling factor  for a desired
   vector quantity.

 The following methods are specifically for stress analysis problems:

 * Deformed boundary and  shape indicated by means of  deformed and original
   rectangular grid.

 * Stress tensor display as a pair  of eigenvectors reflecting the direction
   of principal axes, magnitudes and signs of principal stresses (blue color
   denotes tension, red color-compression);

   With these  methods, you can  change the grid  cell size and  the scaling
   factors in order to manipulate the appearance.

 It is possible to combine several visualization methods in the same picture
 to obtain the most expressive result.

       9.2.3 Field Picture Constructing

 When  entering the  Postprocessor, the  default form  of the  field picture
 appears on  the screen. You may  use "Field View" from main  menu to select
 other display methods or quantities.
 Shown dialog box corresponds to the problem of magnetics.

 To choose desired visualization method, select corresponding check box. You
 can select any  combination of methods at  once. If none of  the methods is
 selected, only the model's geometry is shown.

 This  dialog box  also allows  to  change scaling  parameters for  selected
 methods of  presentation. When  you select  some edit  box, you  can choose
 "Suggest" button to obtain suggested value of corresponding parameter. Note
 that suggested values for "Minimum" and "Maximum" fields are calculated for
 the currently visible part of the model.

 In case of  harmonic magnetics problem, equilines and vectors  are drawn at
 specified phase. The "Field View" dialog box allows to set phase value. For
 more expressive field picture, you can order the second family of equilines
 or vectors, shifted with regard to the first by 90..

 The "Field View"  dialog box for  the stress analysis  problem additionally
 allows to select tensor quantity visualization.

 Selecting   the  "Deformed Shape"   option  turns   on  "Deformed Boundary"
 automatically.

 Sizes  of  the  vector  symbols  for   all  vector  quantities  except  the
 displacement  vector are  determined by  the  corresponding physical  value
 multiplied by  the scaling factor and  by the cell size.  Similar method is
 used for stress tensor components. Unlike other vector quantities, the size
 of the displacement vector on the screen  does not depend on the cell size.
 It is  determined by the  dimensionless scaling factor,  the unit  value of
 which means that the displacement is shown in its natural scale.

 Color map of  temperature difference in stress  analysis problem visualizes
 temperature distribution as  it is defined by user or  imported from linked
 heat transfer problem. In the last case, temperature is shown only in those
 blocks, where it is really taken into account.

 The "Failure Index"  option is available when  the model contains  at least
 one block with correctly defined allowable stresses.

 Choosing the "OK" button causes redrawing  the field picture on the screen.
 "Cancel" closes the dialog box without  redrawing the picture and preserves
 preceding values of all the parameters.

       9.2.4 Zooming

 To adjust the scale of the field picture, choose "Zoom" from the menu. This
 command is very  similar to the analogous command of  the Model Editor, but
 the default window dimensions cannot be  altered, they retain values set in
 the Model Editor.

 "Keyboard" allows you  to type in dimensions of the  visible region. Limits
 of  the visible  region can  be  automatically adjusted  to preserve  equal
 horizontal (X or Z) and vertical (Y or R) scales.

 "Default" sets visible region dimensions to  the default values. The region
 visible in the large window becomes the same as in the small one.

 "Large Window" controls the  dimensions of the visible  region using rubber
 band  rectangle in  the large  window. The  rubber rectangle  is controlled
 using mouse or  cursor keys. First, choose position of  the lower left hand
 corner, then of the upper right hand one.

 "Small Window"  does the  same, but  rubber band  rectangle appears  in the
 small window. This  mode is recommended when whole or  part of the required
 region lies outside the large window.
 "Maximize" enlarges  the large window to  the full screen for  hard copying
 and  taking photos.  Pressing  any key  returns  the  Postprocessor to  its
 preceding state. The color map legend  could be shown in maximized view. To
 switch  legend on  or off,  choose "Show Legend"  in "Options"  menu before
 maximizing.


           9.3 Access to Local Field Data


 The Postprocessor  displays local  field data in  "Values" mode.  Click the
 point where you need  to know the values of the  field quantities, or press
 TAB and then enter the coordinates of the point with the keyboard. Once you
 choose the point, the values at this  point are displayed on the screen. To
 leave the "Values" mode use ESC key, or press right mouse button.

 While analyzing harmonic magnetics field, you can choose between momentary,
 time  average,  peak  or  complex  form   of  time  dependent  field  data.
 Corresponding dialog box  appears on the screen right after  you choose the
 "Values" mode.

 The local values  of physical quantities obtained in the  "Values" mode can
 be logged  to the table file.  This file has self  explaining ASCII format,
 with values separated with spaces or commas. The table file can be used for
 printing numerical results,  or to pass them to  other application program,
 e.g., a  spreadsheet program to  produce a report.  To open the  table file
 choose "Open Table"  from the "Options  menu. See section  "Exporting Local
 Values to the Table File" for further explanation.


           9.4 X-Y Plots


 With   QuickField  Postprocessor,   you   can   analyze  field   quantities
 distribution  along  user-defined  paths  of  arbitrary  shape  (contours).
 Contours   are  also   used  for   calculating  integral   quantities  (see
 "Calculating Integrals" later  in this chapter) and for  saving local field
 values to the table file (see "Exporting Local Values to the Table File").

 To start  this mode, choose  "X-Y Plot"  from the menu.  If the  contour is
 already  defined,  X-Y plot  is  immediately  shown  in the  large  window.
 Otherwise you should  define the contour, choosing "Edit  Contour" from the
 menu.

       9.4.1 Editing Contours

 The contour is a directed curved  line consisting of line segments and arcs
 (including the edges of the model). Some rules are applied to the contours:

 * The contour may not intersect itself.
 * Open and closed contours are discerned.
 * Multiply  connected contours  have sense  only  for calculating  integral
   quantities.


 Contour is shown in  the window as a set of  directed lines or color-filled
 interior (closed counter-clockwise-directed contours).

 To edit  the contour,  choose "Edit Contour" from  the menu.  The following
 operations change the current contour state:

 "Add Line"   - attaches a line segment or an arc to the contour. The arc is
                specified by  its degree measure  (zero means  line segment)
                and  two end  points. The  contour  may be  initiated by  an
                arbitrary line, but only adjacent  lines are accepted later.
                The line cannot be added to the closed contour. Adding lines
                is terminated  by pressing ESC  or when the  contour becomes
                closed.

 "Close Contour"     -    closes an open contour by connecting its open ends
                with a straight line or an arc.

 "Add Edge"   - append the  contour with an edge  of the model.  The contour
                may be  initiated by  an arbitrary  edge, but  only adjacent
                edges are  accepted later. The edge  cannot be added  to the
                closed contour.  Adding edges is terminated  by pressing ESC
                or when the contour becomes closed.

 "Add Block"  - considers  the current  closed contour  as a  border of  the
                plane  region   and  updates  this  region   by  adding  (or
                subtracting)  a block  of  the model  in  the  sense of  set
                theory. Adding blocks is terminated by pressing ESC.

 "Undo"       - reverses the last action done with the contour.

 "Clear"      - deletes the entire contour.

 "Change Direction"  -    alters  the contour  direction.  The direction  is
                shown by the arrows at the contour elements.

 Once  edited,  the  state  of  the contour  is  preserved  until  the  next
 modification or  the end  of postprocessing  session. Depending  on current
 state of the contour, some editing operations may be prohibited.

 The direction of the contour is significant in the following cases:

 * for volume  integrals the domain of  integration lies to the  left of the
   contour.
 * for  surface integrals  the positive  normal vector  points to  the right
   relative to the contour direction.
 * the starting point of the contour corresponds to zero point at the x-axis
   of the X-Y plot.
 * if the  plotted or the  integrated function has  different values  to the
   left and to the right of the contour, the right-hand value is used.


       9.4.2 X-Y Plot Control

 Once  the  contour  has  been  defined,  the  X-Y  plot  is  drawn  showing
 distribution  of the  default  field quantity.  In  order  to change  shown
 quantity, choose "View" from "X-Y Plot" menu.

 Few quantities having the same unit of measurement can be shown at the same
 X-Y plot. According to this, all  quantities are combined into groups. Full
 list  of  quantities  includes  all  those  available  for  the  color  map
 representation  (see   "Interpreted  Quantities"),  and  also   normal  and
 tangential components of vector and scalar quantities.

 When you select the appropriate group of quantities, the list titled "Show"
 contains the  quantities selected  for display,  and the  "Quantities" list
 contains available but not selected quantities. You can use buttons located
 between  the lists,  or simply  double-click  in the  lists,  to move  some
 quantity from one list to another.

 In  the dialog  box, you  can also  modify the  range of  y coordinate.  By
 default,  it fits  all  the  currently selected  curves.  You  can get  the
 suggested value of lower or upper limit by selecting the corresponding text
 box ("Minimum" or "Maximum") and choosing "Suggest" button.
 With  the problems  of  harmonic magnetics,  you  can  also switch  between
 momentary (at given phase), time average and peak values of  time dependent
 quantities.

 You can  turn on  or off  the switches for  displaying coordinate  grid and
 markers  on  the curves.  The  last  mode  allows  you to  distinguish  the
 coinciding curves.

       9.4.3 Zooming the X-Y Plot

 "Zoom In"  position  in "X-Y Plot"  menu  allows  you  to change  the  plot
 scaling,  using the  rubber band  rectangle.  Then you  can  return to  the
 default ranges for both axes, choosing "Zoom Out".

 Choosing  "Maximize"  enlarges the  X-Y  plot  window  to the  full  screen
 dimensions without changing  axes ranges. Then press any key  to return the
 Postprocessor to its  normal state. The legend is shown  in maximized view,
 if "Show Legend" in "Options" menu has been switched on earlier.


           9.5 Calculating Integrals


 QuickField calculates line, surface and volume integrals. In plane-parallel
 problem, a  contour defines cylindrical  (in generalized sense)  surface of
 infinite depth, or volume of that  cylinder for volume integral. Therefore,
 in plane-parallel  formulation surface and volume  integrals are calculated
 per  unit  depth.  In axisymmetric  problem,  a  contour  defines  toroidal
 surface, or toroid for volume integral.

 Positive direction of a contour is  counter-clockwise. The direction of the
 contour is accounted as follows:

 * For volume  integrals the domain of  integration lies to the  left of the
   contour.
 * For  surface integrals  the positive  normal vector  points to  the right
   relative to the contour direction.
 * If the  plotted or the  integrated function has  different values  to the
   left and to the right of the contour, the right-hand value is used.


 Force,  torque  and  electric  charge  integrals  represent  real  physical
 quantities only  when the contour is  closed. However, these  integrals are
 calculated for the unclosed contours too, commented as part.

 To get the integral quantities, choose "Integrals" from the menu.

 Choose "Edit Contour" button first to create a contour of integration. Some
 integrals require closed counter-clockwise oriented contour, otherwise they
 have no  physical sense. Once  you created the  contour, you can  select an
 integral quantity  from the list and  choose "Calculate" button to  get the
 value. "Copy to File"  button allows  you to  record the  calculated result
 into a text file.

 When the electrostatic or magnetic force, torque, electric charge, electric
 current or heat flux are to be calculated, the domain of integration may be
 chosen by  many different  ways. The  only requirement  for the  surface of
 integration is to contain all the  necessary bodies, but to avoid any extra
 bodies or  field sources. It is  important to understand that  the accuracy
 will be the best  if you choose the integration surface  as far as possible
 from the places with strong inhomogeneity  of field, e.g., field sources or
 boundaries of conducting or ferromagnetic bodies.

 When calculating  the flux linkage the  domain of integration  must exactly
 fit the cross section of the coil.

       9.5.1.1 The quantities available for electrostatic problems:

 * Total electric charge in a particular volume
 * Total  electrostatic force  acting on  bodies contained  in a  particular
   volume
 * Total  torque of  electrostatic forces  acting on  bodies contained  in a
   particular volume

   The  torque  vector  is  parallel  to  z-axis  in  planar  case,  and  is
   identically equal to  zero in axisymmetric one. The  torque is considered
   relative to the  origin of the coordinate system. The  torque relative to
   any  other arbitrary  point  can  be obtained  by  adding  extra term  of
   [F , r0] (cross product F and  r0), where F is the total  force and r0 is
   the radius vector of the point.

 * Electric field energy

       9.5.1.2 For magnetostatic problems:

 * Total  magnetostatic force  acting on  bodies contained  in a  particular
   volume
 * Total  torque  of  magnetic  forces  acting  on  bodies  contained  in  a
   particular volume

   The  torque vector  is parallel  to  z-axis in  the planar  case, and  is
   identically  equal  to  zero  in the  axisymmetric  one.  The  torque  is
   considered relative  to the origin of  the coordinate system.  The torque
   relative to  any other arbitrary  point can be  obtained by  adding extra
   term of [F , r0], where F is the total  force and r0 is the radius vector
   of the point.

 * Magnetic field energy
 * Flux linkage per one turn of the coil

       9.5.1.3 For harmonic magnetics problems:

 * Complex magnitude of  electric current through a  particular surface, and
   also its source and eddy components I0 and Ie.
 * Time average and peak Joule heat in a volume
 * Time average and peak magnetic field energy
 * Time  average and  peak power  flow through  the given  surface (Poynting
   vector flow)
 * Time  average and  oscillating part  of  Maxwell force  acting on  bodies
   contained in a particular volume
 * Time average and peak Maxwell force  torque acting on bodies contained in
   a particular volume
 * Time average and  oscillating part of Lorentz force  acting on conductors
   contained in a particular volume
 * Time average and peak Lorentz force  torque acting on bodies contained in
   a particular volume

   The  torque vector  is parallel  to  z-axis in  the planar  case, and  is
   identically  equal  to  zero  in the  axisymmetric  one.  The  torque  is
   considered relative  to the origin of  the coordinate system.  The torque
   relative to  any other arbitrary  point can be  obtained by  adding extra
   term of [F , r0], where F is the total  force and r0 is the radius vector
   of the point.

     Note.  The   Maxwell  force  incorporates  both   force  acting  on
     ferromagnetic  bodies  and  Lorentz  force,   which  acts  only  on
     conductors.  If  the  first  component  is  negligible  or  is  not
     considered, we  recommend calculating the electromagnetic  force as
     Lorentz force. Its precision is less sensitive to the contour path,
     and  you  can  simply select  conductors  via  block  selection  to
     calculate the force. With Maxwell force,  this method leads to very
     rough results,  and you  need to avoid  coinciding of  your contour
     parts  and  material  boundaries,  as  described  earlier  in  this
     chapter.


       9.5.1.4 For problems of current flow:

 * Electric current through a given surface
 * Power losses in a volume

       9.5.1.5 For heat transfer problems:

 No integral quantities are available for stress analysis.


           9.6 Saving Prepared Results to Files


       9.6.1 Saving the Screen Picture

 The postprocessor is  capable of storing current field picture  or X-Y plot
 in widely supported  graphics file formats. Graphic objects  in these files
 are  stored in  vector form,  independent of  output device  resolution. It
 guaranties maximum quality pictures on different  printers. These files can
 be directly printed, as well as  included into other documents. There are a
 number  of word  processors  and desktop  publishing  systems, which  could
 import vector-formatted graphics files for editing and printing.

 The postprocessor supports following graphics formats:

 * Computer Graphics Metafile - CGM (ISO 8632-3:1992 compliant).
 * PostScriptR  language  by  AdobeR System  Incorporated.  PostScript  file
   created by QuickField could be directly sent to any PostScript  printer.
 * Encapsulated   PostScript  -  EPS.   An   EPS   file   is   a  standard
   PostScript language   file,   destined   to   be   included   in   other
   documents  as  an illustration.  EPS file  created  by QuickField   also
   conforms to  Adobe  Illustrator ( R) format,  that in many cases  allows
   not only to print, but also to edit the graphics image.

 To save the field picture to file, choose "Export" in the "File" menu.

 The  "Line Styles" box  allows you  to select  appropriate line  styles and
 widths for separate  field picture elements. The line width  is measured in
 points-typographic  unit equal  to 1/72  inch.  "Hair" line  means line  of
 minimum width  allowed for the printer  device. "Dot" means dotted  line of
 the same width. To revert line styles to default settings, choose "Reset".

     Note:  Appearance  of  imported  field  picture  elements  in  some
     applications depends on the features of graphics import filter used
     by those applications, e.g., several filters  do not support dotted
     line style.


 With the Color Grades text box you can change the number of colors used for
 the color map.  If the exporting color  mode is black and  white, shades of
 gray are used instead of rainbow colors.
 We  recommend exporting  in  "Full Color" mode  only  when  you are  really
 planning to use the color printer.

 To export  the X-Y plot currently  drawn on the screen,  choose "Export" in
 the  "File"  menu.   The  corresponding  dialog  box  is   similar  to  the
 "Export Picture" dialog box.

       9.6.2 Exporting Local Values to the Table File

 The local values of physical quantities  obtained in the "Values" mode (see
 "Access to Local  Field Data") can be  logged to the table  file. This file
 has  self explaining  ASCII format,  with values  separated with  spaces or
 commas. The  table file can be  used for printing numerical  results, or to
 pass  them to  other application  program, e.g.,  a spreadsheet  program to
 produce a report.

 To open the table file choose "Open Table" from the "File" menu. The dialog
 box will appear, asking for the name of  the table file, its format and the
 set of the field quantities to be included in the table. The table also may
 contain optional  header. Existing  files may  be appended  or overwritten.
 Once this  option is activated, for  every point you click  in the "Values"
 mode, a line is written to the table file.

 If you wish other filename, than what is  suggested, you can type it in the
 "File"  text  box,  or  choose  "Browse" to  pick  the  filename  from  the
 directory.

 The list  of currently  selected quantities is  displayed in  the "Columns"
 list box. To add some quantity to the list:

 1. Select  the option  button corresponding  to  the group,  to which  that
    quantity belongs. The  list of available quantities  will be redisplayed
    in accordance to the group chosen.
 2. Select  the needed  quantity from  the  list box  and  choose "Add",  or
    double-click in  the list.  That quantity will  appear in  the "Columns"
    list box.


 To delete  some quantity  from the list  of currently  selected quantities,
 select  that quantity  in the  "Columns" list  box and  choose "Delete"  or
 double-click in the list.

 Values in  the table can  be separated with  spaces or commas  (the default
 extensions are .TXT and .CSV, respectively). In some cases, comma-separated
 tables are better understood by the spreadsheet applications.

 To close output to the table  file, choose "Close Table" from the "Options"
 menu.

       9.6.3 Exporting Field Values along the Contour to the Table File

 You can  save field  data in  the points,  distributed along  the currently
 selected contour,  to the table file  of the same  format that is  used for
 exporting local field  values, described in "Exporting Local  Values to the
 Table File".  To save the data,  choose "Tabulate" in "X-Y Plot"  menu. The
 dialog box appears,  allowing you to manage the format  and contents of the
 table.

 In addition to the controls in the "Open Table" dialog box, this dialog box
 allows you to  control the number of rows  in the table. You  can enter the
 value in the  "Rows Number" text box. Its meaning depends  on option button
 selection below the text box. If  "At Whole Contour" is selected, the table
 will contain that number of rows, equally distributed along the contour and
 accounting  its ends.  If selected  is "In Each Segment",  given number  of
 points will  be equally  distributed along  each segment,  constituting the
 contour.  The  total number  of  rows  in the  table  will  be that  number
 multiplied  by the  number of  segments (plus  one additional  row, if  the
 contour is not closed).

 Also,  some additional  quantities  are available:  the  distance from  the
 contour  start, and  normal and  tangential  components of  the vector  and
 tensor quantities, with respect to local contour direction.

       9.6.4 Fast Printing the Results

 If you do not need high quality printing, or if you want to get hardcopy to
 the printer, that  does not support PostScript  language, QuickField offers
 some special capabilities.

 QuickField  supports special  mode for  screen hardcopies,  when the  field
 picture or  X-Y plot is enlarged  to entire screen ("Maximize"  position in
 the menu).  There is  also a  color scheme  suited for  creating monochrome
 screen hardcopies. You  can select this color  scheme with "Options Colors"
 command, which is available in main QuickField and Postprocessor menus.

 If you run  QuickField under MS-DOS 5.0 or higher and  the GRAPHICS program
 is   resident,   you  can   obtain   the   screen  hardcopy   by   pressing
 SHIFT+PRINT SCREEN on the keyboard.

 If  you run  QuickField under  Windows,  pressing PRINT  SCREEN copies  the
 QuickField screen  image to  the clipboard,  which allows  you to  use this
 image in Windows based applications.


           9.7 Additional Options


       9.7.1 Saving the Postprocessor State

 Current state of the Postprocessor can  be saved to the special ."SST" file
 and restored  from it later. The  current state includes: chosen  method of
 presentation,  selected quantity,  scales, ranges,  current contour  state,
 color table, etc. If you analyze several similar problems or the results of
 the same problem several times,  you can save a lot of  work by reusing the
 same Postprocessor parameters once saved in the .SST file.

 Choose "Save Setup" from  the "Options" menu to  save current Postprocessor
 state and  "Load Setup" from the same  menu to restore this  state from the
 file. In  both cases  you will  be inquired  to supply  the file  name. The
 default file  name is constructed  from the current  problem name  and .SST
 extension.

       9.7.2 Controlling Legend Display

 The legend  for the color map  shows the correspondence between  colors and
 number; and for X-Y plot-between curves and quantities.

 The legend  appears in  special window  after each  redrawing of  the field
 picture or  X-Y plot until any  key pressed. It  can be displayed  again by
 choosing "Legend" from the menu.

 To control  the legend visibility  in maximized view,  choose "Show Legend"
 toggle in "Options" menu.

       9.7.3 Changing Color Scheme

 The  QuickField package  has  several alternative  color  schemes. You  can
 switch between these schemes  from the main menu of the  package as well as
 form the  main menu of  the postprocessor. In  both cases,  choose "Colors"
 from "Options" menu.

 QuickField stores chosen scheme in QFIELD.INI file.


                                 10. Examples


 This chapter contains descriptions of the  example problems supplied in the
 EXAMPLES directory.  Each problem in this  directory is represented  by the
 complete data  base, which includes  geometric model, finite  element mesh,
 definition of material properties, loads and boundary conditions, and ready
 analysis results. Supplied analysis results allow  you to look instantly at
 the postprocessing  capabilities without spending  time for  preparing data
 and solving the problem.

 Some  of the  example descriptions  included in  this chapter  represent an
 alternative approach with detailed step-by-step description of the modeling
 process,  data preparation,  and postprocessing  of the  results. They  are
 provided to  illustrate effective  modeling techniques and  to give  you an
 opportunity to learn QuickField by following an example.


           10.1 Magnetic Problems


       10.1.1 MAGN1: Nonlinear Permanent Magnet

 A permanent magnet and a steel keeper in the air.

 Problem Type:

 A nonlinear plane-parallel problem of magnetostatics.

 Geometry:

    +------------------------------------------------------+
    !Q                                                  R  !
    !                                                      !
    !                                                      !
    !      M  +----------------------------------+ N       !
    !         !                                  !         !
    !         !                                  !         !
    !         !              Iron                !         !
    !         !                                  !         !
    !         !                                  !         !
    !      K  +----------------------------------+ L       !
    !                                                      !
                                                           !
    !      G  +------+H                I ------- + J       !
    !         !      !                   !       !         !
    !         !Alnico!                   !Alnico !         !
    !         !      !D                E !       !         !
    !      C  +------+------------------ +------ + F       !
    !         !                                  !         !
    !         !                Iron              !         !
    !         !                                  !         !
    !         +----------------------------------+         !
    !         A                                  B         !
    !                                                      !
    !O                                                  P  !
    +------------------------------------------------------+


 The permanent magnets are made of ALNICO, coercive force is 147218 A/m. The
 polarizations  of the  magnets are  along  vertical axis  opposite to  each
 other.

 The demagnetization curve for ALNICO:

  H (A/m)  -147218 -119400  -99470  -79580   -53710  -19890   0

  B (T)    0.      0.24     0.4     0.5      0.6     0.71     0.77


 The B-H curve for the steel:

  H (A/m)  400   600   800   1000   1400    2000   3000    4000   6000

  B (T)    0.73  0.92  1.05  1.15   1.28    1.42   1.52    1.58   1.60

 Comparison of Results
 Maximum flux density in Y-direction:

      ANSYS          0.42

      Students'      0.40
      QuickField

      Professional   0.417
      QuickField


 See the MAGN1.PBM problem in the EXAMPLES directory.

 All dimensions are in centimeters.

 Step-by-step Description

 Let us  learn, how  to solve  this problem from  scratch. We'll  forget the
 solution made in MAGN1.PBM, and start a new problem, MAGNET.PBM.

 To create a new problem:

 1. Choose "New"  in the "Files"  menu (ALT+F, N);  the dialog  box appears,
    asking for the filename for new problem.
 2. Change, if  needed, the  drive and directory  in the  "Directories" list
    box.
 3. Type magnet in the "Filename" box.
 4. Choose "OK".

 The extension .PBM will be added automatically.

 To select convenient length measurement units (millimeters):

 1. Choose "Length Units" in the "Options" menu. A dialog box appears.
 2. Select "Millimeters".
 3. Choose "OK".

 To assign the problem with appropriate features:

 1. Choose    "Problem"   in    the   "Edit"    menu    (ALT+E,   P).    The
    "Problem Description" dialog box appears.
 2. Select "Magnetostatics" in the "Problem Type" drop-down list box.
 3. Select "XY Plane".


 We'll  agree with  suggested  model and  data  file  names (MAGNET.MOD  and
 MAGNET.DMS.) If  the "Library Data"  filename box is  not empty,  clear it,
 since we'll define all the labels in the local data file (MAGNET.DMS.)

 We   can  start   editing  the   model  or   the  data   directly  in   the
 "Problem Description" dialog box. To edit the model:

 1. Select the "Geometry" text box (click  anywhere in the box with a mouse,
    or press ALT+G, or press TAB until the selection reaches the box.)
 2. Choose the "Open" button.

 The Model Editor starts.

 First, we  should make  a decision concerning  dimensions of  the problem's
 region.  Since the  given  problem is  physically  unbounded, the  magnetic
 system must be surrounded  with a layer of air thick  enough to neglect the
 influence of the boundary. We suppose that three times the width of the air
 gap  between  the magnet  and  the  steel  keeper  will be  a  satisfactory
 thickness of the  air layer around the magnet, so  the rectangle 100'100 mm
 will fit our region's geometry.

 The first  step with  the new  model in  Model Editor  is to  adjust window
 dimensions fitting  the problem's  region. Since  the problem  has vertical
 axis of  symmetry, it is convenient  to set zero of  x-axis at the  axis of
 symmetry.  So the  region fits  the square  (-50 # x # 50, 0 # y # 100)  To
 assign these values to the window limits:

 1. Choose "Keyboard" in the "Zoom" menu.
 2. Type the values in appropriate text boxes.
 3. Press ENTER or click the dialog box background anywhere outside options.

 Now  we can  proceed  with  defining the  geometry  itself.  To define  the
 vertices which correspond to points labeled with letters A through R on the
 sketch:

 1. Enter "Add Vertex"  mode in the "Model"  menu. The plus sign  cursor (+)
    arises in the large window indicating the point locating mode.
 2. Use DIRECTION  keys or a mouse  to move cursor  from point to  point and
    press ENTER or click  left mouse button where you want  the vertex to be
    located. New vertices  immediately appear in the window.  Or, press TAB,
    type coordinates,  and press ENTER for  each new vertex  Create vertices
    with coordinates:  (-20, 20), (20, 20), (-20, 30),  (-10, 30), (10, 30),
    (20, 30), (-20, 40), (-10, 40), (10, 40), (20, 40), (-20, 50), (20, 50),
    (-20, 70), (20, 70), (-50, 0), (50, 0), (-50, 100), and (50, 100). Don't
    worry about making mistakes-you can remove erroneous vertices later.
 3. Press ESC to return to the "Model" menu.

 If you have created excess points, you can remove them now:

 1. Choose  "Delete Vertex". The  X-shaped cursor  appears  to indicate  the
    picking  mode. Consecutively  pick  excess  vertices, which  immediately
    disappear.
 2. Press ESC to return to the "Model" menu.

 Now we can create edges connecting the vertices:

 1. Choose "Add Edge".  A dialog box  appears asking the  arc angle  for new
    edges.
 2. Press ENTER (or  click gray background of the dialog  box) to agree with
    suggested  zero value,  which  means creating  the  straight lines.  The
    picking mode (X-shaped) cursor appears in the window.
 3. Pick  points  A,  B,  F,  C, A  consecutively  to  create  edges,  which
    constitute  the rectangle  ABFC.  The edges  immediately  appear on  the
    screen. In  fact, we created  six edges, not  four, because edge  FC was
    split into three (FE, ED and DC) while creating.
 4. Press ESC to break the chain of edges and start a new one.
 5. Repeat last two actions to create  chains CGHD, EJGF, rectangle KLNM and
    bounding rectangle OPRQ.
 6. Press ESC to return to the "Model" menu.

 You can remove erroneous edges, using the "Delete Edge" command.
 We  are  done with  the  model's  geometry. Now  we  can  assign labels  to
 geometrical objects  to describe material properties,  sources and boundary
 conditions.

 The problem contains  four materials having different  properties: the air,
 the steel and two pieces of  permanent magnet, which differ in direction of
 magnetization  vector. To  be clear,  we  can use  the  labels Air,  Steel,
 ALNICO Up and ALNICO Dn to label appropriate blocks. To assign these labels
 to blocks:

 1. Press ESC to close the  "Model" menu and return to the  main menu of the
    Model Editor.
 2. Choose  "Label Blocks" in  the  "Label" menu.  The  picking mode  cursor
    arises.
 3. Pick inside  the CDHG rectangle. The  block becomes highlighted  and the
    dialog box appears asking for the label value.
 4. Type ALNICO Dn and press ENTER. The X-shaped cursor appears again.
 5. Repeat the  last two actions to  label the CDJI rectangle  as ALNICO Up,
    the ABFC rectangle as Steel and the OPRQ as Air.
 6. Pick inside the KLNM rectangle. Because  the Steel label already exists,
    you can simply pick it in the  list of existing labels instead of typing
    and then press  ENTER. (You can also use the  "Select" command to assign
    some label to several blocks at once.)
 7. Press ESC to return to the "Label" menu.

 Edge labels  are used to define  specific boundary conditions on  inner and
 outer  boundaries of  the region.  In  our case,  we need  to specify  zero
 Dirichlet boundary  condition for the  outer boundary (rectangle  OPRQ). To
 assign labels to edges:

 1. Choose   "Select"  and   then  double-click   "Edges"   option  in   the
    corresponding dialog box. The picking mode cursor arises.
 2. Pick  consecutively four  edges, which  constitute  the rectangle  OPRQ.
    Those edges become highlighted that indicates the selection. If you have
    selected excess edge, pick it once more to unselect it.
 3. Press ESC to cancel selection mode.
 4. Choose  "Label Selected". A  dialog  box appears  asking  for the  label
    value.
 5. Type Zero and press ENTER to assign the label to selected edges.


 Now we have finished with assigning  labels to geometrical objects. You can
 check their values in the "Find Label" mode.

 We can proceed with building a mesh  of finite elements. To define the mesh
 density, we need  to define mesh spacing parameters in  several vertices of
 the model.  We suppose that  the field is  most non-homogeneous  around the
 magnets, so the  mesh there must be maximum dense.  Therefore, we'll assign
 the spacing value  of 1 mm to the vertices G,  H, I and J and  the value of
 5 mm to the vertices O, P, R and Q  to build the mesh of approximately 2000
 nodes. To define spacing values:

 1. Press ESC to return from the "Label" menu to the main menu.
 2. Choose "Mesh" to open the mesh building menu.

 3. Choose  "Select"   and  then  double-click  "Vertices"   option  in  the
    corresponding dialog box. The picking mode cursor arises.
 4. Select vertices  G, H, I  and J and  press ESC to  return to  the "Mesh"
    menu.
 5. Choose "Set Spacing". A dialog box appears asking for the spacing value.
 6. Type 1 and press ENTER. This value is now assigned to selected vertices.
 7. Choose "Select"  and double-click "Unselect All" option  to unselect all
    previously selected objects.
 8. Choose "Select" and double-click "Vertices" option again.
 9. Select vertices O, P, R and Q.
 10.Choose "Set Spacing", type 5 and press  ENTER. The model is now ready to
    build the mesh.
 11.Choose "Build Mesh". A dialog box appears  asking, which blocks you want
    to mesh.
 12.Choose "In All Blocks" to build the meshes for all blocks at once.

 Now the model is ready. To exit the Model Editor with saving the file:

 1. Press  ESC twice  to close  the "Mesh"  menu and  quit. The  box appears
    prompting you to save the model file.
 2. Choose "Yes" to confirm saving operation.

 You have returned to the "Problem Description"  dialog box. Let us continue
 with  defining data  for material  properties and  boundary conditions.  To
 start editing data file:

 1. Select the "Data" text box.
 2. Choose the "Open" button. A dialog box appears warning you that the file
    MAGNET.DMS does not exist.
 3. Choose "OK" to create new data file.

 The "Properties Description File"  dialog box appears. It  contains labels,
 which you have just  defined in the model. The label  names are marked with
 asterisks to outline the  fact, that the data for these  labels are not yet
 defined. Now we need to select the labels one-by-one and to define the data
 for them.

 To define the data for block label Air:

 1. Select its name in the  list box (click it with a  mouse, or press ALT+B
    and use DOWN key to highlight the name's field.)
 2. Choose "Open" button (or press ENTER as "Open" is the default button, or
    double-click on the name's field.)

 A  dialog  box   appears,  prompting  to  enter   material  properties  and
 distributed source for block label Air. To assign values:

 1. Type 1 in any text box for components of magnetic permeability tensor.
 2. Choose "OK".

 Now we'll learn  how to describe nonlinear magnetic properties  by means of
 editing the B-H curve. To start editing for block label Steel:

 1. Select its name  in the list box and choose  "Open" button. The property
    editing dialog box appears.
 2. Select the "Nonlinear" box. This causes starting the B-H Curve Editor.

 With the  Curve Editor,  you can  simply enter the  values from  the table,
 point by point, checking the  curve in the graph to the  left of the table.
 The point (0; 0)  is always presented in the table,  which cannot be edited
 nor deleted. Since  the cursor is already in  the box for new  B value, you
 can  start entering  new points.  To  create the  first point  (B = 0.73 T,
 H = 400 A/m, see the steel magnetisation table:

 1. Type 0.73 and press ENTER. The cursor will move to the box for H value.
 2. Type 400 and press ENTER.  The new point will be added  to the table and
    immediately displayed in  the graph. The cursor will return  back to the
    box for B value.
 3. Repeat  these actions  for other  points  of the  table.  Points may  be
    entered in any order.

 In  case of  mistyping, the  erroneous  point would  in  general produce  a
 noticeable anomaly in the displayed curve. You can select this point in the
 graph or in the table and then delete it or correct its coordinates.

 When you  are done with entering  points, and the curve  looks like classic
 B-H curve, choose the "Close" button  to finish curve editing and return to
 property editing  dialog. Since we do  not want to change  any more values,
 choose "OK" button to finish editing data for label Steel.

 Describing data  for the  permanent magnet  is a  bit more  complicated. In
 addition to demagnetization curve, the direction of resistant magnetization
 should be  specified by means  of the vector  of coercive force.  Now we'll
 define the demagnetization curve for label ALNICO Up:

 1. Select its name  in the list box and choose  "Open" button. The property
    editing dialog box appears.
 2. Type 1 in  any text box for components of  magnetic permeability tensor.
    This is void  action, the only purpose  of which is to  specify that the
    data for the  label is not empty,  so that other text  boxes will become
    available.
 3. Select the text box for y-component of coercive force and type 147218.
 4. Choose the "Nonlinear" box. This starts the B-H Curve Editor.


 Note that  the predefined point is  now at (-147218, 0). It  is exactly the
 first point from the  B-H curve table. Now we can  continue with adding all
 other points  from the  table. When  this job is  done, choose  the "Close"
 button to finish curve editing and  return to property editing dialog. Then
 choose "OK" button to finish editing data for label ALNICO Up.

 To define data for label ALNICO Dn, we need not repeat all this actions. We
 can simply  copy the data from  ALNICO Up, and change the  direction of the
 coercive force. To do this:

 1. Select ALNICO Up in the list box.
 2. Choose "Copy". The dialog box appears asking for destination label name.
 3. Change ALNICO Up to ALNICO Dn and choose "OK". The data for these labels
    are now the same.
 4. Select ALNICO Dn in the list box and choose "Open".
 5. Select the text  box for y-component of coercive force  and insert minus
    sign before  digits to  change the  direction of  coercive force  to the
    opposite one.
 6. Choose "OK".

 Now we'll continue  with edge labels' data. We'll define  the label Zero as
 homogeneous Dirichlet  boundary condition (A = 0).  To define the  data for
 edge label Zero:

 1. Select its  name and choose  "Open". A dialog  box appears,  allowing to
    assign to edge label any of possible boundary conditions.
 2. Select  the   "Dirichlet Condition"  box.  Zero  value   of  pre-defined
    potential will be suggested.
 3. Choose "OK".

 All the data needed to solve the problem  is now defined. To exit from data
 editing mode:

 1. Choose "Close" button in the "Properties Description File" dialog box. A
    dialog box appears, prompting you to save changes to data file.
 2. Choose   "Yes"    to   save   changes.    Now   you   return    to   the
    "Problem Description" dialog box again.
 3. Choose "OK".

 At last, we can solve  the problem and analyze the solution.  To do this in
 one step:

 1. Choose "Analyze" from the "Results" menu. You will be suggested to solve
    the problem first, as the results are absent.
 2. Choose "OK".

       10.1.2 MAGN2: Solenoid Actuator

 A solenoid  actuator consists of  a coil enclosed  in a  ferromagnetic core
 with a  plunger. Calculate the  magnetic field and  a force applied  to the
 plunger.

 Problem Type:

 A nonlinear axisymmetric problem of magnetics.

 Given:
   Relative permeability of air and coil    m = 1;
   Current density in the coil              j = 1x10  A/m ;
   The B-H curve for the core and the plunger:

        H (A/m) 460   640   720   890   1280  1900  3400  6000

        B (T)   0.80  0.95  1.00  1.10  1.25  1.40  1.55  1.65

 Problem:

 Obtain  the magnetic  field in  the  solenoid and  a force  applied to  the
 plunger.

 Solution:

 This magnetic  system is almost closed,  therefore outward boundary  of the
 model can be put relatively close to  the solenoid core. A thicker layer of
 the outside  air is  included into  the model region  at the  plunger side,
 since the magnetic field in this area cannot be neglected.

 Mesh density  is chosen by default,  but to improve the  mesh distribution,
 three  additional vertices  are added  to  the model.  We put  one of  this
 vertices at  the coil  inner surface  next to the  plunger corner,  and two
 others next to the corner of the core at the both sides of the plunger.

 A contour for the force calculation encloses  the plunger. It is put in the
 middle of the air gap between the  plunger and the core. While defining the
 contour of  integration, use a  strong zoom-in mode  to avoid  sticking the
 contour to existing edges.

 The calculated force applied to the plunger F = 374.1 N.

 See the MAGN2.PBM problem in the EXAMPLES directory. Load the Postprocessor
 setup from the  MAGN2.SST file to get the predefined  contour for the force
 calculation.

 Comparison of Results

 Maximum flux density in Z-direction in the plunger:

                                     Bz (T)

                 Reference             0.933

                 QuickField           1.0183


 Reference

 D.  F.  Ostergaard, "Magnetics  for  static  fields", ANSYS  revision  4.3,
 Tutorials, 1987.

       10.1.3 MAGN3: Ferromagnetic C-Magnet

 A permanent  C-magnet in  the air.  The example  demonstrates how  to model
 curved permanent magnet using the equivalent surface currents.

 Problem Type:

 Plane problem of magnetics.

 Given:
   Relative permeability of the air m = 1;
   Relative permeability of the magnet m = 1000;
   Coercive force of the magnet Hc = 10000 A/m.

 The polarization of the magnet is along its curvature.

 Solution:

 To  avoid the  influence of  the  boundaries while  modeling the  unbounded
 problem,  we'll enclose  the magnet  in  a rectangular  region  of air  and
 specify zero Dirichlet boundary condition on its sides.

 Magnetization of  straight parts  of the  magnet is  specified in  terms of
 coercive force vector. Effective surface currents simulate magnetization in
 the middle curved part of the magnet.

 See the MAGN3.PBM problem in the EXAMPLES directory.

           10.2 Time-Harmonic Magnetic Problems

       10.2.1 HMAGN1: Slot Embedded Conductor

 Problem Type:

 A plane problem of time-harmonic magnetic field.

 Geometry:

      +--------------+---------+---------------+
      |              |         |               |
      |              |  Air    |               |
      |              |         |               |
      |              +-------- +               |
      |    Steel     |         |      Steel    |
      |              |         |               |
      |       +------+         +------+        |
      |       |                       |        |
      |       |                       |        |
      |       |      Cooper Bar       |        |
      |       |                       |        |
      |       |                       |        |
      |       +-----------------------+        |
      |                                        |
      +----------------------------------------+


 A  solid copper  conductor embedded  in  the slot  of  an electric  machine
 carries a current I at a frequency f.

 Given:
   Magnetic permeability of air mu = 1;
   Magnetic permeability of copper mu = 1;
   Conductivity of copper sigma = 5.8005x10e7 S/m;
   Current in the conductor I = 1 A;
   Frequency f = 45 Hz.

 Problem:

 Determine current  distribution within the conductor  and complex impedance
 of the conductor.

 Solution:

 We assume that  the steel slot is infinitely permeable  and may be replaced
 with  a  Neumann boundary  condition.  We  also  assume  that the  flux  is
 contained within  the slot, so  we can put  a Dirichlet  boundary condition
 along the top of the slot. See HMAGN1.PBM problem in the EXAMPLES directory
 for the complete model.

 The complex impedance per unit length of the conductor can be obtained from
 the equation

      Z = V / I,

 where  V is  a voltage  drop  per unit  length. This  voltage  drop can  be
 obtained  in  the  Postprocessor (choose  "Results",  "Analyze",  "Values",
 "Complex", and then pick an arbitrary point within the conductor.)
 Comparison of Results

                          Re Z (Ohm/m)   Im Z (Ohm/m)

            Reference     1.7555x10e-4   4.7113x10e-4

            QuickField    1.7550x10e-4   4.7112x10e-4

 Reference

 A.   Konrad,    "Integrodifferential   Finite   Element    Formulation   of
 Two-Dimensional Steady-State Skin Effect  Problems", IEEE Trans. Magnetics,
 Vol MAG-18, No. 1, January 1982.

       10.2.2 HMAGN2: Symmetric Double Line of Conductors

 Problem Type:

 A plane problem of time-harmonic magnetic field.

 Geometry:

      +---------------------------------------------------+
      |                      Coating                      |
      |    +-----------------------------------------+    |
      |    |                                         |    |
      |    |                   Air                   |    |
      |    |    +-----------+      +------------+    |    |
      |    |    |           |      |            |    |    |
      |    |    | Conductor |      |  Conductor |    |    |
      |    |    |           |      |            |    |    |
      |    |    |           |      |            |    |    |
      |    |    |           |      |            |    |    |
      |    |    |           |      |            |    |    |
      |    |    +-----------+      +------------+    |    |
      |    |                                         |    |
      |    |                                         |    |
      |    +-----------------------------------------+    |
      |                                                   |
      +---------------------------------------------------+


 Two copper square cross-section conductors with equal but opposite currents
 are contained inside rectangular ferromagnetic  coating. All dimensions are
 in millimeters.

 Given:
   Magnetic permeability of air mu = 1;
   Magnetic permeability of copper mu = 1;
   Conductivity of copper sigma = 5.6x10e7 S/m;
   Magnetic permeability of coating mu = 100;
   Conductivity of copper sigma = 1.0x10e6 S/m;
   Current in the conductors I = 1 A;
   Frequency f = 100 Hz.

 Problem:

 Determine  current  distribution within  the  conductors  and the  coating,
 complex impedance of the line, and power losses in the coating.
 Solution:

 We assume that  the flux is contained within  the coating, so we  can put a
 Dirichlet  boundary condition  on the  outer  surface of  the coating.  See
 HMAGN2.PBM problem in the EXAMPLES directory for the complete model.

 The complex impedance per unit length of  the line can be obtained from the
 equation

      Z = (V1 - V2) / I,

 where V1 and V2 are voltage drops  per unit length in each conductor. These
 voltage drops  are equal  with opposite  signs due to  the symmetry  of the
 model.  To obtain  a voltage  drop choose  "Results", "Analyze",  "Values",
 "Complex", and then pick an arbitrary point within a conductor.

 The impedance of the line Z = 4.93x10e-4 + i 7.36x10e-4 Ohm/m.

 To obtain power losses in the coating:

 1. In   the  postprocessing   mode   choose  "Integrals",   "Edit Contour",
    "Add Block" and pick the coating block.  Press right mouse button or ESC
    key twice to return to the Integral Calculator dialog box.
 2. Select  Joule heat  from  the list  of  integral  quantities and  choose
    "Calculate".

 The power losses in the coating P = 4.65x10-5 W/m.


           10.3 Electrostatic Problems

       10.3.1 ELEC1: Microstrip Transmission Line

 A  shielded  microstrip  transmission  line  consists  of  a  substrate,  a
 microstrip, and a shield.

 Problem Type:

 Plane-parallel problem of electrostatics.

 Geometry:

 The transmission line is directed along  z-axis, its cross section is shown
 on the sketch. The rectangle  ABCD is a section of the  shield, the line EF
 represents a conductor strip.

 Geometry:

                        Shield
                       -------
                      /
                     /
    D +----------------------------------------- + C
      !                                          !
      !                                          !
      !       Air                 Conductor      !
      !                          -----------     !
      !                         /                !
      !                        /                 !
      !                       /                  !
    G !              E       / F                 ! H
      +---------------=========----------------- +
      !                                          !
      !         Substrate                        !
      !                   J                      !
    A +-------------------o--------------------- + B


 Given:
   Relative permittivity of air e = 1;
   Relative permittivity of substrate e = 10.

 Problem:

 Determine the capacitance of a transmission line.

 Solution:

 There are several different approaches to  calculate the capacitance of the
 line:

 * To apply  some distinct  potentials to  the shield and  the strip  and to
   calculate the charge that arises on the strip;
 * To apply zero potential to the shield and to describe the strip as having
   constant  but unknown  potential and  carrying  the charge,  and then  to
   measure the potential that arises on the strip.


 Both these approaches make use of the equation for capacitance:

      C = q / U.

 Other  possible approaches  are based  on calculation  of stored  energy of
 electric field. When the voltage is known:

      C = 2 * W / (U * U),

 and when the charge is known:

      C = q*q / (2 * W)

 Experiment with this example shows that energy-based approaches give little
 bit less  accuracy than approaches  based on charge  and voltage  only. The
 first approach needs  to get the charge  as a value of  integral along some
 contour, and  the second  one uses  only a local  value of  potential, this
 approach is the simplest and in many cases the most reliable.

 The first and  third approaches are illustrated in  the ELEC1_1.PBM problem
 in the EXAMPLES directory, and the  ELEC1_2.PBM explains the second and the
 fourth approaches.

 Results:

 Theoretical result:        C = 178.1 pF/m.

 Approach 1:                C = 177.83 pF/m (99.8%).

 Approach 2:                C = 178.47 pF/m (100.2%).

 Approach 3:                C = 177.33 pF/m (99.6%).

 Approach 4:                C = 179.61 pF/m (100.8%).

 Step-by-step Description

 Let us  learn, how  to solve  this problem from  scratch, using  the second
 approach. We'll  forget the solution made  in ELEC1_2.PBM, and start  a new
 problem, STRIP.PBM.

 To create the new problem:

 1. Choose "New"  in the "Files"  menu (ALT+F, N);  the dialog  box appears,
    asking for the filename for new problem.
 2. Change, if  needed, the  drive and directory  in the  "Directories" list
    box.
 3. Type strip in the "Filename" box.
 4. Choose "OK".


 The extension .PBM will be added automatically.

 To select convenient length measurement units (centimeters):

 1. Choose "Length Units" in the "Options" menu. A dialog box appears.
 2. Select "Centimeters".
 3. Choose "OK".

 To assign the problem with appropriate features:

 1. Choose  "Problem"   in  the  "Edit"   menu  (ALT+E,  P).   The  "Problem
    Description" dialog box appears.
 2. Select "Electrostatics" in the "Problem Type" drop-down list box.
 3. Select "XY Plane".
 We'll  agree  with suggested  model  and  data  file names  (STRIP.MOD  and
 STRIP.DES.) If  the "Library  Data" filename  box is  not empty,  clear it,
 since we'll define all the labels in the local data file (STRIP.DES.)

 We  can start  editing  the model  or  the data  directly  in the  "Problem
 Description" dialog box. To edit the model:

 1. Select the "Geometry" text box (click  anywhere in the box with a mouse,
    or press ALT+G, or press TAB until the selection reaches the box.)
 2. Choose the "Open" button.

 The Model Editor starts.

 The first  step with  the new  model in  Model Editor  is to  adjust window
 dimensions fitting  the problem's  region. Since  the problem  has vertical
 axis of  symmetry, it is convenient  to set zero of  x-axis at the  axis of
 symmetry. So the region fits the square (-5 # x # 5, 0 # y # 10.) To assign
 these values to the window limits:

 1. Choose "Keyboard" in the "Zoom" menu.
 2. Type the values in appropriate text boxes.
 3. Press ENTER or click the dialog box background anywhere outside options.

 Now  we can  proceed  with  defining the  geometry  itself.  To define  the
 vertices which correspond to points labeled with letters A through F in the
 sketch:

 1. Enter "Add Vertex"  mode in the "Model"  menu. The plus sign  cursor (+)
    arises in the large window indicating the point locating mode.
 2. Use DIRECTION  keys or a mouse  to move cursor  from point to  point and
    press ENTER or click  left mouse button where you want  the vertex to be
    located. New vertices immediately appear in the window.
 3. Or, press  TAB, type coordinates,  and press ENTER  for each  new vertex
    Create  vertices with  coordinates (-5, 0),  (5, 0), (5, 10),  (-5, 10),
    (-0.5, 1),  and  (0.5, 1). Don't  worry  about  making mistakes-you  can
    remove erroneous vertices later.
 4. Press ESC to return to the "Model" menu.

 If you have created excessive points, you can remove them now:

 1. Choose  "Delete Vertex". The  X-shaped cursor  appears  to indicate  the
    picking  mode. Consecutively  pick  excess  vertices, which  immediately
    disappear.
 2. Press ESC to return to the "Model" menu.

 Now we can create edges connecting the vertices:

 1. Choose "Add Edge".  A dialog box  appears asking the  arc angle  for new
    edges.
 2. Press ENTER (or  click gray background of the dialog  box) to agree with
    suggested zero value,  which means creating straight  lines. The picking
    mode (X-shaped) cursor appears in the window.
 3. Pick  points  A,  B,  C,  D, A  consecutively  to  create  edges,  which
    constitute  the rectangle  ABCD.  The edges  immediately  appear on  the
    screen.
 4. Press ESC twice to return to the "Model" menu.

 You can remove erroneous edges, using the "Delete Edge" command.
 We need some  additional constructing to create  edges separating substrate
 from the air. The easy way  to create them is to copy  the edge AB shifting
 it 1 cm up. To make a copy:

 1. Choose "Select" and  then double-click "Edges" option.  The picking mode
    (X-shaped) cursor appears.
 2. Pick the edge AB and press ESC to return to menu.
 3. Choose  "Copy Selected".  A  dialog box  with  the  parameters for  copy
    operation appears.
 4. Select delta-y box and type 1.
 5. Choose OK, and then confirm the operation by choosing "Create".

 The copy of the line segment AB crosses vertices E and F and produces three
 edges separated by these vertices.

 We  are  done with  the  model's  geometry. Now  we  can  assign labels  to
 geometrical objects  to describe material properties,  sources and boundary
 conditions.

 The model contains two blocks having different material properties: the air
 and the substrate. To be clear, we can use  the word Air to label the upper
 block and Substrate for the lower one. To assign these labels to blocks:

 1. Press ESC to close the  "Model" menu and return to the  main menu of the
    Model Editor.
 2. Choose  "Label Blocks"  in the  "Label"  menu. The  picking mode  cursor
    arises.
 3. Pick the upper block. It becomes  highlighted and the dialog box appears
    asking for the label value.
 4. Type Air and press ENTER. The X-shaped cursor appears again.
 5. Pick the lower block, type Substrate and press ENTER.
 6. Press ESC to return to the "Label" menu.

 Edge labels  are used to define  specific boundary conditions on  inner and
 outer boundaries  of the region. In  our case, we need  to specify boundary
 conditions for the shield (rectangle ABCD)  and for the strip (line EF). To
 assign labels to edges:

 1. Choose "Select"  and double-click "Edges"  option (we'll  select several
    edges to assign a label to them at once.)The picking mode cursor arises.
 2. Pick consecutively six edges, which constitute the rectangle ABCD. Those
    edges  become highlighted  that  indicates the  selection.  If you  have
    selected excess edge, pick it once more to unselect it.
 3. Press ESC to cancel selection mode.
 4. Choose  "Label Selected".  A dialog  box  appears asking  for the  label
    value.
 5. Type Shield and press ENTER to assign the label to selected edges.
 6. Choose  "Label Edges".  The picking  mode cursor  appears. This  mode is
    convenient for assigning labels edge-by-edge.
 7. Pick the edge EF. A dialog box appears.
 8. Type Strip and press ENTER to assign the label.
 9. Press ESC to return to the "Label" menu.

 We also need to assign vertex label  to any vertex contacting the strip, to
 specify that the  strip is charged. No matter which  vertex you choose, the
 charge will be  distributed through all the conductor. To  assign the label
 to a vertex:

 1. Choose "Label Vertices". The picking mode cursor arises.
 2. Pick one  vertex, E  or F.  A dialog  box appears  asking for  the label
    value.
 3. Type Charge and press ENTER to assign the label to the vertex.
 4. Press ESC to return to the "Label" menu.

 Now we have finished with assigning  labels to geometrical objects. You can
 check their values in the "Find Label" mode.

 We can proceed with building a mesh  of finite elements. To define the mesh
 density, we  need to define spacing  parameters in several vertices  of the
 model. We suppose that the electric  field is most non-homogeneous near the
 ends of the  strip, so the mesh  there must be very  fine. Therefore, we'll
 assign the spacing value of 0.2 cm to the vertices E and F and the value of
 0.5 cm to  the vertices A, B,  C and D to  build the mesh  of approximately
 1000 nodes. To define spacing values:

 1. Press ESC to return from the "Label" menu to the main menu.
 2. Choose "Mesh" to open the mesh building menu.
 3. Choose  "Select" and  double-click "Vertices"  option. We'll  assign one
    spacing value to several vertices at once.
 4. Select vertices  A, B, C  and D and  press ESC to  return to  the "Mesh"
    menu.
 5. Choose "Set Spacing". A dialog box appears asking for the spacing value.
 6. Type  0.5 and  press  ENTER.  This value  is  now  assigned to  selected
    vertices.
 7. Choose "Select" and  double-click "Unselect All" option  to unselect all
    previously selected objects.
 8. Choose "Select" and double-click "Vertices" option.
 9. Select vertices E and F.
 10.Choose "Set Spacing",  type 0.2 and press ENTER. The  model is now ready
    to build the mesh.
 11.Choose "Build All" to build the meshes for both blocks at once.

 Now the model is ready. To exit the Model Editor with saving the file:

 1. Press  ESC twice  to close  the "Mesh"  menu and  quit. The  box appears
    prompting you to save the model file.
 2. Choose "Yes" to confirm saving operation.

 You have returned to the "Problem  Description" dialog box. Let us continue
 with  defining data  for material  properties and  boundary conditions.  To
 start editing data file:

 1. Select the "Data" text box.
 2. Choose the "Open" button. A dialog box appears warning you that the file
    STRIP3.DES does not exist.
 3. Choose "OK" to create new data file.

 The "Properties Description  File" dialog box appears.  It contains labels,
 which you have just  defined in the model. The label  names are marked with
 asterisks to outline the  fact, that the data for these  labels are not yet
 defined. Now we need to select the labels one-by-one and to define the data
 for them.

 To define the data for block label Air:

 1. Select its name in the  list box (click it with a  mouse, or press ALT+B
    and use DOWN key to highlight the name's field.)
 2. Choose "Open" button (or press ENTER as "Open" is the default button, or
    click a mouse once more on the name's field.)
 A  dialog  box   appears,  prompting  to  enter   material  properties  and
 distributed source for block label Air. To assign values:

 1. Type 1 in any text box for components of electric permittivity tensor.
 2. Choose "OK".

 Repeat  last  actions  for  the label  Substrate.  The  value  of  relative
 permittivity of substrate is 10.

 Now we'll continue with edge labels' data. We'll define the label Shield as
 a homogeneous Dirichlet boundary condition (U = 0) and the label Strip as a
 conductor condition (U = const).

 To define the data for edge label Shield:

 1. Select its  name and choose  "Open". A dialog  box appears,  allowing to
    assign to edge label any of possible boundary conditions.
 2. Select  the  "Dirichlet  Condition"  box.   Zero  value  of  pre-defined
    potential will be suggested.
 3. Choose "OK".

 To define the data for edge label Strip:

 1. Select its name and choose "Open".
 2. Select the "Conductor" box.
 3. Choose "OK".

 We need  to define  the vertex  label Charge  to assign  the charge  to the
 strip. To determine the capacitance, the exact value of the charge does not
 matter. We'll choose a value of 1.

 To define the data for vertex label Charge:

 1. Select its  name and choose  "Open". A dialog  box appears,  allowing to
    specify the charge, or to assign the Dirichlet boundary condition.
 2. Select the "Electric Charge" box.
 3. Type 1 in the text box for charge value.
 4. Choose "OK".

 All the data needed to solve the problem  is now defined. To exit from data
 editing mode:

 1. Choose "Close" button in the "Properties Description File" dialog box. A
    dialog box appears, prompting you to save changes to data file.
 2. Choose  "Yes"  to   save  changes.  Now  you  return   to  the  "Problem
    Description" dialog box again.
 3. Choose "OK".

 At last, we can solve  the problem and analyze the solution.  To do this in
 one step:

 1. Choose "Analyze" from the "Results" menu. You will be suggested to solve
    the problem first, as the results are absent.
 2. Choose "OK" to start the solver.
 After  finishing, the  Postprocessor starts  automatically. There  are many
 possibilities to analyze the field in  the Postprocessor. We will show only
 those steps needed to determine the capacitance:

 1. Choose "Values" from the menu. Cross-shaped  cursor appears allowing you
    to pick points to determine the local field data.
 2. Move the cursor to the point  (0.0, 1.0) (exactly; the convenient way is
    to use  the DIRECTION keys,  or to press  TAB and type  coordinates from
    keyboard.)
 3. Press ENTER.

 The box  appears, showing you  the local field  data. The potential  of the
 strip is 5.251e+9 Volts. The capacitance is

      C = q / U = 1 / 5.251e+9 = 190.4 pF/m

 Note that, with plane-parallel problems, we specify the sources as specific
 values per unit  depth (e.g., the charge  of the strip), and  the result is
 specific capacitance per unit depth, measured in F/m.

 Since  the mesh  is rather  rough, the  solution gives  less accuracy  than
 provided in ELEC1_2.PBM.

 If you now look through the model provided with ELEC1_2.PBM, ELEC1.MOD, you
 will find some hints for obtaining a very fine mesh near the vertices E and
 F-the points of singularity.

 Since the Model Editor cannot squeeze the mesh spacing inside the edge, but
 only from one end to another, two extra vertices have been added in central
 points of  edges AB and EF.  The first of  these vertices allows  the Model
 Editor to  adjust automatically the spacing  around it, since the  strip is
 very close  to this  point. The  second vertex is  aimed to  specify manual
 spacing value for it, which helps to  decrease the total number of nodes in
 the mesh, without loss of precision.

       10.3.2 ELEC2: Two Conductor Transmission Line

 Problem Type:

 A plane problem of electrostatics.

 Geometry:

 The problem's region is bounded by ground from the bottom side and extended
 to infinity on other three sides.

 Given:
   Relative permittivity of air e = 1;
   Relative permittivity of dielectric e = 2.

 Problem:

 Determine self and mutual capacitance of conductors.

 Solution:

 To avoid  the influence of outer  boundaries, we'll define the  region as a
 rectangle  large  enough   to  neglect  side  effects.   To  calculate  the
 capacitance matrix we set the voltage U = 1 V on one conductor and U = 0 on
 the another one.

      Self capacitance:   C11 = C22 = q1 / U1;
      Mutual capacitance: C12 = C21 = q2 / U1;


 where  charge  Q1 and  Q2  are  evaluated  on rectangular  contours  around
 conductor 1 and 2 away from their edges.  We chose the contours for the C11
 and C12 calculation to be rectangles  -6 < x < 0, 0 < y < 4 and 0  < x < 6,
 0 < y < 4 respectively.

 Comparison of Results

                           C11 (F/m)     C12 (F/m)

            Reference     9.23x10-11    -8.50x10-12

            QuickField    9.43 10-11    -8.57x10-12

 Reference

 A. Khebir, A. B. Kouki, and R. Mittra, "An Absorbing Boundary Condition for
 Quasi-TEM Analysis of  Microwave Transmission Lines via  the Finite Element
 Method", Journal of Electromagnetic Waves and Applications, 1990.

 See the ELEC2.PBM problem in the EXAMPLES directory.


           10.4 Heat Transfer Problems


       10.4.1 HEAT1: Slot of an Electric Machine

 Temperature field  in the stator tooth  zone of power  synchronous electric
 machine.

 Problem Type:

 The plane-parallel problem of heat transfer with convection.

 Geometry:

 Stator outer diameter  is 690 mm. Domain  is a 10 degree  segment of stator
 transverse  section. Two  armature bars  laying in  the slot  release ohmic
 loss. Cooling is provided by convection  to the axial cooling duct and both
 surfaces of the core.

 Given:
   Specific copper loss: 360000 W/m ;
   Heat conductivity of steel: 25 J/Kxm;
   Heat conductivity of copper: 380 J/Kxm;
   Heat conductivity of insulation: 0.15 J/Kxm;
   Heat conductivity of wedge: 0.25 J/Kxm;

 Inner stator surface:
   Convection coefficient: 250 W/Kxm ;
   Temperature of contacting air: 40.C.

 Outer stator surface:
   Convection coefficient: 70 W/Kxm ;
   Temperature of contacting air: 20.C.

 Cooling duct:
   Convection coefficient: 150 W/Kxm ;
   Temperature of contacting air: 40.C.

 See the HEAT1.PBM problem in the EXAMPLES directory.

       10.4.2 HEAT2: Cylinder with Temperature Dependent Conductivity

 A  very long  cylinder (infinite  length) is  maintained at  temperature Ti
 along its internal  surface and To along its external  surface. The thermal
 conductivity of the cylinder is known to vary with temperature according to
 the linear function l(T) = C0 + C1xT.

 Problem Type:

 An axisymmetric problem of nonlinear heat transfer.

 Geometry:

                To           Ti
               ----       -----
                   \           \
                    \           \
      +--------------------------\--------- +
      !////////////////////////// \ /////// !
      +------------------------------------ +
      !                                     !
      +-.--.--.--.--.--.--.--.--.--.--.--.- +
      !                                     !
      +------------------------------------ +
      !//////////////////////////////////// !
      +------------------------------------ +


 Given:
   Ri = 5 mm, Ro = 10 mm;
   Ti = 100.C, To = 0.C;
   C0 = 50 W/Kxm, C1 = 0.5 W/Kxm.

 Problem:

 Determine the temperature distribution in the cylinder.

 Solution:

 The axial length of the model is arbitrarily chosen to be 5 mm.

 Comparison of Results

  Radius         Quickfield     Theory

  0.6            79.2           79.2

  0.7            59.5           59.6

  0.8            40.2           40.2

  0.9            20.66          20.8

 See the HEAT2.PBM problem in the EXAMPLES directory.


           10.5 Stress Analysis Problems


       10.5.1 STRES1: Perforated Plate


 A thin rectangular sheet with a central hole subject to tensile loading.

 Problem Type:

 Plane problem of stress analysis (plane stress formulation).

 Geometry of the plate:
   Length: 240 mm;
   Width: 180 mm;
   Radius of central opening: 30 mm;
   Thickness: 5 mm.

 Given:
   Young's modulus E = 207000 N/mm ;
   Poisson's ratio n = 0.3.

 The uniform tensile loading (40 N/mm ) is applied to the bottom edge of the
 structure.

 Problem:

 Determine the concentration factor due to presence of the central opening.

 Solution:

 Due  to mirror  symmetry one  quarter of  the structure  is presented,  and
 internal boundaries are restrained in X and Y directions respectively.

 The concentration factor may be obtained from the loading stress (40 N/mm2)
 and the maximum computed stress (146 N/mm2) as

      k = 140.8 / 40 = 3.52.


 See the STRES1.PBM problem in the EXAMPLES directory.


           10.6 Coupled Problems


       10.6.1 COUPL1: Stress Distribution in a Long Solenoid

 A very long, thick solenoid has  an uniform distribution of circumferential
 current. The magnetic flux density and  stress distribution in the solenoid
 has to be calculated.

 Problem Type:

 An axisymmetric problem of magneto-structural coupling.

 Geometry:

      +------------------------------------ +
      !///////// Conducting cylinder ////// !
      +------------------------------------ +
      !              Air                    !
      +-.--.--.--.--.--.--.--.--.--.--.--.- +
      !                                     !
      +------------------------------------ +
      !//////////////////////////////////// !
      +------------------------------------ +


 Given:
   Dimensions Ri = 1 cm, Ro = 2 cm;
   Relative permeability of air and coil mu = 1;
   Current density j = 1x10+5 A/m2;
   Young's modulus E = 1.075x10+11 N/m2;
   Poisson's ratio nu = 0.33.

 Problem:

 Calculate the magnetic flux density and stress distribution.

 Solution:

 Since none of physical quantities varies  along z-axis, a thin slice of the
 solenoid could  be modeled. The  axial length of  the model  is arbitrarily
 chosen to be 0.2 cm.  Radial component of the flux density  is set equal to
 zero at  the outward  surface of  the solenoid.  Axial displacement  is set
 equal to zero at the side edges of the model to reflect the infinite length
 of the solenoid.

 Comparison of Results

 Magnetic flux density and circumferential stress at r = 1.3 cm:


                   Bz (T)         Stheta (N/m2)

    Reference      8.796x10-3     97.407

    QuickField     8.798x10-3     96.301

 Reference

 F.  A. Moon,  "Magneto-Solid Mechanics",  John  Wiley &  Sons, N.Y.,  1984,
 Chapter 4.

 See the  COUPL1MS.PBM and COUPL1SA.PBM  problems in the  EXAMPLES directory
 for magnetic and structural parts of this problem respectively.

 Step-by-step Description

 Let  us learn  how to  solve this  problem from  scratch. We'll  ignore the
 solution made  in COUPL1MS.PBM and COUPL1SA.PBM,  and start a  new problem,
 SOLMAG.PBM. We use a suffix "MAG" to underline that this will represent the
 magnetic part of our problem.

 To create new problem:

 1. Choose "New"  in the "Files"  menu (ALT+F, N);  the dialog  box appears,
    asking for the filename for the new problem.
 2. Change, if  needed, the  drive and directory  in the  "Directories" list
    box.
 3. Type solmag in the "Filename" box.
 4. Choose "OK".

 The extension .PBM will be added automatically.

 To select convenient length measurement units (centimeters):

 1. Choose "Length Units" in the "Options" menu. A dialog box appears.
 2. Select "Centimeters".
 3. Choose "OK".

 To assign the problem with appropriate features:

 1. Choose  "Problem"   in  the  "Edit"   menu  (ALT+E,  P).   The  "Problem
    Description" dialog box appears.
 2. Select "Magnetostatics" in the "Problem Type" drop-down list box.
 3. Select "RZ Plane", since our problem is axisymmetric.

 We'll agree  with suggested data file  name (SOLMAG.DMS), but  change model
 file name to  SOL.MOD to stress out the  fact, that the model  file will be
 shared between magnetic and stress analysis problems. If the "Library Data"
 filename box is not  empty, clear it, since we'll define  all the labels in
 the local data file (SOLMAG.DMS.)

 We  can start  editing the  model or  the data  directly from  the "Problem
 Description" dialog box. To edit the model:

 1. select the "Geometry" text box (click  anywhere in the box with a mouse,
    or press ALT+G, or press TAB until the selection reaches the box.)
 2. choose the "Open" button.

 The Model Editor starts.

 The first  step with  the new  model in  Model Editor  is to  adjust window
 dimensions  fitting  the  problem's region.  Since  none  of  the  physical
 quantities varies along  z-axis, we'll model a thin slice  of the solenoid.
 We'll choose the axial length of this slice to  be 0.2 cm, from -0.1 to 0.1
 along z-axis. The whole model fits  in the square (-1 # z # 1, -0 # r # 2.)
 To assign these values to the window limits:

 1. Choose "Keyboard" in the "Zoom" menu.
 2. Type the values (-1, 1, 0, 2) in appropriate text boxes.
 3. Press ENTER or click the dialog box background anywhere outside options.
 Now we can proceed with defining the  geometry itself. As the first step we
 create vertices,  which represent  specific points  of the  model geometry.
 We'll need six vertices with coordinates:

  z      -0.1   -0.1   -0.1   0.1    0.1    0.1
  r      0      1      2      0      1      2

 To define the vertices:

 1. Enter "Add  Vertex" mode in the  "Model" menu. The plus  sign cursor (+)
    arises in the large window indicating the point locating mode.
 2. Use DIRECTION  keys to move cursor  from point to point  and press ENTER
    where you want the vertex to be located. New vertices immediately appear
    in the window.
 3. Or, press  TAB, type coordinates, and  press ENTER for each  new vertex.
    Don't  worry about  making mistakessyou  can  remove erroneous  vertices
    later.
 4. Press ESC to return to the "Model" menu.

 If you have created excess points, you can remove them now:

 1. Choose  "Delete Vertex".  The X-shaped  cursor appears  to indicate  the
    picking  mode. Consecutively  pick  excess  vertices, which  immediately
    disappear.
 2. Press ESC to return to the "Model" menu.

 Now we can create edges connecting the vertices:

 1. Choose "Add  Edge". A dialog  box appears asking  the arc angle  for new
    edges.
 2. Press ENTER (or  click gray background of the dialog  box) to agree with
    suggested  zero value,  which  means creating  the  straight lines.  The
    picking mode (X-shaped) cursor appears in the window.
 3. Pick vertices consecutively  to create two rectangles one on  the top of
    another. Press ESC to break the chain of edges and start a new one.
 4. Press ESC to return to the "Model" menu.

 You can remove erroneous edges, using the "Delete Edge" command.

 We  are  done with  the  model's  geometry. Now  we  can  assign labels  to
 geometrical objects  to describe material properties,  sources and boundary
 conditions.

 The  bottom rectangle  represents the  air  inside the  solenoid, so  we'll
 assign the label air  to it. The top rectangle represents  the slice of the
 solenoid coil  itself, so we'll  label it coil.  To assign these  labels to
 blocks:

 1. Press ESC to close the  "Model" menu and return to the  main menu of the
    Model Editor.
 2. Choose  "Label Blocks"  in the  "Label"  menu. The  picking mode  cursor
    arises.
 3. Pick inside the bottom rectangle. The  block becomes highlighted and the
    dialog box appears asking for the label value.
 4. Type air and press ENTER. The X-shaped cursor appears again.
 5. Pick inside  the top  rectangle. The block  becomes highlighted  and the
    dialog box appears asking for the label value.
 6. Type coil and press ENTER.
 7. Press ESC to return to the "Label" menu.

 Edge  labels are  used  to define  the  boundary  conditions. For  magnetic
 problem we need to specify only a zero flux condition at outward surface of
 the solenoid, but  to make the model suitable for  the stress analysis too,
 we'll also assign labels to the side edges of the coil. To assign labels to
 edges:

 1. Choose "Label Edges". The picking mode cursor arises.
 2. Pick  the top  edge. The  edge becomes  highlighted and  the dialog  box
    appears asking for the label value.
 3. Type outer and press ENTER. The X-shaped cursor appears again.
 4. Pick one of the side edges of the top rectangle and type no axial displ.
 5. Pick another side  edge of the coil  and type no axial  displ, or double
    click the corresponding line in the "Existing Labels" list box.
 6. Press ESC to return to the "Label" menu.

 Now we have finished with assigning  labels to geometrical objects. You can
 check their values in the "Find Label" mode.

 We can proceed  with building a mesh of finite  elements. For simplicity we
 will  use a  homogeneous  mesh with  element  size  approximately equal  to
 0.025 cm. To build the mesh:

 1. Press ESC to return from the "Label" menu to the main menu.
 2. Choose "Mesh" to open the mesh building menu.
 3. Choose "Set Spacing". The X-shaped pick-mode cursor appears on a screen.
 4. Pick any vertex, a dialog box appears asking for the spacing value.
 5. Type 0.025 and press ENTER. This value is now assigned to the vertex and
    will control the mesh density in the whole region.
 6. Choose "Build Mesh". A dialog box  appears asking, which blocks you want
    to mesh.
 7. Choose "In All Blocks" "to build the meshes for all blocks at once.

 Now the model is ready. To exit the Model Editor with saving the file:

 1. Press  ESC twice  to close  the "Mesh"  menu and  quit. The  box appears
    prompting you to save the model file.
 2. Choose "Yes" to confirm the saving operation.

 You have returned to the "Problem  Description" dialog box. Let us continue
 with  defining data  for material  properties and  boundary conditions.  To
 start editing the data file:

 1. Select the "Data" text box.
 2. Choose the "Open" button. A dialog box appears warning you that the file
    SOLMAG.DMS does not exist.
 3. Choose "OK" to create new data file.

 The "Properties Description  File" dialog box appears.  It contains labels,
 which you have just  defined in the model. The label  names are marked with
 asterisks to outline the  fact, that the data for these  labels are not yet
 defined. Now we need to select the labels one-by-one and to define the data
 for them.

 To define the data for block label air:

 1. Select its name in the  list box (click it with a  mouse, or press ALT+B
    and use DOWN key to highlight the name's field.)
 2. Choose "Open" button (or press ENTER as "Open" is the default button, or
    double-click on the name's field.)
 A  dialog  box   appears,  prompting  to  enter   material  properties  and
 distributed source for block label air. To assign values:

 1. Type  1  in  any one  of  two  text  boxes  for components  of  magnetic
    permeability tensor.
 2. Choose "OK".

 To define the data for block label coil:

 1. Select its name in the  list box (click it with a  mouse, or press ALT+B
    and use DOWN key to highlight the name's field.)
 2. Choose "Open" button (or press ENTER as "Open" is the default button, or
    double-click on the name's field.)

 A  dialog  box   appears,  prompting  to  enter   material  properties  and
 distributed source for block label coil. To assign values:

 1. Type  1  in  any one  of  two  text  boxes  for components  of  magnetic
    permeability tensor.
 2. Type 1e6 in the "Current Density" text box.
 3. Choose "OK".

 Now  we'll continue  with edge  labels'  data. We'll  specify  a zero  flux
 condition (Bn = 0)  for the outer  label. To define  the data for  the edge
 label outer:

 1. Select its  name and choose  "Open". A dialog  box appears,  allowing to
    assign to edge label any of possible boundary conditions.
 2. Select the "Zero Flux Condition" box.
 3. Choose "OK".

 To define a natural boundary condition for the edge label no axial displ:

 1. Select its name and choose "Open".
 2. Choose "OK", the  dialog box by default represents  the natural boundary
    condition.

 All the data needed to solve the  magnetic problem are now defined. To exit
 from data editing mode:

 1. Choose "Close" button in the "Properties Description File" dialog box. A
    dialog box appears, prompting you to save changes to data file.
 2. Choose  "Yes"  to   save  changes.  Now  you  return   to  the  "Problem
    Description" dialog box again.
 3. Choose "OK".

 At last,  we can solve the  problem and analyze  the magnetic field.  To do
 this in one step:

 1. Choose "Analyze" from the "Results" menu. You will be suggested to solve
    the problem first, as the results are absent.
 2. Choose "OK".
 3. Choose "Values" to get the field  values in a particular point. The plus
    sign cursor (+) arises in the large window indicating the point locating
    mode.
 4. Use DIRECTION  keys to move cursor  from point to point  and press ENTER
    where you want to see the field values. Or, press TAB, type coordinates,
    and press ENTER for each new point.
 5. Press ESC  to exit the "Values"  mode and another  ESC to return  to the
    main QuickField menu.

 Once  we got  the results  for the  magnetic part  of our  problem, we  can
 proceed with  the stress analysis. To  perform the stress analysis  we will
 need a new problem description.

 To create new problem description:

 1. Choose "New"  in the "Files"  menu (ALT+F, N);  the dialog  box appears,
    asking for the filename for the new problem.
 2. Type solstr in the "Filename" box.
 3. Choose "OK".

 The extension .PBM will be added automatically.

 To assign the problem with the appropriate features:

 1. Choose    "Problem"   in    the   "Edit"    menu    (ALT+E,   P).    The
    "Problem Description" dialog box appears.
 2. Select "Stress Analysis" in the "Problem Type" drop-down list box.

 We'll  agree with  suggested data  file name  (SOLSTR.DMS), but  change the
 model file name to the existing SOL.MOD.

 To specify the problem coupling:

 1. Choose Imported Data  button in the Problem Description  dialog box. The
    Data Imported from Other Problems dialog box appears.
 2. Choose "Magnetic forces" option in "Data Type" drop-down list box.
 3. Choose "Browse" button, and double-click a SOLMAG.PBM file.
 4. Choose "Add" button, a new line will appear in "Data Sources" list box.
 5. Choose "Close" button to return to the "Problem Description" dialog box.

 Next our step is to define  material properties and boundary conditions for
 the structural problem. To start editing the data file:

 1. Select the "Data" text box.
 2. Choose the "Open" button. A dialog box appears warning you that the file
    SOLSTR.DMS does not exist.
 3. Choose "OK" to create new data file.

 The "Properties Description  File" dialog box appears.  It contains labels,
 which you assigned to the model.  The label names are marked with asterisks
 to outline the  fact, that the data  for these labels are  not yet defined.
 Now we  need to select  the labels  one-by-one and to  define the  data for
 them.

 To define data for the block label air:

 1. Select its name in the  list box (click it with a  mouse, or press ALT+B
    and use DOWN key to highlight the name's field.)
 2. Choose "Open" button (or press ENTER as "Open" is the default button, or
    double-click on the name's field.)

 A  dialog  box   appears,  prompting  to  enter   material  properties  and
 distributed source  for block label  air. The block  labeled air has  to be
 excluded  from stress  calculation. Since  the text  boxes for  the Young's
 moduli already contain word None,  the all we need to do  is to choose "OK"
 button.

 To define data for the block label coil:

 1. Select its name in the  list box (click it with a  mouse, or press ALT+B
    and use DOWN key to highlight the name's field.)
 2. Choose "Open" button (or press ENTER as "Open" is the default button, or
    double-click on the name's field.)

 A  dialog box  appears, prompting  to enter  material properties  for block
 label coil. To assign values:

 1. Type 1.075e11 in any one of three text boxes for Young's moduli.
 2. Type 0.33 in any one of three text boxes for Poisson's ratios.
 3. Choose "OK".

 Now we'll continue with edge labels' data.  To define the data for the edge
 label no axial displ:

 1. Select its  name and choose  "Open". A dialog  box appears,  allowing to
    assign to edge label any of possible boundary conditions.
 2. Check  the "Z"  check  box inside  "Fixed  Displacement" rectangle.  The
    displacement is zero by default.
 3. Choose "OK".

 To define the natural boundary condition for the edge label outer:

 1. Select its name and choose "Open".
 2. Choose "OK", the  dialog box by default represents  the natural boundary
    condition.

 All the  data needed to  solve the structural  problem are now  defined. To
 exit from data editing mode:

 1. Choose "Close" button in the "Properties Description File" dialog box. A
    dialog box appears, prompting you to save changes to data file.
 2. Choose  "Yes"  to   save  changes.  Now  you  return   to  the  "Problem
    Description" dialog box again.
 3. Choose "OK".

 Now we can solve the  problem and analyze stresses in the  coil. To do this
 in one step:

 1. Choose "Analyze" from the "Results" menu. You will be suggested to solve
    the problem first, as the results are absent.
 2. Choose "OK".
 3. Choose "Values" to get the field  values in a particular point. The plus
    sign cursor (+) arises in the large window indicating the point locating
    mode.
 4. Use DIRECTION  keys to move cursor  from point to point  and press ENTER
    where you want to see the stress value.
 5. Or, press TAB, type coordinates, and press ENTER for each new point.
 6. Press ESC  to exit the "Values"  mode and another  ESC to return  to the
    main QuickField menu.

       10.6.2 COUPL2: Cylinder Subject to Temperature and Pressure

 A very long, thick-walled cylinder is subjected to an internal pressure and
 a  steady state  temperature distribution  with Ti  and To  temperatures at
 inner and outer surfaces respectively. Calculate the stress distribution in
 the cylinder.

 Problem Type:

 An axisymmetric problem of thermal-structural coupling.

 Geometry:

                To           Ti
               ----       -----
                   \           \
                    \           \
      +--------------------------\--------- +
      !////////////////////////// \ /////// !
      +------------------------------------ +
      !                                     !
      +-.--.--.--.--.--.--.--.--.--.--.--.- +
      !                                     !
      +------------------------------------ +
      !//////////////////////////////////// !
      +------------------------------------ +


 Given:
   Dimensions Ri = 1 cm, Ro = 2 cm;
   Inner surface temperature Ti = 100.C;
   Outer surface temperature To = 0.C;
   Coefficient of thermal expansion alpha = 1x10-6 1/K;
   Internal pressure P = 1x10+6 N/m2;
   Young's modulus E = 3x10+11 N/m2;
   Poisson's ratio nu = 0.3.

 Problem:

 Calculate the stress distribution.

 Solution:

 Since none of physical quantities varies  along z-axis, a thin slice of the
 cylinder  can be  modeled. The  axial length  of the  model is  arbitrarily
 chosen to be  0.2 cm. Axial displacement is  set equal to zero  at the side
 edges of the model to reflect the infinite length of the cylinder.

 Comparison of Results

 Radial and circumferential stress at r = 1.2875 cm:


                   Sr (N/m2)      Stheta (N/m2)

    Theory         -3.9834x10+6   -5.9247x10+6

    Students'      -3.827x10+6    -5.882x10+6
    QuickField

    Professional   -3.959x10+6    -5.924x10+6
    QuickField

 Reference

 S. P. Timoshenko and Goodier, "Theory of Elasticity", McGraw-Hill Book Co.,
 N.Y., 1961, pp. 448-449.

 See the  COUPL2HT.PBM and COUPL2SA.PBM  problems in the  EXAMPLES directory
 for the corresponding heat transfer and structural parts of this problem.

       10.6.3 COUPL3: Temperature Distribution in an Electric Wire

 Calculate the temperature distribution in a long current carrying wire.

 Problem Type:

 An axisymmetric problem of electro-thermal coupling.

 Geometry:

      +------------------------------------ +
      +//////////////////////////////////// +
      +////////------> Current //////////// +
      +//////////////////////////////////// +
      +------------------------------------ +


 Given:
   Wire diameter            d = 10 mm;
   Resistance               R = 3x10-4 Ohm/m;
   Electric current         I = 1000 A;
   Thermal conductivity     lambda = 20 W/Kxm;
   Convection coefficient   alpha = 800 W/Kxm2;
   Ambient temperature      To = 20.C.

 Problem:

 Calculate the temperature distribution in the wire.

 Solution:

 We arbitrary chose  a 10 mm piece of  wire to be represented  by the model.
 For data  input we need  the wire radius  r = 5 mm, and the  resistivity of
 material:

      rho = (PI * d*d * R) / 4 = 2.356e-8 Ohm*m,

 and voltage drop for our 10 mm piece of the wire:

      DU = I*R*l = 3e-3 (V).

 For  the current  flow problem  we specify  two different  voltages at  two
 sections of the wire, and a zero current condition at its surface. For heat
 transfer problem  we specify zero  flux conditions at  the sections  of the
 wire and a convection boundary condition at its surface.

 Comparison of Results

 Center line temperature:

                 T
                 (centigrade)

    Theory       33.13

    QuickField   32.83

 Reference

 W. Rohsenow and H. Y. Choi,  "Heat, Mass, and Momentum Transfer", Prentice-
 Hall, N.J., 1963.

 See the  COUPL3CF.PBM and COUPL3HT.PBM  problems in the  EXAMPLES directory
 for the corresponding current flow and heat transfer parts of this problem.

 Center line temperature:

                 T
                 (centigrade)

    Theory       33.13

    QuickField   32.83

