Deformation of Solids

Professor: Donald S. Stone
Office :Room M161 Materials Science And Engineering Building
Phone :(608) 262-8791

Student Asistant: Sadi Kose
Office :Room 243 Materials Science And Engineering Building
Phone :(608) 232-9873
Office Hours:




The FE method (finite element method) was developed more by engineers using physical insight than by mathematicians using abstract methods. It was first applied to problems of stress analysis, and has since been applied to other problems of continua. In all applications the analyst seeks to calculate a field quantity: in stress analysis it is the displacement field or the stress field; in thermal analysis it is the temperature field or the heat flux; in fluid flow it is the stream function or the velocity potential function; and so on. Results of greatest interest are usually peak values of either the field quantity or its gradients. The FE method is a way of getting a numerical solution to a specific problem. An FE analysis does not produce a formula as a solution, nor does it solve a class of problems. Also, the solution is approximate unless the problem is so simple that a convenient exact formula is already available.

An unsophisticated description of the FE method is that it involves cutting a structure into several elements (pieces of the structure), describing the behavior of each element in a simple way, then connecting elements together again . This process results in a set of simultaneous algebraic equations. In stress analysis these equations are equilibrium equations of the connection points. There may be several hundred or several thousand such equations, which means that computer implementation is mandatory. A more sophisticated description of the FE method regards it as piecewise polynomial interpolation. That is, over an element, a field quantity such as displacement is interpolated from values of the field quantity at the connection points. By connecting elements together, the field quantity becomes interpolated over the entire structure in piecewise fashion, by as many polynomial expressions as there are elements. The "best" values of the field quantity at the connection points are those that minimize some function such as total energy. The minimization process generates a set of simultaneous algebraic equations for values of the field quantity at the connection points.

The power of the FE method resides in its versatility. The object analyzed may have arbitrary shape, arbitrary supports, and arbitrary loads. Such generality does not exist in classical analytical methods. For example, temperature-induced stresses are difficult to analyze with classical methods, even when the structure geometry and the temperature field are both simple. The FE method treats thermal stresses as easily as stresses induced by mechanical load, and the temperature distribution itself can be calculated by FE.

Preprocessing and postprocessing.

The theory of FE includes matrix manipulations, numerical integration, equation solving, and other procedures carried out automatically by commercial software. The user may see only hints of these procedures as the software processes data. The user deals mainly with preprocessing (describing loads, supports, materials, and generating the FE mesh) and postprocessing (sorting output, listing, and plotting of results). In large software packages the analysis portion is accompanied by preprocessors and postprocessors. There exist stand-alone pre- and postprocessors that can communicate with various large programs. The specific procedures of "pre" and "post" are different in different programs. Learning to use them is often a matter of trial, assisted by introductory notes, manuals, and on-line documentation that accompanies the software. Also, vendors of large-scale programs offer various training courses. Fluency with pre- and postprocessors is helpful to the user but is unrelated to the accuracy of FE results produced. This book is emphasizes how to use the FE method properly, not how to use pre- and postprocessors.

Finite Element and the typical user.

The typical user of FE asks what kinds of elements should be used, and how many of them? Where should the mesh be fine and where may it be coarse? Can the model be simplified? How much of the physical detail must be represented? Is the important behavior static, dynamic, nonlinear, or what? How accurate will the answers be, and how can they be checked? One need not understand the mathematics of FE to answer these questions. However, a competent user must understand how elements behave in order to choose suitable kinds, sizes, and shapes of elements, and to guard against misinterpretations and unrealistically high expectations. A user must also realize that FE is a way of implementing a mathematical theory of physical behavior. Accordingly, the assumptions and limitations of the theory must not be violated by what we ask the software to do. Even with all this preparation it is easy to make mistakes in describing the problem to the computer program. Therefore it is also essential that a competent user have a good physical grasp of the problem so that errors in computed results can be detected and a judgment made as to whether the results are to be trusted or not. An analyst unable to do even a crude pencil-and-paper analysis of the problem probably does not know enough about it to attempt a solution by FE!

A short history of Finite Element.

In a 1943 paper, the mathematician Courant described a piecewise polynomial solution for the torsion problem. His work was not noticed by engineers and the procedure was impractical at the time due to the lack of digital computers. In the 1950s, work in the aircraft industry introduced FE to practicing engineers. A classic paper described FE work that was prompted by a need to analyze delta wings, which are too short for beam theory to be reliable.The name "finite element" was coined in 1960. By 1963 the mathematical validity of FE was recognized and the method was expanded from its structural beginnings to include heat transfer, groundwater flow, magnetic fields, and other areas. Large general-purpose FE software began to appear in the 1970s. By the late 1980s the software was available on microcomputers, complete with color graphics and pre- and post-processors. By the mid 1990s roughly 40,000 papers and books about FE and its applications had been published.

Entering ANSYS

Launching ANSYS requires several steps. To save time, you can create a file called START.ANS, which will be read by ANSYS at every start-up. (You can use any editor to create this file. If you are not experienced UNIX user we recommend the editor called vuepad which is extremely easy and user-friendly compared to vi editor. To open vuepad editor, either type vuepad or click on the blue icon which is located on the lower left corner of deshboard. )

Coming back to the START.ANS file. You need to type the following three lines.

Note that you can use X11 in place of 3D, however for a better graphical results we recommend that you use 3D. You don't have to concern yourself with the functionality of the above lines.

Now, you can start ANSYS by simple typing ansys at the prompt (provided you have START.ANS and that it works properly). However we recommend that you specify your Jobname at the start-up.

To do that you will have to use -j flag which stands for Jobname in the following way:

ansys -j any_name

At times you might be kicked out of ANSYS right away. This is because ANSYS is a spoiled program; if it can't find a comfortable environment, it refuses to operate.:) What you can do is to force it to work by using -m flag which stands for memory
ansys -j any-name -m some_number
some_number is between 17 and 60 (these numbers are apprx.)


ANSYS works with multiple files. For a typical analysis ANSYS creates six files. Names of those files are of the form Jobname.Ext. You can specify Jobname at start-up. If you don't specify a Jobename, default which is FILE (or file) will be used. The latter is not recommended. The reason is that every time when you start ANSYS most of your existing ANSYS files that use default name will be replaced with new files.

Tips on File Management in ANSYS

Keep the following points in mind while dealing with ANSYS:

ANSYS Tutorial (for Release 5.3)

There is a very useful booklet called ANSYS Workbook for Release 5.3 which is available at CAE and can be checked out. It contains various step-by-step ANSYS examples. We recommend that you go through at least couple examples therein to become familiar with ANSYS.

More about ANSYS

For more information on ANSYS see ANSYS Operations Guide for Release 5.3 available at CAE. Also on-line available are ANSYS Users Manuals and Verification Manual which contains over 200 sample problems worked out with ANSYS.


1. I am getting the following error message, when I try to solve.

DOF (e.g. Displacements)limit exceeded at time 1 (loadstep 1 substep 1 equilibrium iteration 1) Maximum value = "some number" Limit = 1000000

Try these:

  1. Make sure that your boundary conditions are properly defined
  2. Make sure that your element boundaries are continuous across area boundaries (i.e. when you plot elements the "gridlines" should be continuous between adjacent areas.
  3. You need to merge items. This ensures that overlapped items (i.e. nodes ) are merged so that your model become continuous. To do this :
    • PreProcessor
    • Numbering Ctrls
    • Merge Items
    • Choose "ALL" from the pull-down menu
    • OK

2. Can I transfer a model created using CAD software (i.e, Pro/E , Auto CAD and the like) into ANSYS?

Yes you can import your CAD model ( Solid Model) into ANSYS provided the CAD software can save the geometry in IGES format ( I know AutoCAD and Pro/E does). Ones you have the IGES file, you can read it into ANSYS.(File -> Import)

3. How can I print a graphic display in ANSYS?

Once you have the plot that you want to print out on the ANSYS Graphics window, go to PlotCtrls->Hard Copy under ANSYS/University Utility Menu. Thereafter a window will be opened:

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WebMaster: Sadi Kose
Last Update: 2/9/1997