## USING MAPLE AND MATHEMATICA TO SOLVE ELASTICITY PROBLEMS

The algebraic manipulations involved in solving problems in elasticity are relatively routine, but they can become lengthy and complicated, particularly for three-dimensional problems. There are therefore significant advantages in using a symbolic programming language such as Maple or Mathematica. Before such programs were available, the algebraic complexity of manual calculations often made it quicker to use a finite element formulation, even when it was clear that an analytical solution could in principle be obtained. Apart from the undoubted saving in time, Maple or Mathematica also make it easy to plot stress distributions and perform parametric studies to determine optimum designs for components. From the engineering perspective, this leads to a significantly greater insight into the nature of the subject.

Using these languages efficiently necessitates a somewhat different approach from that used in conventional algebraic solutions. Anyone with more than a passing exposure to computer programs will know that it is almost always quicker to try a wide range of possible options, rather than trying to construct a logical series of steps leading to the required solution. This trial and error process also works well in the computer solution of elasticity problems. For example, if you are not quite sure which stress function to use in the problem, the easiest way to find out is to use your best guess, run the calculation and see what stresses are obtained. Often, the output from this run will make it clear that minor modifications or additional terms are required, but this is easily done. Remember that it is extremely easy and quick to make a small change in the problem formulation and then re-run the program. By contrast, in a conventional algebraic solution, it is essential to be very careful in the early stages because repeating a calculation with even a minor change in the initial formulation is very time consuming.

The best way to learn how to use these programs is also by trial and error. Don't waste time reading a compendious instruction manual or following a tutorial, since these will tell you how to do numerous things that you probably will never need. In the file S522, I provide the source code for the two-dimensional problem treated in Section 5.2.2. This file has sufficient embedded explanation to show what is being calculated and you can easily copy the files and make minor changes to gain experience in the use of the method. An explanation of the commands you will need most often in the solution of elasticity problems is provided in the files Programming in Maple and Programming in Mathematica, respectively.

I also provide electronic versions of the Tables in Chapters 22 and 23, alogorithms for converting complex potentials to real stress functions and vice versa, , and the recurrence relations for generating spherical harmonics.

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