The Mechanical APDL solutions in this document are compared with solutions from textbooks or technical publications. In some cases noted below, the target (theoretical) answers reported in this document may differ from those shown in the reference. Any problems having significantly different recalculated values are noted as such. Differences between Mechanical APDL results and target values are reported as ratios (Mechanical APDL:Target) except in cases where the target solution is zero or non-numerical in nature.

Some textbook solutions are based on slide rule accuracy. For example, the reference for problem number 3 reports the stress to be 10,200 psi. Using a hand calculator to recalculate the results shows the result to be 10,152.258 psi. The Mechanical APDL calculation yields 10,152 psi. In problems like this, an appropriate number of significant digits are used in comparing solutions.

Some references have incorrect answers printed and some have incorrect equations. Reference's answers presented without regard to sign are reported with the appropriate sign. Theoretical derivations not having a specific numerical example in the text are solved for a representative numerical example and both the theoretical and Mechanical APDL results are given. In cases where only the results but not the input data are given in the theoretical reference (for example, where only tabular or graphical results are presented), the input data are back-calculated from a convenient solution point. Graphical solution results are reported to an appropriate accuracy.

Different computers and different operating systems may yield slightly different results for some of the test cases in this document, since numerical precision varies from machine to machine. Solutions which are nonlinear, iterative, or have convergence options activated, are among the most likely to exhibit machine-dependent numerical differences. Because of this, an effort has been made to report an appropriate and consistent number of significant digits in both the target and the Mechanical APDL solution. If you run these test cases on your own computer hardware, be advised that a Mechanical APDL result reported in this document as 0.01234 may very well show up in your printout as 0.012335271.

It should be noted that only those items corresponding to the given theoretical solution values are reported for each problem. In most cases the same finite element solution also contains a considerable amount of other useful numerical solution data.