A new Mathematica package, named SMS (Symbolic Mechanics System), which represents a pragmatic approach to the problem of combining different techniques, will be introduced. A new approach is called Simultaneous Stochastic Simplification of numerical code. It combines a general computer algebra system Mathematica with an automatic differentiation technique and theorem proving by examples in order to automatically generate the finite element code. To alleviate the problem of growth of expressions and redundant calculations, simultaneous simplification of symbolic expressions is used. It is based on a stochastic evaluation of the formulas instead on a conventional pattern matching technique.
The new package was system has already been successfully used for the development of the new 2D and 3D elements based on a modified enhanced strain method. Among the other problems, the well known hour-glassing problem of enhanced strain elements in a presence of large deformations was successfully solved with the help of the new system. It was also applied to develop a 'spline' finite strip element for nonlinear analysis of the prismatic shell structures with the non uniform cross section.
