A computer algebra based finite element development environment

A finite element development environment based on the technical computing p rogram Mathematica is described. The environment is used to automatically p rogram standard element formulations and develop new elements with novel fe atures. Source code can also be exported in a format compatible with commer cial finite element program user-element facilities. The development enviro nment is demonstrated for three mixed Petrov-Galerkin plane stress elements : a standard formulation, an advanced formulation incorporating rotational degrees of freedom and a standard formulation in which the stiffness matrix is integrated analytically, before being exported as ANSYS user elements. The results presented illustrate the accuracy of the standard mixed formula tion element and the enhancement of performance when rotational degrees of freedom are added. Further, the analytically integrated element shows that computational requirements can be greatly reduced when analytical integrati on schemes are used in the formation. (C) 2001 Elsevier Science Ltd. All ri ghts reserved.