A computer algebra based finite element development environment

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

A finite element development environment based on the technical computing program Mathematica is described. The environment is used to automatically program standard element formulations and develop new elements with novel features. Source code can also be exported in a format compatible with commercial finite element program user-element facilities. The development environment 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 formulation 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 integration schemes are used in the formation.
Original languageEnglish
Pages (from-to)913-925
Number of pages12
JournalAdvances in Engineering Software
Volume32
Issue number12
DOIs
Publication statusPublished - Dec 2001

Keywords

  • computer algebra
  • finite element method
  • Petrov-Galerkin plane stress elements

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