On numerically accurate finite element

Abstract

A general criterion for testing a mesh with topologically similar repeat units is given, and the analysis shows that only a few conventional element types and arrangements are, or can be made suitable for computations in the fully plastic range. Further, a new variational principle, which can easily and simply be incorporated into an existing finite element program, is presented. This allows accurate computations to be made even for element designs that would not normally be suitable. Numerical results are given for three plane strain problems, namely pure bending of a beam, a thick-walled tube under pressure, and a deep double edge cracked tensile specimen. The effects of various element designs and of the new variational procedure are illustrated. Elastic-plastic computation at finite strain are discussed.