Generalized Finite Element Evaluation Procedure

Abstract

A rational procedure for evaluating the performance of two and three dimensional finite elements is developed. This procedure compares the strain energy content and the strain distribution of the finite element model to that of the continuum region it represents for well‐defined strain states. The use of Taylor series expansions which relate the displacements, rotations, and strains through strain gradient terms allows the strain energies and the pointwise strains of the finite element model and the continuum to be directly compared. The evaluation procedure is demonstrated by applying it to a six‐node isoparametric element undergoing a series of progressive initial distortions. From these results, a simple algorithm to predict the maximum strain energy error as a function of initial geometry is developed for incorporation into finite element codes at the grid generation level.