A DISTORTION METRIC FOR ISOPARAMETRIC FINITE ELEMENTS

Abstract

Distorted isoparametric elements are frequently encountered in finite element analyses. It is well known that element distortion affects not only the interpolation functions in the physical (x,y,z) domain and convergence rates but can also reduce the accuracy of an analysis. A one-to-one relationship between accuracy and element distortion does not exist because the accuracy of a Finite Element Analysis (FEA) depends on the problem, the governing differential equations and the mesh. It is generally accepted, however, that element distortion should be minimized, except in rare circumstances such as fracture mechanics where it is carefully controlled. A parameter which measures distortion would be useful in assessing the possible performance of distorted elements or where remeshing is required. Knowing when and where to remesh because of excessive distortion is critical in automatic mesh generation or rezoning programs. A measure of element distortion that could be computed a priori would be useful in automatic mesh generation and rezoning programs. The basic criteria which must be met by useful measures of element distortion are described. A distortion metric based on an invarient of the isoparametric transformation is proposed. The proposed metric can be applied to two or three-dimensional elements. Values of the distortion metric obtained for typical distorted two-dimensional elements, as well as examples of how solution accuracy degrades with increased distortion are presented.