FINITE-ELEMENT STRESS EXTRACTION BY THE COMPLEMENTARY ENERGY PRINCIPLE

This paper presents a new method for accurate pointwise stress extract ion from finite element solutions, applied to two-dimensional linear e lastostatic problems having bounded value stresses. The method, denote d by SEC (Stress Extraction by Complementary principle), is based on t he complementary energy principle applied over a local domain in the p ost-processing phase. Detailed formulation of the SEC method is provid ed, and numerical experiments with the h- and p-versions of the finite element method are presented for a family of exact solutions characte rized by varying degree of smoothness. It is shown that on the boundar ies of the domain, as well as in the interior, accurate pointwise stre sses are obtained, and the relative error in the pointwise stresses co nverges with a rate which is as fast as the relative error measured in energy norm or faster. Importantly, the SEC method in conjunction wit h the p-version of the finite element method is virtually independent of the Poisson's ratio,(1) and is equally applicable to nearly incompr essible materials. (C) 1997 by John Wiley & Sons, Ltd.