Finite element stress extraction by the complementary energy principle

This paper presents a new method for accurate pointwise stress extraction from finite element solutions, applied to two-dimensional linear elastostatic problems having bounded value stresses. The method, denoted by SEC (Stress Extraction by Complementary principle), is based on the complementary energy principle applied over a local domain in the post-processing phase. Detailed formulation of the SEC method is provided, and numerical experiments with the h- and p-versions of the finite element method are presented for a family of exact solutions characterized by varying degree of smoothness. It is shown that on the boundaries of the domain, as well as in the interior, accurate pointwise stresses are obtained, and the relative error in the pointwise stresses converges with a rate which is as fast as the relative error measured in energy norm or faster. Importantly, the SEC method in conjunction with the p-version of the finite element method is virtually independent of the Poisson's ratio,¹ and is equally applicable to nearly incompressible materials.