An incremental complementary energy method of nonlinear stress analysis

Abstract

A stress analysis capability to treat orthotropic physically nonlinear materials that behave differently in tension and compression is presented. The analysis is an energy search method based on an incremental complementary energy formulation. Load incrementation is used. Stress solutions are obtained by formulating and minimizing the incremental complementary energy associated with each load increment. Material behavior is conservative during each load increment. Structures are idealized as an assemblage of discrete elements. An Airy stress function is approximated by a sum of unknown coefficients times interpolation polynomials for each element. Equilibrium between adjacent elements is satisfied identically by imposing equality constraints on the unknown coefficients. Applications to structural elements loaded in plane stress or plane strain are presented. Correlations with some experimental results available in the literature are made.