A rational formulation of isoparametric hybrid stress elements for three-dimensional stress analysis

Abstract

Based on the recently proposed method of energy orthogonality enforcement between the stresses and derived strains from the incompatible displacements, three 8-noded hexahedral hybrid stress elements are derived. Stress interpolants for the elements are expressed in terms of uncoupled functions of the natural coordinates, thus Pian's efficient scheme for inverting the complementary energy matrix is applicable. The choice of energy orthoganality instead of equilibrium as a means to eliminate the parasitic stress components not only resolved the commonly encountered problem of rank deficiency but also presents a more rational approach. Numerical examples are given and the achieved accuracy is satisfactory. All the elements are capable of handling nearly incompressible materials. An optical choice is made by further examining the elements' perfommances in a thin plate problem.