New stress assumption for hybrid stress elements and refined four-node plane and eight-node brick elements

Abstract

A new stress assumption for hybrid stress elements is presented. Generalized incompatible modes are proposed and incorporated into the constraint equations for assumed stresses. The physical meaning of the resulting constraint equations is discussed. The present stress assumption, which can consider the mesh distortion more rigorously, is based on the physical interpretation of the role of the generalized incompatible modes and substantiated with simple mesh distortion measures defined in this paper. The stress assumption is adapted to the previous four-node hybrid stress element, 5β-I and the eight-node hybrid stress brick element, 18β, which results in a new four-node plane element, M5β and an new eight-node brick element, M18β. Numerical results show that the refined elements are noticeable in low sensitivity to mesh distortion and in high-accuracy of stresses. © 1997 John Wiley & Sons, Ltd.