On optimization approaches of hybrid stress elements

Abstract

A rational energy constraint to be used as the optimization condition (OPC) for hybrid finite element is presented. Based on OPC, the optimal stress pattern of the element is established in a general formulation. In this approach, the improvement of the element performance is carry out by a pretreatment of the initially assumed stress field. As an alternative way for the optimization of hybrid elements, the penalty-equilibrating approach is also suggested in the paper in which the equilibrium equation is enforced to the individual elements directly. Finally, a discussion on the stress distribution in an element is made. Some requirements on the rational σ-distribution are suggested. All of the points mentioned have been verified by means of some innovative hybrid elements in 2-D, 3-D and axisymmetric problems. © 1995.