New strategy for assumed stresses for 4‐node hybrid stress membrane element

An oblique (skew) co-ordinate system defined at the origin of the isoparametric co-ordinates is introduced as the reference co-ordinate system for assumed stresses in the formulation of a 4-node hybrid membrane element. The initially uncoupled stresses in these reference co-ordinates can be constrained to satisfy the equilibrium conditions pointwise by using the procedure of Pian and Wu7, when suitable incompatible displacements are introduced. Such strategy allows the element stiffness to be formulated by using either the Hellinger-Reissner or the complementary energy functional. Numerical results show that the performances of three elements, constructed by using different sets of incompatible displacements in this paper, are practically identical and are all of slightly higher accuracy than that of the Pian-Sumihara element6.