A New Linear Stress Hybrid Quadrilateral Finite Element And Its Three-dimensional Extension

Based on a modified Hellinger-Reissner principle , a 4-node hybrid stress quadrilateral element is presented by using the Wilson's incompatible displacements and a 9-parameter complete linear stress mode. Theoretical analysis shows that this element is equivalent to the classical 5-parameter hybrid stress element (P-S) proposed by Pian and Sumihara in 1984. Convergence for this method is analyzed. By following the same idea, the element construction is extended to the three-dimensional case, where the three-dimensional Wilson's incompatible displacements and two kinds of 27-parameter stress modes are used. Numerical experiments for two- and three-dimensional cases are also done to confirm the effectiveness of the method.