An alternative version of the Pian-Sumihara element with a simple extension to non-linear problems

Abstract

The stiffness matrix for the Pian–Sumihara element can be obtainedin a different way than originally presented in Pian and Sumihara(1984). Instead of getting the element matrix from a hybrid stressformulation with five stress terms one can use a modified Hu–Washizuformulation using nine stress and nine strain terms as well as fourenhanced strain terms. Using orthogonal stress and strain functionsit becomes possible to obtain the stiffness matrix via sparse B¯-matrices so that numerical matrix inversions can be omitted. Theadvantage of using the mixed variational formulation with displacements,stresses, strains, and enhanced strains is that the extension tonon-linear problems is easily achieved since the final computer implementationis very similar to an implementation of a displacement element.