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

The stiffness matrix for the Pian-Sumihara element can be obtained in a dif ferent way than originally presented in plan and Sumihara (1984). Instead o f getting the element matrix from a hybrid stress formulation with five str ess terms one can use a modified Hu-Washizu formulation using nine stress a nd nine strain terms as well as four enhanced strain terms. Using orthogona l stress and strain functions it becomes possible to obtain the stiffness m atrix via sparse (B) over bar -matrices nn that numerical matrix inversions can be omitted. The advantage of using the mixed variational formulation w ith displacements, stresses, strains, and enhanced strains is that the exte nsion to nonlinear problems is easily achieved since the final computer imp lementation is very similar to an implementation of a displacement element.