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\nin a different way than originally presented in Pian and Sumihara\n(1984). Instead of getting the element matrix from a hybrid stress\nformulation with five stress terms one can use a modified Hu–Washizu\nformulation using nine stress and nine strain terms as well as four\nenhanced strain terms. Using orthogonal stress and strain functions\nit becomes possible to obtain the stiffness matrix via sparse B¯\n-matrices so that numerical matrix inversions can be omitted. The\nadvantage of using the mixed variational formulation with displacements,\nstresses, strains, and enhanced strains is that the extension to\nnon-linear problems is easily achieved since the final computer implementation\nis very similar to an implementation of a displacement element.