An implementation of mixed enhanced finite elements with strains assumed in Cartesian and natural element coordinates using sparse (B)over-bar-matrices

The use of enhanced strains leads to an improved performance of low order f inite elements. A modified Hu-Washizu variational formulation with orthogon al stress and strain functions is considered The use of orthogonal function s leads to a formulation with (B) over bar -strain matrices which avoids nu merical inversion of matrices. Depending on the choice of the stress and st rain functions in Cartesian or natural element coordinates one can recover, for example, the hybrid stress element P-S of Pian-Sumihara or the Trefftz -type element QE2 of Piltner and Taylor With the mixed formulation discusse d in this paper a simple extension of the high precision elements P-S and Q E2 to general non-linear problems is possible, since the final computer imp lementation of the mixed element is very similar to the implementation of a displacement element Instead of sparse B-matrices, sparse (B) over bar -ma trices are used and the typical matrix inversions of hybrid and mixed metho ds can be avoided. The two most efficient four-node (B) over bar -elements for plane strain and plane stress in this study are denoted (B) over bar (x , y)-QE4 and (B) over bar(xi, eta)-QE4.