Finite element formulation by parametrized hybrid variational principles: Variable stiffness and removal of locking

Abstract

In this paper, a new one-parameter hybrid functional is obtained as a special case of Felippa and Militello's parametrized variational principles. The functional contains stress, strain and compatible displacement as the primary fields. It will be proved that some of the existing variable stiffness formulations fall into the framework of the new functional. Novel applications of the functional are also suggested, mainly for removal of locking. Solid element, destabilized 8-node and stabilized 9-plate elements are designed. All of them can handle thin plate/shell analysis. In particular, a prominent method is devised for constructing stabilization vectors. The vectors are explicit linear functions of the nodal coordinates and can be implemented without resorting to Gram-Schmidt orthogonalization or numerical integration. Results of the new elements in popular benchmark tests are encouraging.