An Assumed Strain Mixed Formulation for Nonlinear Shells

Abstract

A mixed finite element formulation with stabilization matrix is presented for geometrically nonlinear thin shells. This formulation is based on the degenerate solid shell element concept and the Hellinger-Reissner principle with independent strain field. The independent strain field is divided into a lower order part and a higher order part. Using the equivalence between displacement formulation and mixed formulation, the lower order part is replaced by the displacement-dependent strain at reduced integration points. The higher order independent strain terms are selected to stabilize the spurious kinematic modes which exist in the element stiffness matrix obtained by using reduced integration. One set of the higher order assumed independent strain components is presented for a four-node degenerate solid shell element. For a nine-node degenerate solid shell element, two versions of the higher order assumed independent strain field are proposed. Numerical results demonstrate that the nine-node shell element based on the present formulation produces very accurate and reliable solutions even for very thin shells undergoing large rotations.