Composite laminated solid shell element for geometrically nonlinear analysis

Abstract

Starting from defining generalized stress, this paper presents a modified stiffness matrix method to overcome the thickness locking of solid shell elements and guarantee the continuous distribution of the transverse normal stress of composite laminate shell structures. By splitting the stress into lower order term and higher order term, a nonlinear variation principle is developed and a 9-node solid shell element with 6 DOF per node is derived for the geometrically nonlinear analysis of composite laminated shells. The higher order assumed stress modes are judiciously selected to vanish at the sampling points of the second order quadrature and their energy products with the displacement-derived covariant strain can be programmed without resorting to numerical integration. The accuracy of the present element is virtually identical to that of the uniformly reduced integration (URI) element yet with a little additional computational cost for the stabilization matrix. The stabilization matrix is of prime importance as the global tangential stiffness matrices resulting from the URI elements often become singular after a few iterations.