A finite element formulation with stabilization matrix for geometrically non-linear shells

An assumed strain finite element formulation with a stabilization matrix is developed for analysis of geometrically nonlinear problems of isotropic and laminated composite shells. The present formulation utilizes the degenerate solid shell concept and assumes an independent strain as well as displacement. The assumed independent strain field is divided into a lower order part and a higher order part. Subsequently, the lower order part is set equal to the displacement-dependent strain evaluated at the lower order integration points and the remaining higher order part leads to a stabilization matrix. The strains and the determinant of the Jacobian matrix are assumed to vary linearly in the thickness direction. This assumption allows analytical integration through thickness, independent of the number of plies. A nine-node element with a judiciously chosen set of higher order assumed strain field is developed. Numerical tests involving isotropic and composite shells undergoing large deflections demonstrate the validity of the present formulation.