Effect of thickness on the large elastic deformation behavior of laminatedshells

A serendipity type surface-parallel cubic (24-node) isoparametric element f or analysis of thick deep imperfect laminated shells is developed. The elem ent is capable of accurately modeling the curved geometry of a laminated sh ell by laking advantage of general tensorial formulation and using the surf ace-parallel curvilinear coordinates of non-Euclidean geometry. The present nonlinear finite element solution methodology is based on the hypothesis o f layerwise linear displacement distribution through thickness (LLDT) and t he total Lagrangian formulation, which accounts for fully nonlinear kinemat ic relations so that stable equilibrium paths in the advanced nonlinear reg ime call be accurately computed. An important computational feature is the successful implementation of the BFGS (Broyden-Fletcher-Goldfarb-Shanno) it erative scheme, used to solve the resulting nonlinear equations. First, the large strain behavior of a two-dimensional rubber sheet, made of Mooney-Ri vlin type hyperelastic material, under tension is evaluated for the purpose of comparison with available experimental results. Then, thin/shallow clam ped cylindrical cross-ply [0 degrees/90 degrees] panels, subjected to radia l pressure loading, are investigated to test the convergence of the present element. A new concept of relative(-to-linear) nonlinear membrane-to-shear factor, defined to be the ratio of normalized deflections computed using t he nonlinear and linear analyses, is introduced to determine the relative r oles of interlaminar shear/normal deformation and surface parallel membrane effects in thin to thick laminated perfect shell regimes, subjected to rad ial pressure loading. (C) 1999 Elsevier Science Ltd. All rights reserved.