Effect of thickness on the large elastic deformation behavior of laminated shells

A serendipity type surface-parallel cubic (24-node) isoparanietric element for analysis of thick deep imperfect laminated shells is developed. The element is capable of accurately modeling the curved geometry of a laminated shell by taking advantage of general tensorial formulation and using the surface-parallel curvilinear coordinates ofnon-Euclidean geometry. The present nonlinear finite element solution methodology is based on the hypothesis of layerwise linear displacement distribution through thickness (LLDT) and the total Lagrangian formulation, which accounts for fully nonlinear kinematic relations so that stable equilibrium paths in the advanced nonlinear regime can be accurately computed. An important computational feature is the successful implementation of the BFGS (Broyden Fletcher Goldfarb-Shanno) iterative scheme, used to solve the resulting nonlinear equations. First, the large strain behavior of a two-dimensional rubber sheet, made ofMooney-Rivlin type hyperclastic material, under tension is evaluated for the purpose of comparison with available experimental results. Then. thin/shallow clamped cylindrical cross-ply [0°/90°] panels, subjected to radial 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 the nonlinear and linear analyses, is introduced to determine the relative roles of interlaminar shear/normal deformation and surface parallel membrane effects in thin to thick laminated perfect shell regimes, subjected to radial pressure loading. © 1999 Elsevier Science Ltd. All rights reserved.