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

摘要

A serendipity type surface-parallel cubic (24-node) isoparametric 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 tonsorial formulation and using the surface-parallel curvilinear coordinates of non-Euclidean geometry. The present nonlinear finite element solution methodology is based on the hypothesis of layerwise linear displacement distribution thorough thickness (LLDT) and the total Lagrangian formulation, which accounts for fully nonlinear kinematics reactions so that stable equilibrium paths in the advanced nonlinear regime can be accurately competed. An important computational feature is the successful implementation of the BFGS (Broyden-Fetcher-Goldfarb-Shanno) iterative scheme, used to solve the resulting nonlinear equations. First, the large strain behavior of a two-dimensional rubber sheet, made of Mooney-Rivlin type hyperelastic material, under tension is evaluated for the purpose of comparisons with available experimental results. Then, thin/shallow clamped cylindrical cross-ply [0 deg/90 deg] 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 shearormal deformation and surface parallel membrane effects in thin to thick lamina