Higher order theory based Fourier analysis of cross-ply plates and doubly curved panels

Abstract

An analytical solution to the static analysis of a general cross-ply finite-dimensional doubly curved panel of rectangular plan-form, modeled using a higher order shear deformation theory, is presented. A solution methodology, based on boundary-discontinuous generalized double Fourier series approach is used to solve a system of five highly coupled linear partial differential equations, generated by the higher order-based laminated shell analysis, with the fully clamped type 4 (C4) boundary condition prescribed on two opposite edges, while the remaining two edges are subjected to the simply supported type 4 (SS4) constraint. The numerical accuracy of the solution is ascertained by studying the convergence characteristics of the deflection and moment of a cross-ply spherical panel, and also by comparison with the available results in literature. Additional comparisons were made with the finite element counterparts using commercially available software for distributed load. Hitherto unavailable important numerical results presented include sensitivity of the predicted response quantities of interest to shell geometry (cylindrical and spherical), lamination, lamina material property, thickness and membrane effects as well as their interactions.