Fourier solution to higher order theory based laminated shell boundary-value problem

Abstract

A complete (i.e., particular as well as complementary ) Fourier solution to the boundary-value problem of static response under transverse load of a general cross-ply thick doubly curved panel of rectangular planform is presented. A boundary-discontinuous double Fourier series approach is used to solve a system of five partial differential equations, generated by a higher order shear deformation theory-based shell analysis, with the SS2-type of simply supported boundary condition prescribed at all four edges. Unlike the conventional Navier and Levy type approaches which can only provide particular solutions, the present method is general enough to provide the complete (particular as well as the complementary) solution for any arbitrary combination of admissible boundary conditions with almost equal ease. The numerical accuracy of the solution is ascertained by studying the convergence characteristics of deflections and moments of cross-ply spherical panels and also by comparison with the available first-order shear deformation theory- and classical lamination theory-based analytical solutions. Hitherto unavailable important numerical results presented include sensitivity of the predicted response quantities of interest to lamination, boundary constraint, and thickness and curvature effects, as well as their interactions.