Static and dynamic Fourier analysis of finite cross-ply doubly curved panels using classical shallow shell theories

Abstract

Analytical solutions to the boundary-value problems of static response under transverse load and free vibration of a general cross-ply doubly curved panel of rectangular planform are presented. Four classical shallow shell theories (namely, Donnell, Sanders, Reissner and modified Sanders) are used in the formulation, which generates a system of one fourth-order and two second-order (in terms of the transverse displacement) partial differential equations with constant coefficients. A recently developed boundary-discontinuous double Fourier series approach is used to solve this system of three partial differential equations with the SS2-type simply supported boundary conditions prescribed at all four edges. The accuracy of the solutions is ascertained by studying the convergence characteristics of deflections, moments and natural frequencies of cross-ply panels, and also by comparison with the available analytical solutions. Also presented are comparisons of numerical results predicted by the four classical shallow shell theories considered for cross-ply panels over a wide range of geometric and material parameters. Comparisons with the available FSDT (first-order shear deformation theory)-based analytical solutions are presented for the purpose of establishing the upper limit (with respect to the thickness-to-length ratio) of validity of the present CLT (classical lamination theory)-based solutions for both symmetric and antisymmetric cross-ply panels. Other important numerical results presented include variation of displacements, moments and the two lowest natural frequencies with the shell geometric parameters, such as radius-to-length ratio.