STATIC AND DYNAMIC FOURIER-ANALYSIS OF FINITE CROSS-PLY DOUBLY-CURVEDPANELS USING CLASSICAL SHALLOW SHELL THEORIES

Analytical solutions to the boundary-value problems of static response under transverse load and free vibration of a general cross-ply doubl y curved panel of rectangular planform are presented. Four classical s hallow 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 displac ement) partial differential equations with constant coefficients. A re cently 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 a ll four edges. The accuracy of the solutions is ascertained by studyin g the convergence characteristics of deflections, moments and natural frequencies of cross-ply panels, and also by comparison with the avail able analytical solutions. Also presented are comparisons of numerical results predicted by the four classical shallow shell theories consid ered for cross-ply panels over a wide range of geometric and material parameters. Comparisons with the available FSDT (first-order shear def ormation theory)-based analytical solutions are presented for the purp ose of establishing the upper limit (with respect to the thickness-to- length ratio) of validity of the present CLT (classical lamination the ory)-based solutions for both symmetric and antisymmetric cross-ply pa nels. Other important numerical results presented include variation of displacements, moments and the two lowest natural frequencies with th e shell geometric parameters, such as radius-to-length ratio.