A BOUNDARY-CONTINUOUS-DISPLACEMENT BASED FOURIER-ANALYSIS OF LAMINATED DOUBLY-CURVED PANELS USING CLASSICAL SHALLOW SHELL THEORIES

Hitherto unavailable analytical solutions to the boundary-value problems of static response and free vibration of an arbitrarily laminated doubly-curved panel of rectangular planform are presented. Four classical shallow shell theories (namely, Donnell, Sanders, Reissner and modified Sanders) have been utilized in the formulation, which generates a system of one fourth-order and two third-order partial differential equations with constant coefficients. A novel double Fourier series approach has been developed 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 the lowest two natural frequencies, deflections and moments of angle-ply panels, and also by comparison with the available FSDT-based analytical and CLT-based Galerkin solutions. Also presented are comparisons of deflections and moments of antisymmetric angle-ply cylindrical panels, computed using the four classical shallow shell theories considered. 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 angle-ply panels. Also studied is the highly complex interaction of bending-stretching type coupling effect with the effects of transverse shear deformation, rotatory inertias, inplane inertias, and membrane action due to shell curvature. Other important numerical results presented include variation of the response quantities of interest with geometric and material parameters, such as radius-to-length ratio, length-to-thickness ratio and angle of fiber orientation.