Boundary-discontinuous fourier analysis of doubly-curved panels using classical shallow shell theories

Abstract

A hitherto unavailable analytical solution to the boundary-value problem of deformation of a doubly-curved panel of rectangular planform is presented. Four classical shallow shell theories (namely, Donnell, Sanders, Reissner and presently developed modified Sanders) are used in the formulation, which generates a system of one fourth-order and two second-order partial differential equations (in terms of the transverse displacement) 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 the central deflection and moment, and also by comparison with the available finite element solutions. Also presented are comparisons of numerical results predicted by the four classical shallow shell theories considered for isotropic panels over a wide range of geometric and material parameters. Other important numerical results presented include variation of the central deflection and moment, with the shell geometric parameters, such as length-to-thickness and radius-to-length ratios. Effect of boundary condition over the entire range of length-to-thickness and radius-to-length ratios is investigated by comparing the present SS2 results with their SS3 counterparts. Also presented are variations of displacement and moment along the center line of a spherical panel.