BOUNDARY-DISCONTINUOUS FOURIER-ANALYSIS OF DOUBLY-CURVED PANELS USINGCLASSICAL SHALLOW SHELL THEORIES

A hitherto unavailable analytical solution to the boundary-value probl em of deformation of a doubly-curved panel of rectangular planform is presented. Four classical shallow shell theories (namely, Donnell, San ders, Reissner and presently developed modified Sanders) are used in t he formulation, which generates a system of one fourth-order and two s econd-order partial differential equations (in terms of the transverse displacement) with constant coefficients. A recently developed bounda ry-discontinuous double Fourier series approach is used to solve this system of three partial differential equations with the SS2-type simpl y supported boundary conditions prescribed at all four edges. The accu racy of the solutions is ascertained by studying the convergence chara cteristics of the central deflection and moment, and also by compariso n with the available finite element solutions. Also presented are comp arisons of numerical results predicted by the four classical shallow s hell theories considered for isotropic panels over a wide range of geo metric and material parameters. Other important numerical results pres ented 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 com paring the present SS2 results with their SS3 counterparts. Also prese nted are variations of displacement and moment along the center line o f a spherical panel.