Flattening Effect of Negative Gaussian Curvature on Simply Supported Thick Asymmetric Cross-Ply Panels in the Absence of Surface-Parallel Edge Restraints

Abstract

This paper investigated the flattening effect of negative Gaussian curvature on simply supported (SS) thick asymmetrically laminated cross-ply panels in the absence of surface-parallel edge restraints. A higher-order shear deformation theory (HSDT) was employed to model the thick laminated cross-ply saddle-shaped shell with a square planform under consideration. The resulting boundary-value problem comprising a system of five highly coupled partial differential equations, in conjunction with the SS1-type (i.e., with no surface-parallel boundary constraints) simply supported boundary condition prescribed on all four edges, is solved by employing a boundary-discontinuous double Fourier series approach. Of particular importance are heretofore unavailable numerical results pertaining to the effects of panel Gaussian curvature, surface-parallel edge constraints, lamination sequence, and thickness effects, as well as their intricate interactions. Interaction of the membrane action due to negative Gaussian curvature with the higher-order (respectively, first-order) bending-stretching coupling producing beam–column- and tie bar–type softening/hardening effects in thick (respectively, thin) cross-ply panels also constitute an important focus of this investigation. These results serve as benchmarks for numerical techniques such as finite-element and boundary element methods.