Levy-Type Boundary Fourier Analysis of Thick Clamped Hyperbolic-Paraboloidal Cross-Ply Panels

Abstract

An analytical solution to the problem of deformation of a finite dimensional general cross-ply, thick doubly curved panel with negative Gaussian curvature and of rectangular planform, modeled using a higher-order shear deformation theory, is presented. A solution methodology, based on a boundary-discontinuous, generalized double Fourier series approach is used to solve a system of five highly coupled linear partial differential equations, generated by the higher-order shear deformation-theory-based laminated shell analysis, with the C4-type rigidly clamped boundary condition prescribed on two opposite edges, whereas the remaining two edges are subjected to the SS3-type constraint. Hitherto unavailable important numerical results presented include sensitivity of the predicted response quantities of interest to applied loading, shell geometry (negative or positive Gaussian curvature), edge clamping constraints, and lamination and thickness effects, as well as their possible interactions. Comparison with their nonnegative Gaussian curvature counterparts demonstrates the effect of negative Gaussian curvature on the deflections and moments of these doubly curved panels.