Fourier solution to a thick cross-ply Levy type clamped plate problem

Abstract

A hitherto unavailable Levy type analytical solution to the problem of deformation of a finite-dimensional general cross-ply thick rectangular plate, modeled using a higher order shear deformation theory (HSDT), 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 HSDT-based laminated plate analysis, with the C4-type clamped boundary condition prescribed on two opposite edges, while the remaining two edges are subjected to the SS3-type constraint. The numerical accuracy of the solution is ascertained by studying the convergence characteristics of deflections and moments of a square cross-ply plate. Hitherto unavailable important numerical results presented include sensitivity of the predicted response quantities of interest to lamination, lamina material property, and thickness-to-length ratio, as well as their interactions. Comparison with their SS2 counterparts demonstrates the effect of end clamping on the deflections and moments of thin to thick cross-ply plates.