Stability of Plates and Shell Panels Under Non-uniform In-Plane Loadings

Abstract

AbstractIn this chapter, the linear and non-linear stability analyses of plates and shell panels subjected to various types of non-uniform edge in-plane loadings are presented. Kinematics of the plates and panels are formulated based on higher-order shear deformation theory (HSDT) and incorporating von Kármán type of non-linearity. As the applied edge load is non-uniform, the pre-buckling stress distributions within the plates and shell panels are not known a priori. These stress distributions are obtained by solving in-plane elasticity problems. Using these stresses, the non-linear partial differential equations (PDEs) of the cylindrical shell panels and plates are developed by minimization of the total potential energy. These PDEs are reduced into a set of non-linear algebraic equations via Galerkin’s method when the plates and panels are reinforced with constant fibers orientation, and via the Ritz method when the plates and panels are reinforced with variable fibers orientation. After dropping the nonlinear terms, the buckling load of the plate/panel is computed via the associated eigenvalue problem. The post-buckling equilibrium path is traced by solving non-linear algebraic equations via the Newton–Raphson method in conjunction with Rik's approach. In the end, the influence of various types of non-uniform edge loadings, constant and variable fibers orientations and porosity distributions, and their magnitude on the buckling load and post-buckling equilibrium path are investigated in detail.KeywordsPlates and shell panelsNon-uniform edge loadingHigher-order shear deformation theoryPorosityVariable fiber orientation