Stability of a three-layered rectangular plate with prestressedmiddle layer

Abstract

Within the framework of the nonlinear elasticity, the problem on stability of a three-layered rectangular plate with prestressed core is solved. The model of neo-Hookean incompressible material (Treloar’s model) was used for description of material behavior. The middle layer of the plate is subjected to initial uniform compression or stretching and then combined with other two layers in three-layered plate. Further, the three-layered plate with prestressed middle layer (core) subjected to uniform lateral compression. For analysis of instability, Euler’s method is applied. The method consists of determination of such values of deformation parameter for which linearized boundary-value problem has non-trivial solutions. For each layer the linearized equilibrium equations were derived. Using Fourier’s method of variable separation, the solutions of the linearized equilibrium equations are obtained. Analysis of dependence of critical stress resultant on initial strains of prestressed core is performed.