ABSTRACT
Within three-dimensional (3D) nonlinear elasticity we solve the problem of instability of a compressed or stretched three-layer rectangular plate, the middle layer of which is pre-compressed or pre-stretched. The neo-Hookean incompressible material is used as the constitutive relation of the material. The plate with prestressed middle layer is subjected to lateral compression/stretching. We analyze static stability using bifurcation theory technique. We obtain the critical values of load parameters for which the linearized boundary-value problem yields non-trivial solutions. Using Fourier’s method, the solutions of the 3D linearized equilibrium equations are obtained. Analysis of dependence of critical stress resultants on initial strains of prestressed core layer is performed.
