Buckling of a two-layered circular plate with a prestressed layer

Abstract

Within the framework of nonlinear elasticity we analyze instability of a uniformly compressed circular two-layered plate with an initially compressed or stretched layer. For a constitutive relation of the material we use the incompressible neo-Hookean model. We assume that the lower layer is subjected to radial tension or compression. As a result in this layer there are initial strains and stresses. The two-layered plate is subjected to a uniform lateral compression. We study the stability of the plate with the use of the static Euler method. Within the method we determine loading parameters for which the linearized boundary-value problem has non-trivial solutions. We derive the three-dimensional linearized equilibrium equations for each layer. The solutions of the latter equations are obtained with the help of the Fourier method. The equation for critical strains is derived. We present an analysis of dependence of critical stress resultants on the initial strains and stiffness parameters.