The non-axisymmetric loading of an elastoplastic three-layer plate in its plane

Abstract

The statement of the boundary value problem on the deformation of a circular three-layer plate in its plane under the action of a non-axisymmetric load is herein presented. The materials of thin carrier layers obey the hypotheses of the theory of small elastoplastic deformations. The relatively thick filler is physically non-linearly elastic. A system of non-linear differential equilibrium equations in partial derivatives is obtained. A general technique for solving the problem in displacements based on the Fourier method and Ilyushin’s method of elastic solutions is proposed. The case of an external cosine load is considered. An iterative solution of a boundary value problem for a physically non-linear plate is obtained. The corresponding solution of the elastic problem is written out in the final form. The obtained solution is numerically tested.