Deformation of an Elastoplastic Three-Layer Circular Plate in a Temperature Field

Abstract

A boundary-value problem on axisymmetric deformation of a circular elastoplastic plate, asymmetric across its thickness, in a temperature field is formulated. The physical equations of state used correspond to the theory of small elasticoplastic strains. The effect of a temperature field on the stress-strain state of the plate is considered. The intensity of thermal flow is constant. To describe the kinematics of the plate package, the hypotheses of a broken line are accepted: in the thin load-bearing layers, the Kirchhoff hypotheses are valid; in the rigid core, incompressible across it thickness, the Tymoshenko hypothesis is valid. The work of core in the tangential direction is taken into account. The equilibrium equations are derived by the variational method. An analytical solution of the boundary-value problem is obtained by the method of elastic solutions. A numerical analysis of the stress-strain state of a plate with a hinged contour is carried out.