A model of the deformation of a non-uniformly heated three-layer rod with delaminations

Abstract

A complete system of relations, which govern the bending stress-strain state of non-uniformly heated three-layer rods with an asymmetric structure, a stiff compressible filler and delamination-type defects on the surfaces of contact between the carrying layers and the filler, is constructed by a variational method. These relations include the equilibrium differential equations in an invariant form for the whole domain of integration, the end conditions, the matching conditions on the boundaries of the defect-free and defective domains and elasticity relations. The initial equations of equilibrium in terms of the forces and moments are reduced to normal systems of differential equations in terms of the generalized forces and displacements which are convenient for the numerical solution.