EFFECT OF HEAT FLOW ON THE STRESSED STATE OF A THREE-LAYER ROD

This paper considers the change in the stressed state of a three-layer elastoplastic rod with a compressible fi ller in a heat fl ow. The temperature change was calculated with the help of the formula obtained by averaging the thermal properties of the materials of the layers over the rod thickness. To describe kinematically the thickness asymmetric stack, broken line hypotheses were assumed: in thin bearing layers Bernoulli hypotheses hold; in the thin thickness-compressible fi ller the Timoshenko hypothesis with a linear approximation of displacements in the layer thickness holds. The work of the fi ller in the tangential direction is taken into account. The physical relations between stresses and deformations agree with the theory of small elastic deformations. The system of differential equilibrium equations was obtained by the variational method. At the boundary, kinetic conditions of rest of rod ends on rigid supports fi xed in the space are assumed. The solution of the boundary-value problem was reduced to the obtaining of four sought functions — bendings and longitudinal displacements of median surfaces of the bearing layers. The analytical solution was obtained by the method of elastic solutions in the case of uniformly distributed continuous and local loadings. Its numerical analysis has been carried out. The change in stresses on the outer planes of the rod layers and in the cross section in the middle of the rod under the action of the heat fl ow has been investigated.
   
Author:  É. I. Starovoitov and L. V. Leonenko
Keywords:  three-layer rod, stressed state, plasticity, compressible filler, heat flow.
Page:  60