Deformation of a Three-Layer Rod with a Compressible Core in a Neutron Flow*

Abstract

We studied the deformation of a three-layer elastoplastic rod with a compressible core in a neutron flow. To describe the kinematics of the sandwich asymmetric across the thickness, the broken line hypothesis are adopted: Bernoulli’s hypothesis for the thin face layers and Tymoshenko’s hypothesis with linear approximation of displacements over the thickness for the compressible core. The resistance of the core in the tangential direction is taken into account. The constitutive stress–strain relations correspond to the theory of small elastoplastic deformations. The system of differential equilibrium equations is derived using the variational method. The kinematic boundary conditions of the rod is free support of the ends by fixed rigid supports. The boundary-value problem is solved by determining four functions of deflections and longitudinal displacements of the midsurfaces of the face layers. The analytical solution is obtained on the basis of the method of elastic solutions. Its numerical analysis is carried out in the case of an evenly distributed load.