The Second Deformation of the Three-Layer Elastoplastic Rod by Local Load

Abstract

Within the framework of the theory of small elastoplastic deformations one class of simple variables local loading of sandwich bars of rectangular transverse-cross section with elastoplastic bearing layers and physically nonlinear elastic fillers, for which the possibility of constructing a solution of the boundary value problem under repeated loading is indicated, if the solution during loading from the natural state is known (hypothesis of Moskvitin). The paper shows the formulation and methodology of solving boundary value problem of the deformation of the threelayer asymmetric thickness of the rod by repeated exposure to the local rectangular load. To describe the kinematics of asymmetrical thickness rod package were adopted by the broken normal hypothesis: in thin layers bearing valid hypo-theses Bernoulli, in a hard incompressible thickness relatively thick filler normal is straight. It does not change its length, but some extra turns at an angle. The equilibrium equations are derived using the Variational method of Lagrange the work of the filler in the tangential direction is taken into account. Analytic solutions of problems of the theory of small elastic deformations during the forward and backward on-laden are obtained by the method of elastic solutions Ilyushin. The numerical analysis of the solutions is given.

Keywords

• second local loading
• plasticity
• three-layer beam