FINITE DIFFERENCE METHOD FOR SOLVING THE ELASTOPLASTIC PROBLEMS OF ANISOTROPIC BODIES

Abstract

Usually, for the numerical solution of elastoplastic boundary value problems based on deformation theory of plasticity is used an elastic solutions method proposed by A.A. Ilyushin. In literatures the method of elastic solutions relative to boundary value problems of the theory of plastic flow is called the method of initial stresses or the method of initial deformations. In this paper, to solve the boundary value problems of the deformation theory of plasticity of transversally isotropic bodies, it is used relatively “simple” finite-difference method considered in combination with the iterative method, that is, the elastic solution method. The essence of the method is to construct symmetric finite-difference equations, separately for internal and boundary nodes of the area under consideration, and to solve them with respect to “central” or boundary node displacements and the organization of the iterative process. Elastoplastic problems are solved numerically for isotropic and transversely isotropic parallelepipeds under various boundary and boundary conditions. The obtained results are consistent with the known solutions, which shows the validity of the applied methodology. It is explored the spreading of the zone of plasticity and the effect of anisotropy on their distribution.