Об одном подходе численного решения упругопластических краевых задач

Usually, for the numerical solution of elastoplastic boundary value problems based on deformation theory of plasticity is used an elastic solutions method. For the numerical solution of elastoplastic problems based on ow theories usually, an initial stress and initial strain methods are applied. The base of the initial stress and initial strain methods also consist the elastic solutions method. In this paper, the elastic solutions method is used for the numerical solution of the elastoplastic problem based on deformation theory in a new manner. The main idea of this approach consists in constructing nite-dierence equations separately for internal and boundary points of the considered area, and resolving them relative to nodal displacements, and organizing an iterative process. Some elastoplastic problems for isotropic and transversely isotropic parallelepipeds under the dierent boundary conditions are solved. The results were compared with known solutions and received a good convergence. The propagation of the plasticity zone and the influence of anisotropy on their distribution are investigated.

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