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An approximate solution of elastic-plastic problem of circular strength different (SD) plates

The study of a deformation features of metal alloys with anisotropy of plastic properties under biaxial stress state is an important technical challenge in the design and creation of a new shipbuilding and aircraft constructions. The study of alloys which are sensitive to tension or compression loading is complicated nonlinear problem. To solve this problems, the Mises-Hill's theory of plasticity and the Ilyushin's theory of perfect plasticity are used. Different mathematical models ([1], [2]) are used for the such materials research where anisotropy parameters and SD(strength-different) parameters are taken into account. Their impact is significant during the analysis of the overall picture of the stress deformed structure condition. The problem is solved analytically and numerically. As an example of the material with the SD-effect steel A40X is considered. The solutions for beam made of isotropic material and material with the SD-effect are compared. Such parameters introduction complicates the baseline ratio and construction of the solution, particularly for the study of elastic-plastic bending of a circular plates under the action of hydrostatic pressure. So it is necessary to assess the impact of these parameters for the solution and build an approximate solution for special cases.