К моделированию расчета упругопластических стержней при пространственно-переменном нагружении с учетом накопления повреждаемости

In this article is given the problem and the algorithms for calculating thin-walled rods of arbitrary cross section under spatially variable loading based on the theory of small elastoplastic deformations and refined theory of rods are presented. Using the variational Lagrange principle, mathematical models are developed for the deformation and damage of thin-walled rods in a cylindrical coordinate system. To describe the elastoplastic properties of the rod under variable loads, the generalized Masing principlewith allowance for damage and a cyclic diagram in current values is used by Academician T. Burieva. A system of differential equilibrium equations for a rod is obtained under spatially variable loading in vector form. To solve the boundary-value problem, the central difference scheme of the second order of accuracy and the matrix sweep method are used.

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