ПРИМЕНЕНИЕ МЕТОДА ПЕРЕМЕННЫХ ПАРАМЕТРОВ УПРУГОСТИ ПРИ РЕШЕНИИ ЗАДАЧ ЗНАКОПЕРЕМЕННОГО УПРУГО-ПЛАСТИЧЕСКОГО НАГРУЖЕНИЯ МЕТАЛЛИЧЕСКИХ КОНСТРУКЦИЙ С УЧЕТОМ ОСТАТОЧНЫХ НАПРЯЖЕНИЙ.

Abstract

When calculating metal structures, as a rule, assumptions are made that allow us to consider the complex nonlinear operation of the structure in a linear formulation, namely, the absence of initial stresses, the absence of kinematic and isotropic changes in the flow surface of the material during plastic deformations, the identity of the behavior of the material during loading and unloading, etc. This approach is laid down in regulatory documents and is due to the following arguments: self-balanced stresses affect the deformability of the section, but cannot affect the kinematic boundary of its strength under the assumption of an ideally elasticplastic behavior of the material; the design works for a single load; initial stresses in some zones slow down the development of plastic deformations, and in others accelerate, etc. These assumptions seem to be justified in the classical problems of structural strength, in which the development of plastic deformations is allowed. However, in some tasks, these assumptions can lead to a distorted or erroneous result. The article describes the addition of the method of variable elasticity parameters in the formulation of a nonlinear deformation model, which makes it possible to remove the above assumptions. The algorithm is implemented in Python and tested on two verification tasks, and the process of loading the I-beam section taking into account residual stresses is also considered. The results of numerical calculation showed similar values with analytical solutions and qualitatively correspond to well-known ideas about the cyclic operation of structures.