Algorithm of finite elemental SSS analysis of thin-walled technosphere objects based on a triangular discretion element with elastic-plastic deformation

Abstract

The article describes an algorithm for the strength calculation of thin-walled objects of the technosphere, taking into account the plastic stage of the work of the material used, which is quite relevant with the increased requirements for material saving of designed and reconstructed objects. The finite element method is used as a tool for studying the stress-strain state of technosphere objects, taking into account the physical nonlinearity of the applied structural material. As a sampling element, a fragment of the middle surface of a thin-walled triangular technosphere object with main nodes at the vertices of the triangular element and additional nodes at the midpoints of the sides is used. The sought unknowns at the main nodes at the loading step are the increments of the displacement vector components and their first derivatives with respect to the curvilinear coordinates of the middle surface. At additional nodes, Lagrange multipliers act as unknowns, introduced to improve the consistency of the bin along the boundaries with adjacent elements. When deriving the plasticity matrix at the loading step, we used the hypothesis that the components of the stress increment tensor are proportional to the components of the strain increment tensor. The developed algorithm was implemented as a package of applied programs and verified by the example of calculating a rigidly restrained cylinder loaded with internal pressure.