Nonlinear problem of structural deformation in interaction with elastoplastic medium

Abstract

The use of numerical methods in the calculation of machines and structures, taking into account their interaction with the elastic-plastic medium is largely determined by the complexity or even impossibility of analytical calculation due to the complexity of structural schemes, heterogeneity of material features, uneven soil layers, implementation of step-by-step work execution technologies and so on.
 Compatible calculations of structures and nonlinear basis, which are described by modern mechanical and soil models in one problem is a significant technical problem. And neither the existing “problem-oriented” software packages, nor the “universal” ones - do not fully contain such models.
 The tasks solution is possible only within the framework of numerical methods, the most common of which is the finite element method (FEM). The construction of the calculated finite element model raises many complex questions that require additional detailed study. In addition, the compliance with the state building norms and regulations is an important factor for further practical use.
 The combination of the latest achievements in the field of structural mechanics and soil mechanics is a promising direction for the development of effective approaches for building discrete models of spatial systems “structure-nonlinear base” for solving applied problems.
 On the basis of modern numerical implementations of the finite element method the article presents the theoretical foundations of the analysis of deformation processes of machines and structures in their contact interaction with the elastic-plastic nonlinear soil medium within the three-dimensional spatial problem taking into account the previous stress state and load history. The methodology of construction of computational models of joint deformation and mutual influence of rigid structures and essentially plastic external medium is developed, new special heterogeneous finite elements of SAFEM of general form with variable geometrical and physical-mechanical parameters and arbitrary boundary conditions for approximation of arrays of hardly connected reinforced soils are developed.

Determining the patterns of asymmetric interaction of plastic medium with counter-directional metal flow

“…Solving the problems considered in [5] is possible only within the framework of numerical methods, the most common of which is the finite element method. Some ways to overcome such difficulties are proposed in [6] using a procedure for constructing computational models of joint deformation and the mutual influence of rigid structures and the plastic external environment.…”