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.
Highlights
Development of new and improvement of existing production technologies, application of new materials, effective constructive schemes is explained by constant complication of operating conditions
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
On the basis of modern numerical implementations of the finite element method, the theoretical foundations of the analysis of nonlinear deformation processes of machines and structures in their contact interaction with the elastic-plastic medium within the threedimensional spatial problem taking into account the previous stress state and load history are presented
Summary
Development of new and improvement of existing production technologies, application of new materials, effective constructive schemes is explained by constant complication of operating conditions. The description of prismatic bodies and rotation bodies with variable geometrical and physical-mechanical parameters is most naturally carried out in the orthogonal cylindrical: g1 1 g2 2 1 , g3 3 In this case, the metric tensor components in the local coordinate system are presented through the components in the basic by the formula: gij z1,i z1, j z,2i z,2j z,3i z,3j g3 3. The variable value of the angle of internal friction determines the nature of the dilatancy elastic-plastic model hardening, and the loading surfaces represent a family of straight lines on the plane (Fig. 2). The above ratios make it possible to model the stress-strain state of the soil medium, to determine the pressure distribution in the soil under its own weight and various external influences, taking into account the medium heterogeneity, changes in the relief and physical and mechanical characteristics in the deformation process.
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