MATHEMATICAL MODELLING OF DYNAMIC PROCESSES IN A LAYERED INCOMPRESSIBLE HALF-SPACE WITH INITIAL STRESSES UNDER THE ACTION OF A MOVING LOAD

Abstract

This work is devoted to the study of the influence of the protective coating, initial stresses, mechanical characteristics of materials, movement parameters of the surface load on the stress-deformed state of the elastic base. The relevance of the research results is related to the possibility of their use in the creation of qualitatively new materials, structures and building structures. Two models of a layered incompressible half-space are considered and compared: 1) an elastic plate on an elastic half-space; 2) the top layer (protective coating) is modelled by concentrated masses. The concentrated force moves along the free surface of the protective layer at a constant speed at a certain angle to the surface of the half-space. The solution of the problem was obtained using the method of integral Fourier transformations. Analytical results are given in a general form for materials with an arbitrary elastic potential, for cases of unequal and equal roots of characteristic equations, for various conditions of combination of elements of a layered medium and for any speed of movement of the load. The material with the Bartenev-Khazanovich potential was considered for numerical analysis. The calculations were carried out within the framework of the theory of finite initial deformations. The impact of the moving load, initial stresses and mechanical parameters of the elements of the layered base on the main characteristics of its stress-strain state was studied.