DYNAMIC INTERACTION OF STRINGER AND CURVILINEAR ORTHOTROPIC HALF-SPACE

Abstract

The relevance of studies of the dynamic interaction of a curvilinear orthotropic half-space with an inclusion should not cause doubts. Such problems of load transfer from the reinforcing fiber to the matrix are directly related to the mechanics of composites and help in the study of the problems of the destruction of such materials. As is known, the structure of the initial stresses has an arbitrary nature. So, for example, they can arise as a result of technological operations in the manufacture of modern construction materials and machines. Internal stresses, which can be considered initial in structural elements and machine parts, affect the properties of materials and change the dynamic characteristics of structures. Solving complex contact problems by the asymptotic method makes it possible to obtain results that can be used for streaming numerical data, evaluating the methodology of setting up certain experiments. Achieving satisfactory practical accuracy of the solutions obtained by the proposed perturbation method was also repeatedly demonstrated on test tasks. The purpose of this study is to apply an efficient asymptotic method for obtaining an analytical solution for the case of dynamic interaction of a stringer and an orthotropic half-space. An elastic orthotropic semi-finite body with cylindrical anisotropy reinforced by a rod of circular cross-section under dynamic load is considered. The radius of the rod is considered small. It is necessary to find the distribution of contact forces in the matrix and forces in the rod. As in the flat case, the boundary value problem is reduced to the sequential solution of potential theory problems (the main functions are from Laplace’s equations). Boundary conditions are formulated for each type of stress state. The distribution of forces in the rod and the function determining the distribution of contact stress were found. It is shown that without considering inertial forces, the forces in the stringer do not depend on time (quasi-static calculation). A number of boundary transitions connecting the dynamic and static formulation of the problem have been performed. The corresponding behavior of the main searched functions is shown.