PROBLEM OF THERMOELASTICITY OF THE COMPOSITE BAR WITH A PLAIN AXIS OF AN ARBITRARY SHAPE IN THE NATURAL COORDINATE SYSTEM

Abstract

Heterogeneity of the structure of composite construction elements leads to temperature deformations and strains within them, even when staying in a stationary uniform temperature field. Therefore, for such elements, it is necessary to take into account changes in a temperature field while in operation when predicting their strength and rigidity. Among the scientific papers devoted to the problems of thermal elasticity of composite elements, multilayer plates and shells and rectilinear bars are predominantly considered. At the same time, thermal elasticity of composite rod elements with a curvilinear axis remains a poorly studied problem of applied mathematics and mechanics. In this paper, we obtained equations and formed boundary conditions of different types for the coupled thermal conductivity problem of the curvilinear composite bar with invariable length structure in its natural coordinate system. The equations describe the process of propagation of a temperature field taking into account a deformation field inside a discrete-inhomogeneous composite bar consisting of homogeneous or continuous-inhomogeneous phases with curvilinear orthotropy of thermophysical and elastic characteristics and containing internal sources of heat. On the basis of the accepted general initial data on the shape of outer bar surfaces and internal bar structure, the boundary conditions of three types are obtained in the natural coordinate system and the conditions of heat transfer at the boundary of phases in case of their ideal thermal contact and in the presence of contact thermal resistance are made out. The obtained equations, along with the system of elasticity theory equations in the natural coordinate system, integral and differential dependences for internal force factors and relations for modeling loads of various types developed in previous papers, represent the necessary analytical basis for solving a wide range of problems as to thermoelastic deformation of composite bars with a plain axis of an arbitrary shape.