Determination of the Thermoelastic States of Piecewise Inhomogeneous Thermosensitive Bodies with Cylindrical Interfaces

Abstract

We suggest a method for the determination of the thermoelastic state caused by plane axisymmetric temperature fields and surface loads in layered isotropic bodies with cylindrical interfaces. The temperature and coordinate dependences of the moduli of elasticity, coefficients of linear temperature expansion, and Poisson ratios are taken into account. The method is based on the solution of the systems of integral-algebraic equations for radial displacements. In the case of a cylinder, these systems are obtained from the integral representation of the solution of the problem for the ordinary differential equation with generalized derivatives. In this case, we use the Green function of the elasticity problem for a homogeneous cylinder. In the cases of a layered space with cylindrical cavity, a continuous cylinder, and the continuous space, the corresponding systems and the remaining relations required for the determination of the thermoelastic state are obtained as a result of the limit transitions. The relations for the determination of thermal stresses in the corresponding single-layer bodies are presented. The numerical investigations are performed for a three-layer cylinder with functionally gradient layer.