Unsteady thermoelastic state of a cylinder of finite length

Abstract

The method of initial functions as applied to the solution of problems of elasticity was developed in [2, 3, 5]. In the present paper this method is modified to apply to axially symmetric problems of thermoelasticity and used to obtain the thermal stress in a cylinder of finite length subjected to a time-dependent axisymmetric temperature field. It is shown that the conditions for a plane stress field in a half space, elastic layer, and finite cylinder, as formulated in [i], are sufficient. The stress in the cylinder is studied numerically as a function of the parameters of the heat load. i. We consider the thermoelastic equilibrium of a finite isotropic cylinder of height h and radius R under an applied axisymmetric temperature field T(r, z). The solution is found by the method of initial functions [2, 3], which are taken to be the axial and radial displacements m(r, z) and u(r, z) and the axial and tangential stresses Oz(r, z) and ~(r, z)