An analytical solution to the axisymmetric thermoelasticity problem for a cylinder with arbitrarily varying thermomechanical properties

Abstract

Analytical solutions to the axisymmetric heat-conduction and thermoelasticity problems for a long solid cylinder are constructed for arbitrary variation of the thermomechanical properties within the radial coordinate. By making use of the direct integration method, the steady-state heat-conduction equation is reduced to an integral equation of second kind. The numerical, analytical-numerical and analytical methods for solving the latter equation are suggested. The one-to-one relations between the stresses and displacements on the boundary are established, which allows for the reduction of the thermoelasticity problems with various types of the boundary conditions to the one in terms of stresses. The explicit expressions for the stress-tensor and displacement-vector components are obtained and analyzed for different types of inhomogeneity.