Analytical solutions to the axisymmetric elasticity and thermoelasticity problems for an arbitrarily inhomogeneous layer

摘要

In this paper, we present a technique for constructing an analytical solution to the axisymmetric elasticity and thermoelasticity problems in terms of stresses for an inhomogeneous layer, whose elastic and thermophysical properties vary arbitrarily within the thickness-coordinate. By making use of the direct integration method, the equilibrium and compatibility equations are reduced to the governing Volterra-type integral equations accompanied with both integral and local boundary conditions for the key functions. To solve the obtained governing equations, we employed the resolvent-kernel technique which results in closed-form analytical expressions for the key functions. Having determined the key functions, the stress-tensor components are found through the relationship established by the integration of equilibrium equations. The same solution procedure is employed for solving the steady-state heat-conduction problem in an inhomogeneous layer. Typical numerical examples are discussed. (C) 2015 Elsevier Ltd. All rights reserved.