Analytical solutions to the planar non-axisymmetric elasticity and thermoelasticity problems for homogeneous and inhomogeneous annular domains

Abstract

This paper presents an analytical approach to solving the plane non-axisymmetric elasticity and thermoelasticity problems in terms of stresses for isotropic, homogeneous or inhomogeneous annular domains. The key feature of this approach is integration of the equilibrium equations in order to: a) express all the stress-tensor components in terms of a governing stress; b) deduce the integral equilibrium conditions, which are vital for the solution. Because the equilibrium equations are insensitive of material properties, the obtained expressions and integral conditions fit both homogeneous and inhomogeneous cases. The governing stress is derived out of the compatibility equation. Regarding complete construction of the solution, the integral compatibility conditions are deduced by integrating the strain–displacement relations. In the case of inhomogeneous material, the governing compatibility equation is reduced to Volterra type integral equation which then is solved by simple iteration method. The rapid convergence of the iterative procedure is established.