An analytical solution for a plane thermal stress problem in nonhomogeneous multiply-connected regions. 1st Report. Asymmetric steady-state thermal stresses in a nonhomogeneous hollow circular plate.

Abstract

An analytical solution is presented for a plane thermal stress problem in a nonhomogeneous hollow circular plate subjected to an asymmetric heating as an example of nonhomogeneous multiply-connected regions. The nonhomogeneous plate has the Yong's modulus and thermal conductivity expressed in forms of different power laws of radial co-ordinate, the coefficient of linear thermal expansion given as an arbitrary function of radial co-ordinate and the constant Poisson's ratio. The governing equation of the thermoelastic problem in the nonhomogeneous plate formulated in terms of stress function becomes Euler's differential equation. The problem considered in this paper is restricted to symmetric thermal stress problem with respect to χ and y axes. The single-valuedness of rotation is assumed based on the Michell's condition derived for arbitrary nonhomogeneous body in the previous report by present author. Numerical calculations are carried out for the case of a nonhomogeneous hollow circular plate subjected to an asymmetric heating on the inner boundary surface.