An analytical solution of unaxisymmetric transient thermal stresses in a nonhomogeneous hollow circular plate.

Abstract

This paper is concerned with a transient plane thermal stress problem in a nonhomogeneous hollow circular plate subjected to unaxisymmetric heating on the inner boundary surface. The nonhomogeneous plate has Young's modulus and thermal conductivity expressed in form of the different power laws of radial coordinate, the coefficient of linear thermal expansion given as an arbitrary function of radial coordinate and the constant Poisson's ratio. The transient nonhomogeneous heat conduction problem is solved by applying the Laplace transform. The associated plane thermal stress problem is formulated in terms of stress function, and the governing equation becomes Euler's differential equation. In the formulation, the single-valuedness of rotation is taken into account by the use of the Michell's conditions, which were derived for arbitrary nonhomogeneous properties by the present authors. Numerical calculations are carried out over the wide range of the nonhomogeneous thermal conductivity, Young's modulus and coefficient of linear thermal expansion.