Thermal Stresses in a Plate Containing Two Circular Holes of Different Sizes under Uniform Heat Flow

Abstract

This note deals with the thermal stresses in a plate containing two insulated circular holes of different sizes under uniform heat flow in an arbitrary direction. Bipolar coordinates are used, and the temperature distribution and the stress functions which are adjusted so as to satisfy the boundary conditions at the edge of one hole, are expanded into Fourier's series at the edge of another hole. The parametric coefficients involved in them are determined from the given boundary conditions at the edge of the hole and at infinity. Expression of the thermal stress along the edge of the hole is derived and the values of it are calculated. Some limiting cases are also discussed.