Transient Thermal Stresses in a Non-homogeneous Doubly Connected Region

抄録

A plane thermoelastic problem in a nonhomogeneous doubly connected region under a transient temperature field has been formulated by the stress function method. In the formulation, new integral conditions (i.e., Michell's conditions for a homogeneous doubly connected region) have been derived to assure a single-valuedness of rotation and displacements in the nonhomogeneous doubly connected region. The system of fundamental equations formulated in terms of Airy's stress function has been solved numerically by the use of the finite difference method. To illustrate quantitatively the effects of thermal and mechanical nonhomogeneous properties on the distributions of temperature and thermal stress, numerical calculations have been carried out for the thermal conductivity, Young's modulus and the coefficient of linear thermal expansion, which vary exponentially with the position in a square plate with a square hole.