EVALUATION OF AN ENERGY METHOD USING FINITE DIFFERENCES FOR DETERMINING THERMAL MIDPLANE STRESSES IN PLATES

摘要

A method of obtaining a set of finite-difference expressions for the thermal stress function directly from the complementary strain-energy expression is evaluated. The essential difference between this method and the more usual partial-differential-equation approach is that, in the energy approach, only conditions involving the variation of the stress function and its first normal derivative at the boundary must be satisfied explicitly. These conditions are generally termed the "geometric" boundary conditions. In approaching the problem from the partial-differential-equation viewpoint, rather than from the energy viewpoint, it is necessary to satisfy explicitly additional conditions involving the second and third derivatives which are generally termed "natural" boundary conditions.