OPTIMAL TEMPERATURE PATHS FOR THERMORHEOLOGICALLY SIMPLE VISCOELASTIC MATERIALS WITH CONSTANT POISSON'S RATIO ARE CANONICAL

In this note we discuss the thermal stress problem for a Thermorheologically-simple linearly-viscoelastic body, subjected to a spatially-uniform temperature field and homogeneous boundary conditions, assuming that Poisson's ratio is constant and inertia negligible. In particular, we consider the following optimization problem: of all temperature paths θ(t), 0 ≤ t ≤ tf, which belong to a given function class, is there one which renders a given stress measure a minimum at time tf. We show that a resulting optimal path θ(t) (if it exists) is canonical: θ(t) is independent of the shape of the body and of the particular homogeneous boundary conditions.