Optimal Cool-Down in Linear Viscoelasticity

Abstract

An optimal temperature path is derived for a thin viscoelastic plate which is cooled from a stress-free state against geometric constraints. The optimal path, which minimizes the final residual stress due to cool down, is shown to possess discontinuities at the initial and final times and to be smooth and continuous during all intermediate times. An iterative convergent scheme is provided for a wide class of linear viscoelastic responses and typical paths are determined for two specific cases. In addition, a time-temperature path which maintains constant stress values during cool-down is derived. The problem is motivated by the cooling process of composite materials.