Optimal Cooling Paths for a Class of Thermorheologically Complex Viscoelastic Materials

Abstract

This paper concerns the optimal cooling of thin viscoelastic plates so as to minimize the residual thermal stresses upon completion of the cool-down process. The thermorheological behavior of the plate material is assumed complex in the sense that both horizontal and vertical shift factors are employed. The optimal path is shown to possess initial and final jump discontinuities and to depend on only one of the two components of the vertical shift factor. It is further demonstrated that significant reductions in the level of residual stress may be attained by following the optimal cooling path.