Optimal design of a two-layered elastic strip subjected to transient loading

Analytical solutions play a very important role in the validation of numerical codes. However, exact analytical solutions involving optimal design of transiently loaded multilayered structures, are rare in the literature. In this paper, we solve an optimal design problem involving wave propagation in a two-layered elastic strip subjected to transient loading. We obtain explicit formulas for the stress in each layer using the method of characteristics, and then use these results to identify the designs that provide the smallest stress amplitude. The derived analytical results are then successfully used to validate a previously developed, hybrid computational optimization software.