The study of wave propagation in multilayered media is important in a number of diverse disciplines that include seismology, electromagnetics, optics, acoustics, et cetera. An exhaustive review of the state-of-the-art prior to 1960 can be found in the classic treatise by Brekhovskikh [1]. Despite the vast literature on wave propagation in multilayered media, systematic investigations of the optimal design of multilayered structures subjected to transient loadings are relatively rare in the mechanics literature. This is particularly true for the design of shields, acoustic barriers, or protective structures consisting of materials that exhibit nonlinear and history dependent response to transient loading. Furthermore, because of the complexity of the constitutive behavior, solutions to optimal design problems for multilayered structural applications are only obtainable by purely computational means. This paper summarizes the results of ongoing research in the development and validation of optimization software for the computational design of transiently loaded multilayered structures. The optimization software combines formal nonlinear parameter estimation algorithms (e.g. gradient search methods and genetic algorithms) with computational finite element methods for optimizing structures subjected to transient loading. Three examples are presented that illustrate the use of optimization software for: 1) the optimal design of nonlinear multilayered shield structures subjected to projectile impact and penetration, 2) comparison of exact with computationally-based solutions to optimal design problems in multilayered elastic media subjected to transient loading, and 3) genetic algorithm optimization of periodic, elastic phononic bandgap structures.
1. Brekhovskikh, L. M., Waves in Layered Media, Academic Press, NY, 1960.
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