Twenty-second mathematical and statistical modeling workshop for graduate students

Multilayered structures are of importance for a variety of industrial applications. The temperature at which they are made and used can differ greatly, which can effect the structures’ reliability due to resulting residual stress and deflection. The trial-and-error method often used by experimentalists has improved multilayered structure design, but this approach lacks efficiency in producing desired results. Mathematical modeling, simulation, and computation of multilayered structures provide a way to streamline the process of choosing design parameters for desired results. In this paper, we take an existing model of thermal deformation of multilayered structures and expand it by including temperature dependence of material properties and layer gradation. We demonstrate the efficacy of the model by applying it to three representative structures. We then further analyze multilayered structures both analytically and numerically by studying the models sensitivity, optimization, and uncertainty. We conclude by summarizing our observations and providing design suggestions.