Mathematical Sciences: Analysis of Constitutive Relations and Transport Properties for Composites with Applications toProblems of Optimal Structural Design

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This project will focus on the analysis of transport properties and constitutive relations of composite materials and their application to problems of optimal structural design. Improved bounds and self consistent estimates will be developed for composite systems. The types of composites considered are two phase elastic composites with symmetry, partially debonded two phase elastic composites, two phase thermal conducting media with surface resistance between phases, and random emulsions of two Stokes fluids incorporating surface tension effects. New mathematical techniques involving new applications of null lagrangians, weakly lower semicontinuous functionals, and dual variational principles will be employed. These anticipated results as well as the existing theory will be applied to the numerical solution of optimal structural design problems. The optimal design problem considered here is the previously untreated problem of maximum strength design of composite systems subject to an ensemble of random static loads. Many modern optimal structural designs incorporate the use of composite materials. The goal of the proposed research is to utilize the most recent advances in the characterization of composite systems to facilitate solution of problems of optimal structural design. Anticipated applications include design of offshore oil platforms, large structures subjected to wind loads, and large space structures.