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

该项目将侧重于分析交通运输 复合材料的性能和本构关系， 它们在最优结构设计问题中的应用。 改进的界限和自我一致的估计将开发 对于复合系统。 考虑的复合材料类型有 对称部分脱粘两相弹性复合材料 双相弹性复合材料，双相导热介质 具有相间的表面电阻，以及 两种斯托克斯流体结合了表面张力效应。 新 涉及零的新应用的数学技术 拉格朗日，弱下连续泛函，和对偶 将采用变分原理。 这些预期 结果以及现有的理论将适用于 优化结构设计问题的数值解。 的 这里考虑的最优设计问题是以前的 复合材料最大强度设计的未处理问题 承受随机静态载荷的集合。 许多现代优化结构设计都采用了 复合材料。 拟议研究的目标是 利用最新进展的特点， 复合系统，以促进最佳的问题的解决方案 结构设计 预期的应用包括设计 海上石油平台，承受风荷载的大型结构， 大型空间结构。

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.