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

本项目将重点分析复合材料的输运特性和本构关系，并将其应用于结构优化设计问题。改进的界和自洽估计将用于复合系统。考虑的复合材料类型包括具有对称性的两相弹性复合材料、部分脱粘的两相弹性复合材料、两相之间具有表面电阻的两相导热介质以及具有表面张力效应的两种Stokes流体的随机乳液。新的数学技术，包括零拉格朗日、弱下半连续泛函和对偶变分原理的新应用。这些预期结果以及现有理论将应用于结构优化设计问题的数值求解。这里考虑的优化设计问题是以前未处理的问题，即复合材料系统在随机静载荷集合作用下的最大强度设计问题。许多现代优化结构设计都采用了复合材料。提出的研究目标是利用复合材料系统表征的最新进展，以促进优化结构设计问题的解决。预计应用范围包括海上石油平台、大型风荷载结构和大空间结构的设计。

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.