Mathematical Sciences: Analysis of Transport Properties for Composites and Multi-Phase Flows with Application to Optimal Design

9403866利普顿我们讨论复合材料的设计及其在结构优化设计中的应用。在这里，我们研究了完美和非完美结合的复合材料的宏观性质，以及多相乳液和泡沫的最佳传输性质。在理论层面上，这项工作涉及到齐次化理论、微扰理论和非线性泛函的Gamma收敛的基础研究。最终目标是创造高效的数值方法来优化设计由复合材料建造的结构。在本提案中，我们讨论了在优化结构设计中使用复合材料的几个主题。复合材料及其传输特性是从飞机机翼气动弹性泰勒成形到乳化液优化设计等各种结构设计的核心。本文提出的设计方法侧重于寻找最佳结构性能所必需的最佳复合材料性能。该程序立即应用于各种领域，从设计节油运输系统到生物材料运输特性的建模。

9403866 Lipton We address the design of composite materials and their application to optimal design of structures. Here we investigate the macroscopic properties for perfectly and imperfectly bonded composites as well as optimal transport properties for multi-phase emulsions and foams. On a theoretical level this work involves basic research in homogenization theory, perturbation theory, and gamma convergence of nonlinear functionals. The ultimate goal is the creation of efficient numerical methods for optimal design of structures built from composite materials. In this proposal we treat several topics involving the use of composites in optimal structural design. Composite materials and their transport properties are central to the design of structures ranging from the aeroelastic tayloring of airplane wings to optimal design of emulsions. The design approach put forth here focuses on finding the best composite material properties necessary for optimal structural performance. This program has immediate application to diverse areas ranging from design of fuel efficient transportation systems to the modeling of transport properties of biological materials.