Mathematical Sciences: The Overall Elastic Properties of Transversely Isotropic Composites

8907658立顿这个项目将应用复合材料数学分析中的最新进展，以获得有效的弹性性能横观各向同性复合材料。其目的是获得由两种各向同性弹性材料按规定比例制成的横向各向同性复合材料的六个弹性模数之间的新界限。总体的攻击计划是双重的：所有表现出横向各向同性的有限阶层合板的集合将被刻画。然后，将利用层合板在复合材料集中是极端的这一事实来推导边界。复合材料的性能具有基本的技术重要性。复合材料已被广泛应用于结构优化，以设计航空航天用的坚固而轻便的部件。

8907658 Lipton This project will apply recent advances in the mathematical analysis of composite materials to obtain the effective elastic properties of transversely isotropic composite materials. The goal is to obtain new bounds that correlate the six elastic moduli for transverse isotropic composites made from two isotropic elastic materials in prescribed proportions. The overall plan of attack is twofold: the set of all finite rank laminates exhibiting transverse isotropy will be characterized. Then bounds will be derived using the fact that laminates are extremal in the set of composites. The behavior of composite materials is of fundamental technological importance. Composites have been widely used in structural optimization to design strong but lightweight components for use in aerospace and aviation.