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Optimal Design of Materials, Structures, and Devices

材料、结构和器件的优化设计

基本信息

批准号：
0072469
负责人：
Robert Lipton
金额：
$ 5.9万
依托单位：
Worcester Polytechnic Institute
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2000
资助国家：
美国
起止时间：
2000-08-01 至 2001-12-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=0072469&HistoricalAwards=false
关键词：
Optimal Design Materials Structures Devices

项目摘要

This project addresses a suite of structural optimization problems unified by their mathematical formulation. The problems treated in this project come from several application areas including the design of gradient coils used in magnetic resonance imaging, catalysis design, the design of damage tolerant bridges, and nonlinear optics. Presently there is no systematic design methodology that addresses these problems. The first goal of this project is to extend the mathematical theory of homogenization so that one can systematically describe minimizing sequences of designs. The second goal is to use the homogenization theory to develop numerical methods for the systematic solution of these design problems.This research project focuses on areas of technological interest that require new mathematical and computational techniques for the simultaneous optimization of material properties and structural form. The problems treated in this project come from several application areas including the design of gradient coils used in magnetic resonance imaging, catalysis design, the design of damage tolerant bridges, and nonlinear optics. These problems, although diverse in nature, can be formulated along similar mathematical lines. The goal of this project is to develop a mathematical and computational tool box for the systematic solution of problems requiring the simultaneous design of material and structure.

这个项目解决了一套由其数学公式统一的结构优化问题。该项目所涉及的问题来自几个应用领域，包括用于磁共振成像的梯度线圈的设计、催化设计、损伤容限电桥的设计和非线性光学。目前还没有系统的设计方法来解决这些问题。这个项目的第一个目标是扩展齐次化的数学理论，以便系统地描述最小化设计序列。第二个目标是利用齐次化理论开发数值方法来系统地解决这些设计问题。这项研究项目集中在技术感兴趣的领域，需要新的数学和计算技术来同时优化材料性能和结构形式。该项目所涉及的问题来自几个应用领域，包括用于磁共振成像的梯度线圈的设计、催化设计、损伤容限电桥的设计和非线性光学。这些问题虽然性质各异，但可以沿着相似的数学路线进行表述。这个项目的目标是开发一个数学和计算工具箱，用于系统地解决需要同时设计材料和结构的问题。