Skeletal Reduction of Thin Mechanical Components

薄型机械部件的骨架减少

• 批准号: 0322134
• 负责人: Krishnan Suresh
• 金额: $ 28.75万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-08-01 至 2007-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0322134&HistoricalAwards=false
• 关键词: Skeletal; Reduction; Thin; Mechanical; Components

Thin mechanical components are ubiquitous and constitute a multi-billion dollar industry; examples include outer-shell of automobiles and aircrafts, most plastic components, etc. Like all mechanical components, they are subject to rigorous computational analysis before production. Existing analysis techniques for thin components, for historical reasons, are based on the mid-surface of a thin component. Unfortunately, the mid-surface is often ill defined for complex objects. This has led to fragile and inaccurate algorithms. This project proposes to use of the skeleton of a solid, abandoning the notion of a "mid-surface" approach. The skeleton, unlike the mid-surface, is well defined and can be computed uniquely for a solid. Initial investigation shows that this would result in robust algorithms, involving the combination of the Kantorovich principle of dimensional reduction with the unique topological and geometrical properties of skeleton representation. If successful, the research would lead to a fundamentally new and unified theory of thin component analysis consisting of an unambiguous and complete mathematical language of skeletal reduction, and associated algebra. The mathematical principles would also be of interest to researchers involved in the broad area of boundary value problem analysis. Dissemination of the findings of the research will be articulated to University of Wisconsin students through a graduate course, and students and researchers elsewhere through seminars. It is also the intention to facilitate a transfer of technology of the ensuing theory and algorithms to the CAD/CAE industry. An environmental impact of the project is in the plastics industry where components are almost exclusively thin; better analysis techniques have the potential of significantly reducing the tonnage of plastics used (and discarded) today.

薄型机械部件无处不在，构成了一个数十亿美元的产业；例如汽车和飞机的外壳，大多数塑料部件等。与所有机械部件一样，它们在生产之前要经过严格的计算分析。由于历史原因，现有的薄部件分析技术是基于薄部件的中表面。遗憾的是，对于复杂对象，中间曲面的定义通常不明确。这导致了脆弱和不准确的算法。该项目建议使用实体的骨架，放弃“中间表面”方法的概念。与中间曲面不同，骨架定义得很好，并且可以为实体唯一计算。初步研究表明，这将导致稳健的算法，包括结合Kantorovich降维原理和骨架表示的独特的拓扑和几何属性。如果成功，这项研究将导致一种全新的、统一的瘦成分分析理论，包括一种明确而完整的骨骼约简的数学语言，以及相关的代数。涉及边值问题分析的广泛领域的研究人员也会对数学原理感兴趣。研究结果的传播将通过研究生课程向威斯康星大学的学生传达，并通过研讨会向其他地方的学生和研究人员传播。它的目的也是为了促进将随后的理论和算法的技术转移到CAD/CAE行业。该项目对环境的影响是在塑料行业，那里的组件几乎都很薄；更好的分析技术有可能显著减少今天使用(和丢弃)的塑料的吨位。