Collaborative Research: Engineering Analysis of Imprecise Models

本合作研究奖的研究目标是通过将不精确几何模型的工程分析置于坚实的理论基础上，并基于已开发的理论开发下一代软件工具，打破几何建模与工程分析学科之间的障碍。本研究的重要应用是传统方法无法处理的，包括分析未修复的CAD模型、逆向工程或扫描模型、具有小几何特征的模型、公差模型和概念草图。研究方法是基于将不精确模型视为几何形状族，并根据到不精确几何边界的距离重新制定工程分析问题。具体的研究成果包括分析不精确模型的理论基础，开发有效的几何和数值算法来支持理论，以及在特定应用背景下实现证明所获得的研究结果有效性的原型。如果成功，该研究将导致计算工程领域的重大进步，从而在整个产品设计周期中更广泛地采用分析工具，以及在工程以外的新兴领域。互操作系统的具体实际进展将包括对早期设计概念模型的分析，带有数值误差的构造或获得的模型，以及详细的公差模型。这项研究的结果有可能对教育课程产生重大影响，将学生和实践者从繁琐的数据准备中解放出来，并消除对几何的不切实际假设的需要。

This research objective of this collaborative research award is to break the barriers between the disciplines of geometric modeling and engineering analysis by placing engineering analysis of imprecise geometric models on a solid theoretical foundation and by developing the next generation of software tools based on the developed theory. Significant applications of this research, which cannot be handled by conventional methods, include analysis of unrepaired CAD models, reverse engineered or scanned models, models with small geometric features, toleranced models, and concept sketches. The research approach is based on treating imprecise models as families of geometric shapes, and on reformulating the problems of engineering analysis in terms of distances to the imprecise geometric boundaries. Specific deliverables of the research include theoretical foundations for the analysis of imprecise models, development of efficient geometric and numerical algorithms to support the theory, and implementation of prototypes demonstrating the efficacy of the obtained research results in the context of specific applications. If successful, the research will lead to significant advances in the field of computational engineering, resulting in a substantially wider adoption of the analysis tools throughout the product design cycle, as well as in emerging areas beyond engineering. Specific practical advances in interoperable systems will include analysis of early design concept models, constructed or acquired models with numerical errors, and detailed toleranced models. The results of this research have the potential to make a major impact on the educational curriculum, liberating students and practitioners from dealing with tedious data preparation and eliminating the need for unrealistic assumptions about the geometry.