Meshfree Integration of Geometric Design and Engineering Analysis

这笔赠款提供资金，用于开发一种新技术，利用一种新的混合计算机表示法无缝集成几何设计和工程分析工具。新的表示法结合了几何模型的隐函数表示和分析问题的分段连续模型。这种表示可以自动构建，并支持空间分布问题的无网格分析，其中空间离散化不再需要遵守几何域或边界条件。该项目的具体目标包括：(1)发展基于新的混合表示的建模理论，重点关注计算和数值特性；(2)基于新的混合表示，设计和实现集成几何设计和分析的框架和软件环境；(3)计算无网格解的公式、实验研究以及与其他已知解和/或实验结果的比较；(4)探索新技术在传统方法难以解决的问题上的应用，特别是在形状优化和时变几何仿真问题上的应用。如果研究成功，通过集成跨模型、学科和抽象层次的几何设计和分析，该研究有望在产品开发周期中实现重大收益。消除困难和耗时的啮合过程应该会在自动化解决方案方面取得重大进展，这些解决方案目前需要冗长的手动构造、繁琐的分析和特殊用途的工具。

This grant provides funding for developing a new technology for seamless integration of geometric design and engineering analysis tools using a new hybrid computer representation. The new representation combines an implicit function representation of the geometric model with a piecewise continuous model of the analysis problem. Such representations can be constructed automatically and support meshfree analyses of spatially distributed problems, where the spatial discretization no longer needs to conform to the geometric domain or boundary conditions. Specific goals of this project include: (1) development of a modeling theory based on the new hybrid representation, with focus on computational and numerical properties; (2) design and implementation of a framework and software environment integrating geometric design and analysis, based on the new hybrid representation; (3) formulation, experimental studies, and comparison of computed meshfree solutions with other known solutions and/or experimental results; and (4) investigating application of the new technology to problems that are difficult to solve with traditional methods, in particular to shape optimization and simulation problems with time-varying geometries.If successful, this research has the potential to realize major gains in the product development cycle by integrating geometric design and analysis across models, disciplines, and levels of abstraction. Elimination of the difficult and time-consuming meshing procedures should allow major advances in automating solutions to the problems that today require lengthy manual constructions, tedious analysis, and special-purpose tools.