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，使用新的混合计算机表示法将几何设计和工程分析工具无缝集成。 新的表示法将几何模型的隐函数表示与分析问题的分段连续模型相结合。 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符合几何域或边界条件。 本计画的具体目标包括：（1）发展以新混合表示法为基础的造型理论，着重于计算与数值特性：（2）设计与实作以新混合表示法为基础的整合几何设计与分析的架构与软体环境;（3）公式化、实验研究以及计算的无网格解与其他已知解和/或实验结果的比较;以及（4）研究新技术在传统方法难以解决的问题上的应用，特别是形状优化和具有时变几何形状的模拟问题。如果成功，这项研究有可能在产品开发周期中实现重大收益，通过集成几何设计和分析跨模型，学科，和抽象层次。 消除困难和耗时的网格化过程应该允许在自动化解决方案的问题，今天需要冗长的手动构造，繁琐的分析，和专用工具的重大进展。

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.