Interactive Design with Engineering Analysis

交互式计算机辅助设计主要依赖于在设计过程的各个阶段快速生成和评估众多设计方案的能力。这是为了开发计算基础、算法基础设施和一个完全集成的软件系统，用于交互式参数化机械设计和嵌入式工程分析——这将按需、快速、并行和透明地执行。该技术将在一系列典型的工程分析任务中进行演示，包括那些难以用传统的基于网格的方法解决的任务。该技术的核心是一种用近似距离场到几何特征的函数来表示工程领域问题的新方法。该方法的显著特点是它可以精确地满足所有规定的边界条件，而不需要网格划分。此外，该方法可以与许多其他传统技术相结合，将它们从对网格划分的依赖中解放出来。这种将几何设计和现场建模统一在一个单一的概念和计算框架中，将极大地推动计算机辅助设计和工程领域的发展。这项研究有可能改变物理场的建模、分析和模拟方式——在设计和其他科学和工程领域。它还提供了一个引人注目的教育框架，可以在本科阶段教授，并且已经得到了开发的软件工具的支持，具有前所未有的灵活性和易用性。

Interactive computer-aided design is critically dependent on the ability to rapidly generate and evaluate numerous design alternatives at all stages of the design process. This is to develop computational foundations, algorithmic infrastructure, and a fully integrated software system for interactive parametric mechanical design with embedded engineering analysis -- that will be performed on demand, fast, concurrently, and transparently. The technology will be demonstrated on a range of typical engineering analysis tasks, including those that are difficult to solve with traditional mesh-based methods. At the core of the technology is a novel method for representing engineering field problems in terms of functions of approximate distance fields to geometric features. The salient feature of the approach is that it allows satisfying all prescribed boundary conditions exactly and without meshing. Furthermore, the approach may be combined with many other traditional techniques, liberating them from dependence on meshing. This unification of geometric design and field modeling in a single conceptual and computational framework should substantially advance the field of computer aided design and engineering. This research holds a potential to transform the way physical fields are modeled, analyzed and simulated -- in design and beyond, in other branches of science and engineering. It also offers a compelling educational framework that can be taught on an undergraduate level, and is already supported by the developed software tools with unprecedented flexibility and ease of use.