Towards a New Generation of Robust Interrogation Methods in Computer-Aided Design and Computer-Aided Manufacturing

这个项目的目标是构建数字上鲁棒的和拓扑上可靠的曲面的非结构三角形网格，这些曲面是用于计算流体动力学的复杂实体模型的面。该项目建立在这些研究人员早期在区间实体建模中完成的基础工作之上，以解决实体模型询问方法中的基本鲁棒性问题。研究计划包括首先将旧的遗留设计转换为间隔实体模型，以最大限度地提高该方法在大规模工业中的影响，而不仅仅是学术问题。研究还将探索平面轮廓的分段线性和拓扑可靠逼近的一些基本要素，然后是可以表示任意复杂度的空间间隔非均匀有理b样条曲线的三维轮廓。这将扩展到探索表面斑块和整个固体的表面三角化特征，然后是三维域四面体化。这一系列的问题，其中早期问题的解决有助于解决更复杂的问题，期望允许开发一个可靠和有效的整体算法来解决这类问题。一个工业咨询委员会将跟踪这项工作，并确保其与长期工业利益有关。这项工作旨在通过使用不精确或离散的计算机算法来强大地询问复杂物体的几何形状，并发展必要的理论和相关算法，这些理论和算法可以形成未来计算机辅助设计和计算机辅助制造（CAD/CAM）系统的知识基础。它可以大大减少产品设计所需的时间，从而降低生产成本。它还可以降低设计过程的失败率。它为未来的CAD/CAM系统提供了坚实而灵活的基础，因为这些系统需要在复杂物体的设计、制造和运行期间对其进行精确的运动学、流体、结构和动力学过程的模拟。通过这项研究获得的知识和经验将被整合到麻省理工学院的两门研究生课程的教学课程中。

9500394 Patrikalakis The objective of this project is to construct numerically robust and topologically reliable unstructured triangular meshes of surfaces which are the faces of complex solid models for computational fluid dynamics. The project builds on fundamental work completed earlier by these investigators in interval solid modeling to address basic robustness problems in interrogation methods for solid models. The research plan involves first the conversion of older legacy designs to interval solid models to maximize impact of the method in large-scale industrial rather than only academic problems. The research will also explore some of the essential elements of piecewise linear and topologically reliable approximation of planar contours, followed by three dimensional contours that can represent space interval non-uniform rational B-spline curves of arbitrary complexity. This will be extended to explore features of surface triangularization of surface patches and entire solids, followed by three dimensional domain tetrahedrization. This sequence of problems, where the solution of an earlier problem assists in the solution of a more complex problem, is expected to allow the development of a reliable and efficient overall algorithm for solving such problems. An industrial advisory committee will follow the work and assure its relevance to long-term industrial interests. This work seeks to advance the state of knowledge in robustly interrogating the geometry of complex objects using imprecise or discrete computer arithmetic and developing the necessary theory and relevant algorithms which can form the intellectual basis for computer-aided design and computer-aided manufacturing (CAD/CAM) systems of the future. It could significantly decrease the time required during product design and hence decrease production cost. It could also decrease the rate of failure of design processes. It provides a sound and flexible basis for future CAD/CAM systems because these will need to includ e precise simulation of kinematics, fluid, structural and dynamical process on complex objects during the design, manufacturing and operational period of the object. The knowledge and experience gained through this research will be integrated into the teaching curriculum of two graduate courses at MIT.