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

9500394 Patrikalakis该项目的目标是构建数值健壮和拓扑可靠的表面的非结构三角网格，这些表面是计算流体力学的复杂固体模型的面。该项目建立在这些研究人员早些时候在区间实体建模方面完成的基础工作的基础上，以解决实体模型询问方法中的基本稳健性问题。研究计划首先涉及将较旧的遗留设计转换为区间实体模型，以最大限度地提高该方法在大规模工业问题中的影响，而不仅仅是学术问题。这项研究还将探索分段线性和拓扑可靠的平面轮廓逼近的一些基本元素，然后是可以表示任意复杂的空间区间非均匀有理B-样条曲线的三维轮廓。这将扩展到探索面片和整个固体的表面三角剖分的特征，随后是三维区域四面体剖分。这一系列的问题，其中较早问题的解决有助于解决更复杂的问题，预计将允许开发出可靠和有效的整体算法来解决此类问题。一个产业咨询委员会将跟踪这项工作，并确保其与长期产业利益的相关性。这项工作旨在提高知识的状态，使用不精确或离散的计算机算法来稳健地询问复杂对象的几何形状，并发展必要的理论和相关算法，以形成未来计算机辅助设计和计算机辅助制造(CAD/CAM)系统的智能基础。它可以大大缩短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系统提供了良好和灵活的基础，因为这些系统将需要在对象的设计、制造和运行期间对复杂对象的运动学、流体、结构和动力学过程进行精确的仿真。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.