面向CAD/CAE的T样条实体建模理论与应用研究

等几何分析将精确几何模型直接用于分析，相比于传统等几何分析在精度和效率上有着显著的优势。T样条作为新型几何造型技术允许拓扑结构中T节点的存在，弥补了传统NURBS模型在局部细分和曲面拼接方面的缺陷，也为等几何分析提供了精确的几何模型。但目前许多几何实体模型使用边界网格曲面表示或者边界样条曲面表示，如何将这种传统边界曲面模型转换为T样条曲面模型以及可直接用于分析的T样条实体模型是理论界和工业界亟需解决的难题。基于此，本项目将重点研究：1）任意边界模型向T样条曲面模型的转化；2）由任意边界样条曲面模型构建T样条实体模型；3）构建适分析T样条实体模型，搭建基于T样条实体模型的等几何分析框架，研究基于等几何分析的T样条实体模型局部细化技术。项目研究成果将对推广T样条造型技术在CAD领域的应用、推进等几何分析在工程实际中的应用进程、CAD和CAE领域的无缝集成具有重要意义。

Isogeometric analysis (IGA) employs exact geometrical models to analyze and occupies the dominant position of accuracy and efficiency in comparison with traditional finite element analysis. As a new modeling technology, T-spline allows the existence of T-junction and solves the problems in local refinement and surface joining produced by NURBS technology. Moreover, it provides the exact geometrical models for IGA. The numerous solid models, so far, are represented by boundary mesh models or boundary spline models. Thus, how to convert the boundary surface models to T-spline surfaces and T-spline solid models becomes the impending problem in theoretical and industrial circles. Based on this, this research will focus on the following points:(1) Converting arbitrary surface models to T-spline surface models; (2) Converting arbitrary spline surface models to T-spline solid models; and (3) Constructing analysis-suitable T-spline solid models, building the framework of IGA based on T-spline solids, considering the self-adaptive local refinement of IGA based on T-spline solid. The achievement of research will extend the application of T-splines modeling in the field of CAD, and promote the process of IGA’s application in engineering fields. In addition, it is important to the integration of CAD and CAE fields.