适合分析的T样条

发布时间：2018-05-17 14:32

本文选题：等几何分析 + T样条　；参考：《中国科学技术大学》2016年博士论文

【摘要】：在计算机辅助几何设计分析过程中,传统的有限元分析不能很好与设计结合起来,而等几何分析用样条函数同时作为几何基和分析基,提供了工程设计与分析相融合的可能性。目前,最适合应用在等几何分析中的样条函数是T样条。T样条支持局部细分,可以无缝合并,很好的解决了非均匀有理B样条(NURBS)在设计中的局限性。但是T样条还存在很多缺点,T样条的混合函数存在可能的线性相关性,这意味着会有一些T样条不适合用在等几何分析中。[117]提出了适合分析的T样条(AST样条),在兼具T样条优点的同时还具有混合函数线性无关性及单位分解性,满足了等几何分析的需求。本文在第三章,将双三次AST样条推广到任意次数,并证明了它的线性无关性和单位分解性。样条空间的两大算法,节点插入和升阶,在NURBS中已经取得了很好的进展,而T样条包括AST样条的升阶算法还没有人进行关注。本文在接下来研究讨论了这一问题,为等几何分析的发展包括p-细分,k-细分,甚至是局部的k-细分提供了理论基础。我们在本文中还提出了拟适合分析的T样条,它是一类比AST样条更具一般性的T样条,满足混合函数线性无关性。本文基于拟适合分析的T样条给出了一种优化的局部细分算法,不需要中间过程将一般的T样条转换成混合函数线性无关的T样条,保证了细分之后的T样条是拟适合分析的,可以直接用于分析中。
[Abstract]:In the process of computer-aided geometric design analysis, the traditional finite element analysis can not be well combined with the design, while the spline function is used as the geometric basis and the analysis basis, which provides the possibility of the integration of engineering design and analysis. At present, the most suitable spline function for isometric analysis is T-spline. T-spline supports local subdivision, which can be merged seamlessly, which solves the limitation of non-uniform rational B-spline Nurbs in design. However, there are still many shortcomings in T-spline mixed functions with possible linear correlation. This means that some T splines are not suitable for use in isometric analysis. [117] A T spline AST spline suitable for analysis is proposed, which has the advantages of both T spline and mixed function linear independence and unit decomposition. The requirement of isometric analysis is satisfied. In chapter 3, we generalize the bicubic AST spline to any degree, and prove its linear independence and unit decomposition. Two algorithms of spline space, node insertion and order upgrading, have made good progress in NURBS, but the algorithm of T spline including AST spline has not been paid attention to. In this paper, the problem is discussed, which provides a theoretical basis for the development of isometric analysis, including p- subdivision k- subdivision and even local k- subdivision. In this paper, we also propose a kind of T spline which is more general than AST spline and satisfies the linear independence of mixed function. In this paper, an optimized local subdivision algorithm based on the quasi-suitable T-spline is presented. It does not need the intermediate process to convert the general T-spline into the linear independent T-spline of the mixed function, which ensures that the T-spline after subdivision is quasi-suitable for analysis. Can be directly used in analysis.
【学位授予单位】：中国科学技术大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP391.7;O241.82

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