A unified approach to construct generalized B-splines for isogeometric applications
A unified approach to construct generalized B-splines for isogeometric applications
复制标题
为等几何应用构建广义 B 样条的统一方法
DOI：
10.1007/s11424-017-6026-7
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发表时间：
2017-05
影响因子：
2.1
通讯作者：
Guozhao Wang
中科院分区：
文献类型：
--
作者：
徐岗;Ningning Sun;Jinlan Xu;Kin-chuen Hui;Guozhao Wang
广义b样条已成为等几何分析（IGA）的几何建模和数值模拟工具。然而，以往IGA中使用的三角广义b样条或双曲广义b样条等模型并不是二次曲线和多项式参数曲线/曲面的统一数学表示。本文提出了在{α(t),β(t),ξ(t),η(t), 1,t，···，n- 4}所张成的空间上构造广义非均匀b样条的统一方法，并研究了相应的求解偏微分方程的等几何分析框架。与NURBS-IGA方法相比，该框架具有精度高、导数和积分计算方便等优点。此外，利用所提出的样条模型，可以在以超越曲线/曲面为界的计算域上进行等几何分析，如圆的渐开线、螺旋/螺旋面、链线/链线和摆线。最后给出了几个等几何热传导问题的数值算例，验证了所提方法的有效性。
Generalized B-splines have been employed as geometric modeling and numerical simulation tools for isogeometric analysis (IGA for short). However, the previous models used in IGA, such as trigonometric generalized B-splines or hyperbolic generalized B-splines, are not the unified mathematical representation of conics and polynomial parametric curves/surfaces. In this paper, a unified approach to construct the generalized non-uniform B-splines over the space spanned by {α(t),β(t),ξ(t),η(t), 1,t, · · ·,tn–4} is proposed, and the corresponding isogeometric analysis framework for PDE solving is also studied. Compared with the NURBS-IGA method, the proposed frameworks have several advantages such as high accuracy, easy-to-compute derivatives and integrals due to the non-rational form. Furthermore, with the proposed spline models, isogeometric analysis can be performed on the computational domain bounded by transcendental curves/surfaces, such as the involute of circle, the helix/helicoid, the catenary/catenoid and the cycloid. Several numerical examples for isogeometric heat conduction problems are presented to show the effectiveness of the proposed methods.
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DOI：
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发表时间：
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影响因子：
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发表时间：
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期刊：
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影响因子：
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