A unified approach to construct generalized B-splines for isogeometric applications
| Autor: | Guozhao Wang, Gang Xu, Ningning Sun, Jinlan Xu, Kin-Chuen Hui |
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| Rok vydání: | 2017 |
| Předmět: |
Helicoid
Mathematical analysis 010103 numerical & computational mathematics Isogeometric analysis Computer Science::Numerical Analysis 01 natural sciences Mathematics::Numerical Analysis 010101 applied mathematics Spline (mathematics) Involute Catenoid Conic section Bounded function Computer Science (miscellaneous) 0101 mathematics Parametric equation Information Systems Mathematics |
| Zdroj: | Journal of Systems Science and Complexity. 30:983-998 |
| ISSN: | 1559-7067 1009-6124 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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