Linear Independence of T-Spline Blending Functions of Degree One for Isogeometric Analysis

Aizeng Wang, Ling Li, Wei Wang, Xiaoxiao Du, Feng Xiao, Zhanchuan Cai and Gang Zhao
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Aizeng Wang: School of Mechanical Engineering & Automation, Beihang University, Beijing 100191, China
Ling Li: School of Mechanical Engineering & Automation, Beihang University, Beijing 100191, China
Wei Wang: School of Mechanical Engineering & Automation, Beihang University, Beijing 100191, China
Xiaoxiao Du: School of Mechanical Engineering & Automation, Beihang University, Beijing 100191, China
Feng Xiao: School of Mechanical Engineering & Automation, Beihang University, Beijing 100191, China
Zhanchuan Cai: State Key Laboratory of Lunar and Planetary Sciences, Macau University of Science and Technology, Macau 999078, China
Gang Zhao: School of Mechanical Engineering & Automation, Beihang University, Beijing 100191, China

Mathematics, 2021, vol. 9, issue 12, 1-13

Abstract: Linear independence of the blending functions is a necessary requirement for T-spline in isogeometric analysis. The main work in this paper focuses on the analysis about T-splines of degree one, we demonstrate that all the blending functions of such T-spline of degree one are linearly independent. The advantage owned by one degree T-spline is that it can avoid the problem of judging whether the model is analysis-suitable or not, especially for occasions that need a quick response from the analysis results. This may provide a new way of using T-spline for a CAD and CAE integrating scenario, since one degree T-spline still guarantees the topology flexibility and is compatible with the spline-based modeling system. In addition, we compare the numerical approximations of isogeometric analysis and finite element analysis, and the experiment indicates that isogeometric analysis using T-spline of degree one can reach a comparable result with classical method.

Keywords: T-splines; CAD/CAE; finite element analysis; isogeometric analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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