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

Author

Listed:
  • Aizeng Wang

    (School of Mechanical Engineering & Automation, Beihang University, Beijing 100191, China
    State Key Laboratory of Lunar and Planetary Sciences, Macau University of Science and Technology, Macau 999078, China
    State Key Laboratory of Virtual Reality Technology & Systems, 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
    State Key Laboratory of Virtual Reality Technology & Systems, Beihang University, Beijing 100191, China)

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.

Suggested Citation

  • Aizeng Wang & Ling Li & Wei Wang & Xiaoxiao Du & Feng Xiao & Zhanchuan Cai & Gang Zhao, 2021. "Linear Independence of T-Spline Blending Functions of Degree One for Isogeometric Analysis," Mathematics, MDPI, vol. 9(12), pages 1-13, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1346-:d:572735
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