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

Mathematics

Gang Zhao¹  Wei Wang¹  Ling Li¹  Aizeng Wang¹  Feng Xiao¹  Xiaoxiao Du¹  Zhanchuan Cai² 

[1] 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;

关键词: T-splines;    CAD/CAE;    finite element analysis;    isogeometric analysis;   

DOI  :  10.3390/math9121346

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown