Bivariate Splines and Golden Section Based on Theory of Elasticity
Received:April 02, 2009  Revised:October 14, 2009
Key Word: multivariate spline   smoothing cofactor   conformality condition   bending of thin plate   golden section.  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant Nos.60533060; 60373093; 10726068), the Natural Science Foundation of Hebei Province (Grant Nos.A2009000735; A2010000908), Research Project of Hebei Educational Committee (Grant No.2009448) and Shanghai Key Laboratory for Contemporary Applied Mathamtics (Grant No.09FG067).
Author NameAffiliation
Ren Hong WANG School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
Jin Cai CHANG School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China
School of Sciences, Hebei Polytechnic University, Hebei 063009, P. R. China 
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Abstract:
      Splines are important in both mathematics and mechanics. We investigate the relationships between bivariate splines and mechanics in this paper. The mechanical meanings of some univariate splines were viewed based on the analysis of bending beams. For the 2D case, the relationships between a class of quintic bivariate splines with smoothness 3 and bending of thin plates are presented constructively. Furthermore, the variational property of bivariate splines and golden section in splines are also discussed.
Citation:
DOI:10.3770/j.issn:1000-341X.2011.01.001
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