Bivariate Splines and Golden Section Based on Theory of Elasticity  

作　　者：Ren Hong WANG Jin Cai CHANG 

机构地区：[1]School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China [2]School of Sciences, Hebei Polytechnic University, Hebei 063009, P. R. China

出　　处：《Journal of Mathematical Research and Exposition》2011年第1期1-11,共11页数学研究与评论（英文版）

基　　金：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 Projectof Hebei Educational Committee (Grant No.2009448);Shanghai Key Laboratory for Contemporary AppliedMathamtics (Grant No.09FG067)

摘　　要：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.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.

关 键 词：multivariate spline smoothing cofactor conformality condition bending of thin plate golden section. 

分 类 号：O241.5[理学—计算数学] O343.2[理学—数学]