| 基于弹性理论的二元样条与黄金分割 |
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| 引用本文： | 王仁宏,常锦才.基于弹性理论的二元样条与黄金分割[J].数学研究及应用,2011,31(1):1-11. |
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| 作者姓名： | 王仁宏 常锦才 |
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| 作者单位： | 大连理工大学数学科学研究所, 辽宁 大连 116024;大连理工大学数学科学研究所, 辽宁 大连 116024; 河北理工大学理学院, 河北 唐山 063009 |
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| 基金项目： | 国家自然科学基金 (Grant Nos.60533060; 60373093; 10726068), 河北省自然科学基金 (Grant Nos.A2009000735; A2010000908), 河北省教育厅基金 (Grant No.2009448), 上海市现代应用数学重点实验室基金 (Grant No.09FG067). |
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| 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.
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| 关 键 词： | multivariate spline smoothing cofactor conformality condition bending of thin plate golden section. |
| 收稿时间： | 4/2/2009 12:00:00 AM |
| 修稿时间： | 2009/10/14 0:00:00 |
Bivariate Splines and Golden Section Based on Theory of Elasticity |
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| Ren Hong WANG and Jin Cai CHANG.Bivariate Splines and Golden Section Based on Theory of Elasticity[J].Journal of Mathematical Research with Applications,2011,31(1):1-11. |
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| Authors: | Ren Hong WANG and Jin Cai CHANG |
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| Institution: | 1. School of Mathematical Sciences,Dalian University of Technology,Liaoning 116024,P.R.China
2. 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. |
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| Keywords: | multivariate spline smoothing cofactor conformality condition bending of thin plate golden section |
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