| 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 |
| 基于弹性理论的二元样条与黄金分割 |
| Bivariate Splines and Golden Section Based on Theory of Elasticity |
| 投稿时间：2009-04-02 修订日期：2009-10-14 |
| DOI：10.3770/j.issn:1000-341X.2011.01.001 |
| 中文关键词: 多元样条 光滑余因子 协调条件 薄板弯曲 黄金分割. |
| 英文关键词:multivariate spline smoothing cofactor conformality condition bending of thin plate golden section. |
| 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). |
|
| 摘要点击次数: 2586 |
| 全文下载次数: 1835 |
| 中文摘要: |
| 样条函数在数学与力学中均占有重要地位, 本文研究二元样条与力学之间的联系. 首先,基于梁弯曲的分析回顾了一些一元样条的力学意义. 其次, 构造性的建立了一类5次3阶光滑的二元样条与薄板弯曲之间的联系. 更进一步, 讨论了二元样条的变分性质及样条中的黄金分割. |
| 英文摘要: |
| 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. |
| 查看全文 查看/发表评论 下载PDF阅读器 |
