矩形剖分上一类二元样条空间与薄板纯弯曲

基金项目: 国家自然科学基金资助项目(60533060;69973010;10271022)

A Kind of Bivariate Spline Space Over Rectangular Partition and Pure Bending of Thin Plate

Institute of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116024, P. R. China;

摘要: 构造性地给出了矩形剖分上分片2次一阶光滑的二元样条空间的力学背景．采用力学分析方法,通过在内网线上施加外力偶并适当取值使挠曲面成为分片形式,建立了矩形剖分上一类二元样条与薄板纯弯曲之间的对应关系,并对“光滑余因子”及“协调条件”给出了相应的力学解释．更进一步,通过引入扭矩,对上述空间中任一样条函数建立了相应的力学背景．
- 光滑余因子 /
- 协调条件 /
- 薄板纯弯曲
Abstract: The mechanical background of the bivariate spline space of degree 2 and smoothness 1 on rectangular partition was presented constructively. Making use of mechanical analysis method, by acting couples along the interior edges with suitable evaluations, the deflection surface was divided into piecewise form, therefore, the relation between a class of bivariate splines on rectangular partition and the pure bending of thin plate was established. In addition, the interpretation of smoothing cofactor and conformality condition from the mechanical point of view was given. Furthermore, by introducing twisting moments, the mechanical background of any spline belonging to the above space was set up.
- smoothing cofactor /
- conformality condition /
- pure bending of thin plate

[1]	Schoenberg I J. Contributions to the problem of approximation of equidistant data by analytic functions[J].Quart Appl Math,1946,4(1/2):45-99,112-141.
[2]	王仁宏.多元样条函数及其应用[M].北京：科学出版社,1994.
[3]	王仁宏.多元齿的结构与插值[J].数学学报,1975,18(2):91-106.
[4]	Timoshenko S P,Woinowsky-Krieger S.Theory of Plates and Shells[M].2nd Ed.New York:McGraw-Hill,1959.
[5]	Gere J M, Timoshenko S P.Mechanics of Material[M].3rd Ed.Boston:PWS,1990.
[6]	王仁宏. 任意剖分下的多元样条分析[J].中国科学，数学专辑Ⅰ,1979,(S1):215-226.
[7]	孙家昶, 李炳坤.三向剖分下的二元B样条有限元法[J].数值计算与计算机应用,1991,12(2):102-113.
[8]	刘效尧. 二元B样条有限单元法[J].数值计算与计算机应用,1988,9(3):129-138.
[9]	刘焕文. 解平行四边形板弯曲问题的二元B样条有限元法[J].广西科学,1998,5(1):15-19.

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