矩形剖分上一类二元样条空间与薄板纯弯曲

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

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.

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.