摘要
The mechanical background of the bivariate spline space of degree 2 and smoothness 1 on rectangular partition is presented constructively. Making use of mechanical analysis method, by acting couples along the interior edges with suitable evaluations, the deflection surface is divided into piecewise form, therefore, the relation between a class of bivariate splines on rectangular partition and the pure bending of thin plate is established. In addition, the interpretation of smoothing cofactor and conformality condition from the mechanical point of view is given. Furthermore, by introducing twisting moments, the mechanical background of any spline belong to the above space is set up.
The mechanical background of the bivariate spline space of degree 2 and smoothness 1 on rectangular partition is presented constructively. Making use of mechanical analysis method, by acting couples along the interior edges with suitable evaluations, the deflection surface is divided into piecewise form, therefore, the relation between a class of bivariate splines on rectangular partition and the pure bending of thin plate is established. In addition, the interpretation of smoothing cofactor and conformality condition from the mechanical point of view is given. Furthermore, by introducing twisting moments, the mechanical background of any spline belong to the above space is set up.
基金
Project supported by the National Natural Science Foundation of China(Nos.60533060,69973010 and 10271022)
