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...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.展开更多
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 ...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.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.60533060,69973010 and 10271022)
文摘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Supported by the National Natural Science Foundation of China (Grant Nos. 6053306060373093+4 种基金10726068)the Natural Science Foundation of Hebei Province (Grant Nos. A2009000735A2010000908)Research Projectof Hebei Educational Committee (Grant No.2009448)Shanghai Key Laboratory for Contemporary AppliedMathamtics (Grant No.09FG067)
文摘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.
