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.
