A kind of bivariate spline space over rectangular partition and pure bending of thin plate

The mechanical background of the bivariate spline space of degree 2 and smoothness 1 on rectangular partition is presented constructively.Making use of mechan- ical 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 con- dition 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.     

应用虚拟功的互等定理求解均载悬臂厚矩形板的弯曲

悬臂矩形板的弯曲问题一直是平板经典理论中的著名难题,利用中厚板虚拟功的互等定理,借助付宝连提出的角点静力边界条件,得到了均布载荷作用下悬臂厚矩形板弯曲的封闭解析解,并采用现代数值方法和计算软件对所得解析解进行了数值计算.结果表明功的互等法是求解中厚板弯曲问题的一个简明有效的方法.     

基于弹性理论的二元样条与黄金分割

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.     

矩形剖分上一类二元样条空间与薄板纯弯曲

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．