七次B样条有限元的计算格式

Septuple B spline Finite Element Method

根据ｋ次样条函数的定义得到了七次Ｂ样条，进而应用变分原理导出了适用于各种边界条件且便于在计算机上实现的规则区域上弹性薄板静力问题的统一计算格式．七次Ｂ样条对泛函包括直至六次函数导数的变分问题具有适用性强、精度高等独特的优越性，是对Ｂ样条的有益补充．用七次Ｂ样条有限元对矩形板弯曲问题进行了计算，并与用五次Ｂ样条有限元计算的结果进行了比较．结果说明，七次Ｂ样条有限元比五次Ｂ样条有限元具有精度高、计算量少等优点．

The septuple B spline is attained directly in accordance with the definition of k times spline function firstly. And then, a unified calculation scheme suitable for various boundary conditions and for operations on the computer is derived, and it is used to solve the static problem of elastic thin plate on regular region. The septuple B spline stated in this paper has unique superiority as it is more useful and more accurate for the variational problem in which the functional analysis has a functional differential up to six times, so it is a useful supplement to the B spline. At last, a problem is resolved by using the septuple B spline finite element method. Compared with other methods, the septuple B spline finite element method has the advantages of simplicity and higher accuracy.