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样条有限元

石钟慈,   

  1. 中国科技大学,
  • 出版日期:1979-01-14 发布日期:1979-01-14

石钟慈,. 样条有限元[J]. 计算数学, 1979, 1(1): 50-72.

ON SPLINE FINITE ELEMENT METHOD

  1. Shih Chung-tze (China University of Science and Technology)
  • Online:1979-01-14 Published:1979-01-14
本文用三次B样条变分方法解规则区域上板梁组合弹性结构的平衡问题.推导出了适用于各种边界条件的统一计算格式,便于在计算机上实现.与通常有限元相比,具有计算量少、精确度高等显著特点.文中对自然边界条件作为约束条件的影响给予了考虑,并以板的弯曲问题为例说明影响极微.给出了几个数值的例子.
In this paper a finite element method based on cubic B-spline is presented to obtainnig approximate solution for the equilibrium problems of elastic composite structures on regular regions.A computational scheme well suited for various types of boundary conditions is derived.It is easily carried out by a computer.In comparison with the usual nodal finite element method, the main features of the present method are higher accuracy and more economy in computing storage and time requirements.The effect of imposing natural boundary condition as constraints is considered and it is shown by a plate bending problem that this effect is quite superficial.Several numerical results are presented.
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[1] 冯康,基于变分原理的差分格式,应用数学与计算数学,2:4(1965) ,238-262.
[2] O. C. Zienkiewicz. The Finite Element Method in Engineering Science, 1971.
[3] G. Strang, G. J. Fix. An Analysis of the Finite Element Method. 1973
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