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样条有限点法

秦荣   

  1. 广西大学
  • 出版日期:1981-02-20 发布日期:1981-02-20

秦荣. 样条有限点法[J]. 数值计算与计算机应用, 1981, 2(2): 68-81.

SPLINE FINITE-POINTS METHOD

  1. Qin Rong Kwangsi University
  • Online:1981-02-20 Published:1981-02-20
有限元法是力学的一个有力工具,目前应用日益广泛,研究工作越来越向深入发展.随着有限元法之后,又产生了有限条法及样条变分法.这些方法,对于规则区域,解题比有限元法方便,而且效率较高,我们在学习这些方法的基础上,发扬优点,改正缺点,提出一个有限点法. 有限点法是以样条函数、梁振动函数(或三角函数)及能量法为基础的,因此又叫样条有限点法.本文主要介绍有限点法的基本原理及计算方法.除特别声明者外,所有符号与常用者同.
In this paper, the author presents a method of spline finite-points and derives acomputational scheme well suited for various types of boundary conditions. the method iseasily carried out with a computer. It bases itself on cubic B-spline, function of beamvibrations (or trigonometric funtions) and potential energy method. It is well suited forthe analysis of structure on regular regions. The method presented has great advantageover the conventional finite element method for the structrues on regular regions. Themain features of this method are matrix with narrow bandwidth and higher accuracy andmore economy in computing storage and time requirements. Moreover, a calculated ex-pample for the bending problem of plate is given, which may show the use of splinefinite-points method. This paper further introduces a simple method for the integrationof spline functions.
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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,4,1965.
[2] O. C. Zienkiewiez, The Finite Element Method in Engineering Science, 1971.
[3] P. M. Preter. Spline and Varitional methods. 1975.
[4] 石钟慈,样条有限元,计算数学,1,1979.
[5] Y. K. Cheung, Finite Strip Method in Structural Analysis, 1976.
[6] A. 格哈利,Structural Analysis, 1971.
[7] 秦荣,有限点法,广西大学印刷,1979.
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