嵌入弹性半空间的弹性迴转轴的扭转<sup>*</sup>

云天铨

嵌入弹性半空间的弹性迴转轴的扭转^*

云天铨

华南理工大学力学系

基金项目: * 国家自然科学基金资助项目

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出版历程
- 收稿日期: 1989-11-10
- 刊出日期: 1990-06-15

Torsion of Elastic Shaft of Revolution Embedded in an Elastic Half Space

Yua Tian-quan

Department of Engineering Mechanics, South China University of Technology, Guangzhou

摘要

摘要: 本文用线载荷积分方程法(LLIEM)研究嵌在弹性半空间的弹性迴转轴的扭转问题.将“点环力偶(PRC)”和“半空间点环力偶(PRCHS)”分别分布于迴转轴内和外的轴线上,就能将本问题归结为一维的Fredholm第一种积分方程组.直接用离散法求解时,会发现有时解是不稳定的,也就是病态情形.本文采用以带小参数的Fredholm第二种积分方程代替病态的Fredholm第一种积分方程的方法可以得到稳定的解,此法比Tikhonov正规化法简单,易于在计算机上运行.文中给出圆维、圆柱、圆锥-圆柱、抛物线轴等数值例子.

Abstract: The problem of torsion of elastic shaft of revolution embedded in an elastic half space is studied by the Line-Loaded Integral Equation Method (LLIEM). The problem is reduced to a pair of one-dimensional Fredholm integral equations of the first kind due to the distributions of the fictitious loads "Point Ring Couple (PRC)"and "Point Ring Couple in Half Space (PRCHS)"on the axis of symmetry in the interior and external ranges of the shaft occutied respectively. The direct discrete solution of this integral equations may be unstable, i.e. an ill-posed case occurs. In this paper, such an ill-posed Fredholm integral equation of first kind is replaced by a Fredholm integral equation of the second kind with small parameter, which provides a stable solution. This method is simpler and easier to carry out on a computer than the Tikhonov's regularization method for ill-posed problems. Numerical examples for conical, cylindrical, conical-cylindrical, and parabolic shafts are given.

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参考文献(9)

[1]	云天铨,嵌在弹性半空间的刚性变直径圆轴的扭转,应用数学和力学,9, 5 (1988), 411-416.
[2]	Karasudhi,K.,R.K.N.D.Rajapake and B.Y. Hwang, Torsion of a long cylindrical elastic bar partially embedded in a layered elastic half space, Int. J. of Solids and Structures, 20,1(1984),1-11.
[3]	Delves,L.M.and J.Walsh, Numerical Solution of Integral Equations, Oxford, Clarendon(1974),182-184.
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[6]	Morozov, V.A., Methods for Solving Incorrectly Posed Problem, Springer-Verlag, New York(1984).
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[8]	云天铨,点圆力偶作用于弹性全空间的解及其应用,华中工学院学报,总40期(1982), 98-108.
[9]	云天铨,回转体扭转问题的一个积分方程解法,华中工学院学报,3 (1979,97-104, MR*81Ms73028, (English edition, J, H, I, T 1 (1979), 82-97.)