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

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Yua Tian-quan. Torsion of Elastic Shaft of Revolution Embedded in an Elastic Half Space[J]. Applied Mathematics and Mechanics, 1990, 11(6): 489-498.

Citation:

Yua Tian-quan. Torsion of Elastic Shaft of Revolution Embedded in an Elastic Half Space[J]. Applied Mathematics and Mechanics, 1990, 11(6): 489-498.

Citation:

Yua Tian-quan. Torsion of Elastic Shaft of Revolution Embedded in an Elastic Half Space[J]. Applied Mathematics and Mechanics, 1990, 11(6): 489-498.

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

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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