Applied Mathematics and Mechanics

, Volume 14, Issue 6, pp 507–516

# Saint-Venant's torsion problem for a composite circular cylinder with aninternal edge crack

• Tao Fang-ming
• Tang Ren-ji
Article

## Abstract

In this paper the writer uses Muskhelishvili single-layer potential function solution and single crack solution for the torsion problem of a circular cylinder to discuss the torsion problem of a composite cylinder with an internal crack, and the problem is reduced to a set of mixed-type integral equation with generalized Cauchy-kernel. Then, by using the integration formula of Gauss-Jacobi, the numerical method is established and several numerical examples are calculated. The torsional rigidity and the stress intensity factors are obtained. The results of these examples fit the results obtained by the previous papers better.

### Key words

composite circular cylinder internal crack Cauchy-type integral equation

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### References

1. [1]
Muskhelishvili, N. I.,The Several Basic Questions in Mathematical Elastic Mechanics, Science Press (1958). (Chinese version)Google Scholar
2. [2]
Coyle, E. J. and M. Crochet, Analysis of cylindrical joints of composites materials of torsional loadings,Journal of Reinforced Plastic and Composites,1, 3 (1982), 195–205.Google Scholar
3. [3]
Kuo, Y. M. and H. D. Conway, The torsion of composite tubes and cylinders,International Journal of Solids and Structures,9 (1973), 1553–1565.
4. [4]
Ma Zhi-qing and Tang Ren-ji, Torsion problem solved for a compound cylinder with cracks,Shanghai Journal of Mechanics, 1 (1992), 15–21. (in Chinese)Google Scholar
5. [5]
Tang Ren-ji, Saint-Venant torsion problem for a circular cylinder with cracks,Acta Mechanica Sinica, 4 (1982), 320–340. (in Chinese)Google Scholar
6. [6]
Erdogan, F., G. D. Gupta and T. S. Cook,Numerical Solution of Singular Integral Equations in Fracture Mechanics, G. C. SIH,1 (1973).Google Scholar