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On the torsion of a cylinder with several cracks

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Abstract

In this paper, based on paper [1], the analytic expression of the torsion function for a cylinder containing arbitrary oriented cracks is obtained. The problem is reduced to solve a system of singular integral equations for the unknown dislocation density functions. Using the numerical method of the singular integral equations[2,7] the torsional rigidities and stress intensity factors are evaluated for several multicracked cylinders. Next, the creak-cutting method[5] is firstly extended to lve the torsion problem for a rectangular prism. The numerical results show that the method presented here is successful.

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References

  1. Tang Ren-ji, Saint-Venant's torsion problem for a circular cylinder with cracks,Acta Mechanica Sinica, 4 (1982). (in Chinese)

  2. Wang Xiao-chun, Torsion of cylinders with non-circular cross-section and involving multicracks, The thesis for a master degree, Lanzhou University (1986). (in Chinese)

  3. Yin Chang-yan, Torsional stresses and stress intensity factors of circular cylinder with internal longitudinal crack,Acta Mechanica Solida Sinica, 3 (1982). (in Chinese)

  4. Chien Wei-zang, Lin Hong-sun, Hu Hai-chang and Yeh Kai-yuan,Theory of Torsion for Elastic Prism, Science Press (1956). (in Chinese)

  5. Tang Ren-ji, An integral equation method to analyze the tension and the stress singular behavior at the corner of a clamped rectangular plate,Acta Mechanica Sinica, 1 (1986). (in Chinese)

  6. Muskhelishvili, N.I.,Singular Integral Equations Shanghai Science and Technology Press (1966). (Chinese version)

  7. Erdogan, F., Mixed boundary-value problems in mechanics,Mechanics Today, 4 (1978).

  8. Timoshenko, S.P. and J.N. Goodier,Theory of Elasticity, third edition, New York (1970).

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Authors and Affiliations

  1. Lanzhou University, Lanzhou

    Wang Xiao-chun & Tang Ren-ji

Authors
  1. Wang Xiao-chun
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  2. Tang Ren-ji
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Projects Supported by the Science Fund of the Chinese Academy of Sciences.

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Xiao-chun, W., Ren-ji, T. On the torsion of a cylinder with several cracks. Appl Math Mech 9, 745–754 (1988). https://doi.org/10.1007/BF02465398

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  • DOI: https://doi.org/10.1007/BF02465398

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