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Stresses in an elastic circular cylinder with a prolate spheroidal cavity under torsion

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Abstract

This paper contains an exact solution for the stresses arising from torsion of an elastic circular cylinder with a prolate spheroidal cavity. The solution, which is represented as a combination of a solution that is regular outside the cavity and a solution regular in the solid infinite circular cylinder, is deduced with the aid of a harmonic displacement potential. The two harmonic functions needed are given by simple expressions referred to cylindrical and prolate spheroidal coordinates. The boundary conditions on the surfaces of the cylinder and of the cavity are satisfied by using the relations between cylindrical and prolate spheroidal harmonics. Numerical results are presented for different shapes and sizes of the cavity, and the ensuing stress distribution in the neighborhood of the cavity is illustrated graphically.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Saitama University, 255, Shimo-Okubo, 338, Urawa, Japan

    Toyomi Uchiyama & Eiichiro Tsuchida

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  1. Toyomi Uchiyama
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  2. Eiichiro Tsuchida
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Uchiyama, T., Tsuchida, E. Stresses in an elastic circular cylinder with a prolate spheroidal cavity under torsion. J Elasticity 20, 41–52 (1988). https://doi.org/10.1007/BF00042139

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  • DOI: https://doi.org/10.1007/BF00042139

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