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State of stress around a circular opening in orthotropic spherical shells with linearly varying thickness

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Polymer Mechanics Aims and scope

Abstract

The state of stress of a thin spherical shell of orthotropic material of linearly varying thickness weakened by a circular opening at the pole is investigated. A solution in Bessel functions is constructed for the differential equations describing the state of stress of the shell. Graphs are presented for the dependence of the stress concentration coefficients at the edge of the opening and the uniformity of the state of stress on the coefficient characterizing the variation of the thickness. It is shown that by a suitable choice of this coefficient it is possible to obtain a shell in which the stresses at the edge of the opening and on the equator are equal.

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Literature cited

  1. A. S. Ambartsumyan, Theory of Anisotropic Shells [in Russian], Moscow (1961).

  2. G. A. Van Fo Fy and O. V. Galushchak, in: Calculation and Design of Glass-Reinforced Plastic Articles [in Russian], Kiev (1972), p. 106.

  3. G. N. Savin, Stress Distribution around Openings in Plates and Shells [in Russian], Kiev (1968).

  4. G. N. Watson, Theory of Bessel Functions, Cambridge Univ. (1966).

  5. B. P. Demidovich and I. A. Maron, Fundamentals of Computational Mathematics [in Russian], Moscow (1970).

  6. G. A. Van Fo Fy, Mekhan. Polim., No. 4, 593 (1966).

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Authors
  1. O. V. Galushchak
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  2. I. K. Koshevoi
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Additional information

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 2, pp. 294–298, March–April, 1974.

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Galushchak, O.V., Koshevoi, I.K. State of stress around a circular opening in orthotropic spherical shells with linearly varying thickness. Polymer Mechanics 10, 250–253 (1974). https://doi.org/10.1007/BF00860822

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  • DOI: https://doi.org/10.1007/BF00860822

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