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Closed-Form Saint-Venant Solutions in the Koiter Theory of Shells

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Abstract

In this paper we investigate the deformation of cylindrical linearly elastic shells using the Koiter model. We formulate and solve the relaxed Saint-Venant’s problem for thin cylindrical tubes made of isotropic and homogeneous elastic materials. To this aim, we adapt a method established previously in the three-dimensional theory of elasticity. We present a general solution procedure to determine closed-form solutions for the extension, bending, torsion and flexure problems. We remark the analogy and formal resemblance of these solutions to the classical Saint-Venant’s solutions for solid cylinders. The special case of circular cylindrical shells is also discussed.

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Acknowledgements

This research has been funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation; project no. 415894848).

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  1. Fakultät für Mathematik, Universität Duisburg-Essen, Thea-Leymann Str. 9, 45127, Essen, Germany

    Mircea Bîrsan

  2. Department of Mathematics, Alexandru Ioan Cuza University of Iaşi, Blvd. Carol I, no. 11, 700506, Iaşi, Romania

    Mircea Bîrsan

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Correspondence to Mircea Bîrsan.

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Bîrsan, M. Closed-Form Saint-Venant Solutions in the Koiter Theory of Shells. J Elast 140, 149–169 (2020). https://doi.org/10.1007/s10659-019-09760-w

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