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.

中文翻译：

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壳的 Koiter 理论中的闭式圣维南解

在本文中，我们使用 Koiter 模型研究圆柱形线弹性壳的变形。我们为由各向同性和均质弹性材料制成的细圆柱管制定并解决了松弛圣维南问题。为此，我们采用了先前在三维弹性理论中建立的方法。我们提出了一个通用的求解程序，以确定拉伸、弯曲、扭转和挠曲问题的封闭形式的解决方案。我们注意到这些解与实心圆柱体的经典圣维南解的类比和形式相似性。还讨论了圆柱壳的特殊情况。