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

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...

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Bibliographic Details
Published in:Journal of elasticity 2020-07, Vol.140 (1), p.149-169
Main Author: Bîrsan, Mircea
Format: Article
Language:English
Subjects:
Automotive Engineering
Classical Mechanics
Classroom Note
Closed form solutions
Cylindrical shells
Elastic deformation
Elastic shells
Exact solutions
Flexing
Physics
Physics and Astronomy
Shells
Tubes
Citations: Items that this one cites
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Summary: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.
ISSN:0374-3535
1573-2681
DOI:10.1007/s10659-019-09760-w