Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Buckling of cylindrical shells with small curvature

Author: John Mallet-Paret
Journal: Quart. Appl. Math. 35 (1977), 383-400
MSC: Primary 73.35
DOI: https://doi.org/10.1090/qam/478917
MathSciNet review: 478917
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Abstract: We consider the bifurcation buckling of a rectangular plate with an imperfection of magnitude $ \alpha $ under an applied lateral force of magnitude $ \lambda $. The analysis allows the parameters $ \left( {\lambda ,\alpha } \right)$ to vary independently in a neighborhood of some $ \left( {{\lambda _0}, 0} \right)$, and describes all buckled states of small magnitude. If the plate is represented by the domain $ \left( {0, \sqrt 2 } \right) \times \left( {0, 1} \right)$ in $ {R^2}$, then the lateral force is applied to the edges $ x = 0$, $ \sqrt 2 $, and the imperfection is a small vertical displacement of the form $ z = \left( {\alpha /2} \right){y^2}\left( {\sigma x + \tau } \right)$, where $ \sigma $ and $ \tau $ are fixed. Roughly, then, the plate has a small curvature in the $ y$-direction, of magnitude $ \alpha \left( {\sigma x + \tau } \right)$.

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DOI: https://doi.org/10.1090/qam/478917
Article copyright: © Copyright 1977 American Mathematical Society

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