Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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On finite displacements of curved annular elastic membranes without wrinkling


Authors: Armin Beck and Hans Grabmüller
Journal: Quart. Appl. Math. 53 (1995), 527-550
MSC: Primary 73G05; Secondary 73K10
DOI: https://doi.org/10.1090/qam/1343465
MathSciNet review: MR1343465
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Abstract: Axisymmetric deformations of curved annular elastic membranes subjected to vertical surface loads and radial edge loads or displacements are considered within Reissner's finite-rotation theory of thin shells of revolution, assuming linear stress-strain relations. The principal stresses in the membrane are determined by the solutions of a nonlinear second-order ODE, dependent on a geodesic variable. Analytical methods are used in order to determine the range of those boundary data for which the solutions of the differential equation are wrinkle-free in the sense that both the radial and the circumferential stress components are nonnegative everywhere.


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DOI: https://doi.org/10.1090/qam/1343465
Article copyright: © Copyright 1995 American Mathematical Society


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