Wrinkle-free solutions in the theory of curved circular membranes
type: Item
instance of: scholarly article
title: Wrinkle-free solutions in the theory of curved circular membranes
zbMATH Open document ID: 0792.73044
DOI: 10.1007/BF00128762
published in: Journal of Engineering Mathematics
publication date: 1994-05-08T00:00:00Z
review text: Rotationally symmetric deformations of a curved circular elastic membrane under a vertical surface load are studied, with prescribed radial stresses or radial displacements at the edge. Considering Reissner's theory of thin shells of revolution suffering small strains but arbitrarily large deflections and rotations, the determination of the principal stresses in the membrane is shown to be equivalent to the solution of a single, second-order ODE, expressed in terms of a geodesic variable. Analytical techniques are applied in order to determine a limit curve of those boundary data, which subdivide the parameter range into complementary domains of existence and non-existence of tensile solutions.
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 35Q72
zbMATH DE Number: 561434
zbMATH Keywords: rotationally symmetric deformations
zbMATH Keywords: Reissner's theory
zbMATH Keywords: small strains
zbMATH Keywords: large deflections
zbMATH Keywords: second-order ODE
zbMATH Keywords: geodesic variable
zbMATH Keywords: limit curve
zbMATH Keywords: existence
author: Armin Beck
author: Hans Grabmüller
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 561434