NDLI: Linearly elastic annular and circular membranes under radial, transverse, and torsional loading. Part I: large unwrinkled axisymmetric deformations

Content Provider	Springer Nature Link
Author	Plaut, R. H.
Copyright Year	2008
Abstract	Three theories for determination of the equilibrium states of initially flat, linearly elastic, rotationally symmetric, taut membranes are considered: Föppl-von Kármán theory, Reissner’s theory, and a new generalization of Reissner’s theory that does not restrict the strains to be small. Attention is focused on annular membranes, but circular membranes are also treated. Large deformations are allowed, and the equilibrium equations are written in terms of transverse, radial, and circumferential displacements. Problems considered include radial stretching, transverse displacement of the inner edge, an adhesive punch pull-off test on a circular blister, transverse pressure, ponding of annular and circular membranes, a vertical distributed load with a vertically sliding outer membrane edge, pull-in (snap-down, jump-to-contact) instability of a MEMS device, torsion of the inner or outer edge of a stretched membrane, and a combination of radial stretching, vertical displacement, and torsion. Results for the three theories are compared. Closed-form solutions are available in a few cases, but usually a shooting method is utilized to obtain numerical solutions for displacements, strains, and stresses. Conditions for the onset of wrinkling are determined. In the second part of this two-part study, small vibrations about equilibrium configurations are analyzed.
Starting Page	79
Ending Page	99
Page Count	21
File Format	PDF
ISSN	00015970
Journal	Acta Mechanica
Volume Number	202
Issue Number	1-4
e-ISSN	16196937
Language	English
Publisher	Springer Vienna
Publisher Date	2008-06-10
Publisher Place	Vienna
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Engineering Thermodynamics, Heat and Mass Transfer Vibration, Dynamical Systems, Control Structural Mechanics Continuum Mechanics and Mechanics of Materials Mechanics, Fluids, Thermodynamics Theoretical and Applied Mechanics
Content Type	Text
Resource Type	Article
Subject	Mechanical Engineering Computational Mechanics

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