Large deflections of axisymmetric circular membranes

Kao, Robert; Perrone, Nicholas

doi:10.1016/0020-7683(71)90001-1

Cited by 41 publications

(13 citation statements)

References 7 publications

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“…Gent and Lewandowski (1987) obtained a value of 0.595 using Hencky (1915) series expansion technique. Chien (1948); Dickey (1967); Kao and Perrone (1971) and Kelkar et al (1985) found out the same value of 0.595 with different computing techniques while Christensen and Feng (1986) obtained 0.572. Our current value of 0.60 is within 1% of the value obtained by Hencky (1915).…”

Section: Maximum Displacementsmentioning

confidence: 86%

Pursing of planar elastic pockets

Bouremel

Madaan

Lee

et al. 2017

Journal of Fluids and Structures

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The pursing of a simply-or doubly-connected planar elastic pocket by an applied pressure is analysed from the bending to the stretching regimes. The response is evaluated in terms of maximum deflection and profiles across a range of simply-and doubly-connected circular and square shapes. The study is conducted using experimental and numerical methods and supported by previous analytical results. The experimental method is based on an original 2D optical method that gives access to the pursing direction perpendicular to each image across the field of view. The equations for maximum pursing deflections are developed and compared for a range of thicknesses of silicone samples and shapes from the bending to the stretching regimes. In the case of doubly-connected shapes, dependence of maximum pursing deflection on clamped central circular and square areas or holes is quantified for both regimes. Good agreement is established between the three methods and the study also shows that the optical method may as well be successfully applied to problems of pursing of rubber pockets.

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Section: Maximum Displacementsmentioning

confidence: 86%

Pursing of planar elastic pockets

Bouremel

Madaan

Lee

et al. 2017

Journal of Fluids and Structures

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“…[1][2][3][4][5]. Especially Chen Shan-lin et al obtained the parsed solution of the problem which was expressed by elementary function [5] .…”

Section: Large Deformation Problem Of Circular Membranementioning

confidence: 99%

“…(2), (3) and (4). And for arbitrary w 0 ∈ [u 0 , v 0 ], letting w n = Aw n−1 , n = 1, 2, · · · , there will bez(x) = lim n→∞ w n and the error estimate (9).…”

Section: Existence and Uniqueness Of Solutionmentioning

confidence: 99%

Exact solution of large deformation basic equations of circular membrane under central force

郝际平

颜心力

2006

Appl Math Mech

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Exact solution of the nonlinear boundary value problem for the basic equation and boundary condition of circular membrane under central force was obtained by using new simple methods. The existence and uniqueness of the solution were discussed by using of modern immovable point theorems. Although specific problem is treated, the basic principles of the methods can be applied to a considerable variety of nonlinear problems.

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“…coordinates of the shell (middle) surface. A point in the shell body may then be described by the position vector x(4,, 42, ) = r(4,, 2) + n(4,, 52) where n is the unit normal at the point r(4 1 , 52) of the middle surface (C = 0). The unit vectors Tj = x i/ai with ai = ac(l + /CR), for i = 1, 2, are tangent to the surface coordinate lines k = constant, C = constant, k $ i respectively.…”

Section: Elasticity Theory In Shell Coordinatesmentioning

confidence: 99%

“…These authors calculated formal power series solutions of the relevant differential equation. Various treatments of these two problems by other numerical methods have appeared in the more recent engineering literature (e.g., see [52], where other references are given). The first rigorous result on Hencky's problem was given in [139]; an existence theorem was proved by establishing the convergence of the power series derived in [45].…”

Section: Smallfinite Deflections Of Circular Membranesmentioning

confidence: 99%

On shells of revolution with the Love-Kirchhoff hypotheses

Wan

Weinitschke

1988

J Eng Math

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With fondness and appreciation, the authors dedicate this article to their teacher, collaborator and friend, Professor Eric Reissner, in the year of his seventy-fifth anniversary.Abstract. On the occasion of the 100th anniversary of A.E.H. Love's fundamental paper on thin elastic shell theory, the present article summarizes a line of developments on shells of revolution related to the Love-Kirchhoff hypotheses which form the basis of Love's theory. The summary begins with the Giinther-Reissner formulation of the linear theory which is shown to contain the classical first approximation shell theory as a special case. The static-geometric duality is deduced as a natural and immediate consequence of the more general theory. The repeated applications of this duality greatly simplify the solution process for boundary-value problems in shell theory, including the classical reduction of the axisymmetric bending problem and related recent reductions of shell equations for more general loadings to two simultaneous equations for a stress function and a displacement variable. In the nonlinear range, the article confines itself to Reissner's geometrically nonlinear theory of axisymmetric deformation of shells of revolution and Marguerre's shallow shell theory with special emphasis on recent results for elastic membranes, buckling of shells of revolution and applications of asymptotic methods.

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Large deflections of axisymmetric circular membranes

Cited by 41 publications

References 7 publications

Pursing of planar elastic pockets

Pursing of planar elastic pockets

Exact solution of large deformation basic equations of circular membrane under central force

On shells of revolution with the Love-Kirchhoff hypotheses

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