Wrinkling in Thin Plates due to In-plane Body Forces

Rimrott, F. P. J.; Cvercko, Michal

doi:10.1007/978-3-642-82776-1_2

Cited by 10 publications

(14 citation statements)

References 1 publication

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“…A generalization of the relaxed strain energy approach [Epstein and Forcinito 2001] in terms of a hyperelastic material which saturates when wrinkles form makes it easier to derive consistent expressions for the strain energy variations in the wrinkled state. Wu [1978], Wu andCanfield [1981], andRoddeman et al [1987] have proposed to deal with wrinkling by modifying the deformation tensor such that the principal stress directions are either unchanged, in the case of isotropic membranes, or rotated appropriately in the case of anisotropic membranes. Stein and Hedgepeth [1961] tackled the analysis of a partially wrinkled membrane, which can be divided into taut regions and wrinkled regions, by introducing the concept of a variable Poisson's ratio, which accounts for the geometric strains induced by wrinkling.…”

Section: Review Of Previous Analytical Modelsmentioning

confidence: 99%

“…Hence, it is implicitly assumed that an infinite number of wrinkles of Figure 2. Wrinkles in a hanging "blanket", from [Rimrott and Cvercko 1986].…”

Section: Review Of Previous Analytical Modelsmentioning

confidence: 99%

“…The first study of the shape of a heavily wrinkled membrane (as opposed to the lightly corrugated shape that occurs soon after the onset of wrinkles) which also took into account the role played by the membrane bending stiffness was the "hanging blanket" solution by Rimrott and Cvercko [1986]. Consider a membrane held at two corner points at the same height.…”

Section: Review Of Previous Analytical Modelsmentioning

confidence: 99%

“…The tension-line field, i.e., the stress distribution that occurs in the membrane if out-of-plane displacements are neglected and yet no compressive stress is allowed anywhere in the membrane, had previously been determined by Mansfield [1981] for the case of a rectangular blanket. Rimrott and Cvercko [1986] considered a membrane with sinusoidal, instead of straight boundaries, and for this particular case obtained a solution for the post-wrinkling tension-line field, where the membrane deforms out of plane while forming a number of wrinkles.…”

Section: Review Of Previous Analytical Modelsmentioning

confidence: 99%

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Wrinkled membranes II: analytical models

Wong¹,

Pellegrino

2006

J. Mech. Solids Struct.

141

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We present a general analytical model for determining the location and pattern of wrinkles in thin membranes and for making preliminary estimates of their wavelength and amplitude. A rectangular membrane under simple shear and a square membrane subject to corner loads are analysed. In the first problem, our model predicts the wavelength and the wrinkle amplitude to be respectively inversely proportional and directly proportional to the fourth root of the shear angle. Both values are directly proportional to the square root of the height and thickness of the membrane, and are independent of the Young's modulus. In the second problem two wrinkling regimes are identified. The first regime is characterised by radial corner wrinkles and occurs for load ratios less than 1/( √ 2 − 1); the number of wrinkles is proportional to the fourth root of the radius of the wrinkled region and the magnitude of the corner force, and inversely proportional to the Young's modulus and thickness cubed. The amplitude of these wrinkles is inversely proportional to their number, directly proportional to the square root of the radius of the wrinkled region and the magnitude of the corner force, and inversely proportional to the square root of the Young's modulus and thickness. The second regime occurs for load ratios larger than 1/( √ 2 − 1), and is characterised by a large diagonal wrinkle, plus small radial wrinkles at all four corners. Analytical expressions for the variation of the width and amplitude of the large wrinkle with the load ratio are obtained for this case also. All analytical predictions are compared with experimental and computational results from the other two papers in this series.

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Section: Review Of Previous Analytical Modelsmentioning

confidence: 99%

“…Hence, it is implicitly assumed that an infinite number of wrinkles of Figure 2. Wrinkles in a hanging "blanket", from [Rimrott and Cvercko 1986].…”

Section: Review Of Previous Analytical Modelsmentioning

confidence: 99%

Section: Review Of Previous Analytical Modelsmentioning

confidence: 99%

Section: Review Of Previous Analytical Modelsmentioning

confidence: 99%

See 2 more Smart Citations

Wrinkled membranes II: analytical models

Wong¹,

Pellegrino

2006

J. Mech. Solids Struct.

141

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show abstract

“…The bending stiffness of the membrane, which determines the wavelength of the wrinkles, was considered by several authors (Rimrott and Cvercko, 1986;Cerda et al, 2002;Epstein, 2003). The development of heavily wrinkled configurations, through jumps in which the spatial wavelength of the wrinkles changes suddenly, was studied by Wong & Pellegrino (2006a,b,c).…”

mentioning

confidence: 99%

Wrinkling of transversely loaded spinning membranes

Delapierre¹,

Chakraborty²,

Sader³

et al. 2018

International Journal of Solids and Structures

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Spinning membrane structures provide a mass-efficient solution for large space apertures. This paper presents a detailed study of the wrinkling of spinning circular membranes loaded by transverse, uniform loads. Experimental measurements of the angular velocities at which different membranes become wrinkled, and of the wrinkling mode transitions that occur upon spin down of the membrane, are presented. A theoretical formulation of the problem is presented, from which pairs of critical angular velocities and critical transverse loads are determined. A general stability chart is presented, which identifies the stability limits in terms of only two dimensionless parameters, for any membrane. The transition between bending dominated behavior and in-plane dominated behavior is identified, and it is shown that in the bending-dominated case the critical non-dimensional transverse load is independent from the non-dimensional angular velocity.

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Edge-buckling in stretched thin films under in-plane bending

Coman

2006

Z. angew. Math. Phys.

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The wrinkling instabilities of a stretched rectangular thin film subjected to in-plane bending are investigated within the framework of the linearised Donnell-von Kármán bifurcation equation for thin plates. One of our principal objectives is to assess the role played by the finite bending stiffness of the film on the linear wrinkling mechanism. To this end, we employ a nonhomogeneous linear pre-bifurcation solution and cast the corresponding eigenvalue problem as a singularly-perturbed differential equation with variable coefficients. Numerical simulations of this problem reveal the existence of two different regimes for the behaviour of the lowest eigenvalue. Based on this observation, a WKB analysis is carried out in order to capture the dependence of the critical wrinkling load on the wavelength of the localised oscillatory buckling pattern and the stiffness of the elastic film. The validity of the analytical results is corroborated by independent numerical computations of the eigenvalues using the method of compound matrices.

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Wrinkling in Thin Plates due to In-plane Body Forces

Cited by 10 publications

References 1 publication

Wrinkled membranes II: analytical models

Wrinkled membranes II: analytical models

Wrinkling of transversely loaded spinning membranes

Edge-buckling in stretched thin films under in-plane bending

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