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Research Papers

A Note on the Buckling of an Elastic Plate Under the Influence of Simple Shear Flow

[+] Author and Article Information
C. Pozrikidis1

Department of Chemical Engineering, University of Massachusetts, Amherst, MA 01003cpozrikidis@ecs.umass.edu

Haoxiang Luo

Department of Mechanical Engineering, Vanderbilt University, VU Station B 351592, 2301 Vanderbilt Place, Nashville, TN 37235

1

Corresponding author.

J. Appl. Mech 77(2), 021007 (Dec 10, 2009) (3 pages) doi:10.1115/1.3197255 History: Received March 05, 2009; Revised June 15, 2009; Published December 10, 2009; Online December 10, 2009

The linear von Kármán equation describing the buckling of an elastic flat plate due to a distributed deformation-dependent load is discussed. It is shown that, in the case of buckling under the influence of an over-passing simple shear flow, a detailed hydrodynamic analysis of the disturbance flow due to the buckling is not necessary, and the eigensolutions can be determined exclusively from the stress field of the unperturbed simple shear flow. Corrections to previous results for a circular membrane patch are made.

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Figures

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Figure 1

Illustration of plate buckling under the influence of a body force; b is the body force field in the xy plane and pn is the normal load

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Figure 2

Illustration of shear flow past a spherical protrusion attached to a plane wall

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Figure 3

Distribution of the normal component of the boundary traction along the trace of the wall and protrusion in the xy plane for semi-angle (a) α=π/4, (b) π/8, and (c) π/16. The predictions of the linear theory are represented by the dashed lines.

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Figure 4

Locus of the eigenvalues in the complex plane parameterized by the numerical coefficient β for Poisson ratio (a) ν=0.0 and (b) 0.5

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