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TECHNICAL PAPERS

End Effects in Prestrained Plates Under Compression

[+] Author and Article Information
B. Karp

Department of Mechanical Engineering, Ben-Gurion University of the Negev, P.O.B. 653, Beer-Sheva 84105, Israel

J. Appl. Mech 71(6), 816-824 (Jan 27, 2005) (9 pages) doi:10.1115/1.1794703 History: Received April 21, 2003; Revised June 13, 2003; Online January 27, 2005
Copyright © 2004 by ASME
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References

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Durban,  D., and Stronge,  W. J., 1995, “Plane-Strain Incremental Response and Sensitivity of Stretched Plates,” Eur. J. Mech. A/Solids, 14, pp. 553–575.
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Durban,  D., and Stronge,  W. J., 1992, “Diffusion of Incremental Loads in Prestrained Bars,” Proc. R. Soc. London, Ser. A, 439, pp. 583–600.
Ling,  Y., Engel,  P. A., and Geer,  J. A., 1994, “The End Problem of Incompressible Elastic Cylinders,” ASME J. Appl. Mech., 61, pp. 30–37.
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Knowles,  J. K., and Sternberg,  E., 1977, “On the Failure of Ellipticity of the Equations for Finite Elastostatic Plane Strain,” Arch. Ration. Mech. Anal., 63, pp. 321–336.
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Figures

Grahic Jump Location
Plate, of current length and width 2L and 2H, respectively, subjected to uniform tension (σ>0,λ>1) or compression (σ<0,λ<1) stress in plane strain condition (λy=1) with boundaries x=±H free of traction
Grahic Jump Location
Two lowest eigenvalues (multiplied by factor π/2) in tension (λ>1) and in compression (λ<1) for the BK rubber (2.9). k0 and k1 are the antisymmetric and the symmetric eigenvalues, respectively.
Grahic Jump Location
Two lowest eigenvalues (multiplied by factor π/2) in tension (λ>1) and in compression (λ<1) for the St1 rubber (2.10). k0 and k1 are the antisymmetric and the symmetric eigenvalues, respectively.
Grahic Jump Location
Two lowest eigenvalues (multiplied by factor π/2) in tension (λ>1) and in compression (λ<1) for the St2 rubber (2.11). k0 and k1 are the antisymmetric and the symmetric eigenvalues, respectively.
Grahic Jump Location
Two lowest eigenvalues (multiplied by factor π/2) in tension (λ>1) and in compression (λ<1) for the OG rubber (2.12). k0 and k1 are the antisymmetric and the symmetric eigenvalues, respectively.
Grahic Jump Location
Purely real eigenvalue in compression for the four rubbers BK, St1, St2, OG, and the classical Euler formula for buckling of a pinned-pinned column
Grahic Jump Location
Leading decay exponent in compression for the four rubbers BK, St1, St2 OG, and for a variation of Bk rubber (BK-Var) with compressibility constant n=25

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