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Research Papers

Application of Lamé's Super Ellipsoids to Model Initial Imperfections

[+] Author and Article Information
Isaac Elishakoff

ASME Fellow
Department of Ocean and
Mechanical Engineering,
Florida Atlantic University,
Boca Raton, FL 33431-0991
e-mail: elishako@fau.edu

Yannis Bekel

Ecole Centrale Paris,
Châtenay-Malabry 92 290, France

Manuscript received June 26, 2012; final manuscript received January 15, 2013; accepted manuscript posted February 14, 2013; published online August 19, 2013. Assoc. Editor: Wei-Chau Xie.

J. Appl. Mech 80(6), 061006 (Aug 19, 2013) (9 pages) Paper No: JAM-12-1264; doi: 10.1115/1.4023679 History: Received June 26, 2012; Revised January 15, 2013; Accepted February 14, 2013

In this paper, we investigate initial imperfections of structures that are modeled as belonging to a super ellipse or super ellipsoid. This extends previous analysis of regular ellipsoidal sets. We determine minimum area or minimum volume to which available data may belong. The methodology is illustrated on the case of impact buckling of a column possessing initial imperfections.

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References

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Figures

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Fig. 1

Enclosing of the convex hull of 10 points by a super ellipsoid

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Fig. 2

Set of 10 points listed in Table 1

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Fig. 3

Convex hull of 10 points listed in Table 1 and depicted in Fig. 1

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Fig. 4

Enclosing of the convex hull of 10 points by a candidate rectangle

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Fig. 5

Enclosing of the convex hull of 10 points by a candidate rectangle

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Fig. 6

Enclosing of the convex hull of 10 points by a candidate rectangle

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Fig. 7

Maximum normalized deflection versus normalized time at ξ = 0.5 for different values of the load ratio

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Fig. 8

Maximum normalized deflection versus normalized time for different values of ξ and with load ratio equals 2

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Fig. 9

Maximum normalized deflection versus normalized time at ξ = 0.5 for different values of the load ratio

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Fig. 10

Maximum normalized deflection versus normalized time at ξ = 0.4 for different values of the load ratio

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Fig. 11

Maximum normalized deflection versus normalized time for different values of ξ and with load ratio = 2

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Fig. 12

Maximum normalized deflection versus normalized position (ξ) for different values of normalized time (τ) and with load ratio = 2

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