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Research Papers

Probabilistic and Interval Analyses Contrasted in Impact Buckling of a Clamped Column

[+] Author and Article Information
Isaac Elishakoff

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

Wim Verhaeghe

Ph.D Student
Dept. of Mechanical Engineering
KU Leuven
B3001 Heverlee, Belgium
e-mail: wim.verhaeghe@mech.kuleuven.be

David Moens

Professor
Dept. of Applied Engineering
Lessius Mechelen, Campus De Nayer
B2860 St-Katelijne-Waver, Belgium
and
Associate Professor
Dept. of Mechanical Engineering
KU Leuven
B3001 Heverlee, Belgium
e-mail: david.moens@mech.kuleuven.be

Manuscript received November 28, 2011; final manuscript received June 29, 2012; accepted manuscript posted July 6, 2012; published online November 19, 2012. Assoc. Editor: Vikram Deshpande.

J. Appl. Mech 80(1), 011022 (Nov 19, 2012) (8 pages) Paper No: JAM-11-1452; doi: 10.1115/1.4007084 History: Received November 28, 2011; Revised June 29, 2012; Accepted July 06, 2012

In this study we contrast two competing methodologies for the impact buckling of a column that is clamped at both ends. The initial imperfection is postulated to be co-configurational with the fundamental mode shape of the column without the axial loading. A solution is also furnished for the case when the initial imperfection is proportional to the Filonenko-Borodich “cosinusoidal polynomial”. Probabilistic and interval analyses are conducted for each case; these are contrasted on some representative numerical data.

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Figures

Grahic Jump Location
Fig. 1

Maximum normalized deflection versus normalized time at ξ = 0.25 (dashed lines) and ξ = 0.5 (solid lines). The load ratio is α = 2. The green lines correspond to the solution with the normal mode; the red lines correspond to the solution with the one term Filonenko-Borodich (F-B) approximation.

Grahic Jump Location
Fig. 2

Maximum normalized deflection versus normalized time at ξ = 0.5 for various values of the load ratio. The green lines correspond to the solution with the normal mode; the red lines correspond to the solution with the one term Filonenko-Borodich (F-B) approximation.

Grahic Jump Location
Fig. 3

Maximum integral (span-averaged) deflection versus normalized time for various values of the load ratio. The green lines correspond to the solution with the normal mode; the red lines correspond to the solution with the one term Filonenko-Borodich (F-B) approximation.

Grahic Jump Location
Fig. 4

Reliability as a function of time (α = 0.5)

Grahic Jump Location
Fig. 5

Reliability as a function of time (α = 1)

Grahic Jump Location
Fig. 6

Reliability as a function of time (α = 2)

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