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Research Papers

The Temporal Evolution of Buckling in a Dynamically Impacted Column

[+] Author and Article Information
Wooseok Ji

Research Fellow

Anthony M. Waas

Professor
e-mail: dcw@umich.edu
Department of Aerospace Engineering
Composite Structures Laboratory
University of Michigan
Ann Arbor, MI 48109

1Corresponding author.

Manuscript received January 26, 2012; final manuscript received May 17, 2012; accepted manuscript posted June 7, 2012; published online November 19, 2012. Editor: Robert M. McMeeking.

J. Appl. Mech 80(1), 011026 (Nov 19, 2012) (7 pages) Paper No: JAM-12-1033; doi: 10.1115/1.4006946 History: Received January 26, 2012; Revised May 17, 2012; Accepted June 07, 2012

The time-dependent progressive evolution of transverse displacements of an axially impacted, slender, geometrically imperfect, column is studied here. The analysis is concerned with evaluating the time-history associated with the evolution of the buckling response as a function of the initial geometric imperfection amplitude. The exact solution of the axial stress wave propagation is employed to study the physics of the buckling response with the nonuniform axial strain distribution varying in time and space. The responses of axially impacted columns are examined in light of past experimental results and associated numerical solutions. Results in the present paper are limited to elastic column behavior.

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References

Figures

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Fig. 1

Configuration of a slender column subjected to axial impact

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Fig. 10

Dynamic buckling load as a function of the maximum out-of-plane deformation with various levels of initial imperfection amplitudes for an impacted Teflon column

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Fig. 2

Diverging and bounded out-of-plane motion

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Fig. 3

Convergence study using the maximum transverse displacement measured at t/(L/c0) = 5 as a function of the number of eigenmodes

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Fig. 4

Dynamic buckling mode shapes corresponding to two different impactor velocities

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Fig. 5

Critical wavelength from the imperfection analysis

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Fig. 6

Deformation of a pasta column as a function of time with different impactor velocities

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Fig. 7

Maximum deflection of the pasta column as a function of time with different initial imperfection amplitudes

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Fig. 8

Deformation of the Teflon column as a function of time with different initial imperfection amplitudes

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Fig. 9

Deformation of the steel column as a function of time with different initial imperfection amplitudes

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