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Research Papers

Post-buckling and Snap-Through Behavior of Inclined Slender Beams

[+] Author and Article Information
Jian Zhao, Jianyuan Jia, Hongxi Wang

School of Elec-mechanical Engineering, Xidian University, Xi’an, 710071, P.R.C.

Xiaoping He

 Institute of Electronic Engineering, China Academy of Engineering Physics, Mianyang 621900, P.R.C.

J. Appl. Mech 75(4), 041020 (May 16, 2008) (7 pages) doi:10.1115/1.2870953 History: Received April 16, 2007; Revised November 09, 2007; Published May 16, 2008

Based on the geometrical nonlinear theory of large deflection elastic beams, the governing differential equations of post-buckling behavior of clamped-clamped inclined beams subjected to combined forces are established. By using the implicit compatibility conditions to solve the nonlinear statically indeterminate problems of elastic beams, the strongly nonlinear equations formulated in terms of elliptic integrals are directly solved in the numerical sense. When the applied force exceeds the critical value, the numerical simulation shows that the inclined beam snaps to the other equilibrium position automatically. It is in the snap-through process that the accurate configurations of the post-buckling inclined beam with different angles are presented, and it is found that the nonlinear stiffness decreases as the midpoint displacement is increased according to our systematical analysis of the inward relations of different buckling modes. The numerical results are in good agreement with those obtained in the experiments.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Original state of the bent-beam structure

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Figure 6

Electronic testing device for post-buckling beams

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Figure 7

Elastic force versus displacement for α=9deg. The filled circle “●” stands for the position where the beam configuration changes from symmetric state to asymmetric state.

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Figure 8

Elastic force versus displacement for α=30deg. The filled circle “●” stands for the position where the beam configuration changes from symmetric state to asymmetric state.

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Figure 9

Large deformation of the beam subjected to axial load for α=90deg

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Figure 10

Force-displacement curve for α=90deg

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Figure 2

Post-buckling state of the bent-beam structure

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Figure 3

Deformation of post-buckling beam under a combined load

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Figure 4

Post-buckling configurations for α=9deg

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Figure 5

Post-buckling configurations for α=30deg

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