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Research Papers

Dynamic Buckling Response of Long Plates for the Prediction of Local Plate Buckling of Corrugated Core Sandwich Columns

[+] Author and Article Information
Jae-Yong Lim

New Transportation Systems Research Center,
Korea Railroad Research Institute,
Uiwang, Gyeonggi 16105, South Korea
e-mail: jylim@krri.re.kr

Hilary Bart-Smith

Department of Mechanical and
Aerospace Engineering,
University of Virginia,
Charlottesville, VA 22904
e-mail: hb8h@virginia.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received March 26, 2015; final manuscript received August 5, 2015; published online September 10, 2015. Editor: Yonggang Huang.

J. Appl. Mech 82(11), 111008 (Sep 10, 2015) (12 pages) Paper No: JAM-15-1163; doi: 10.1115/1.4031279 History: Received March 26, 2015; Revised August 05, 2015

An analytical model predicting the dynamic local buckling failure of plates with a large dimension in the longitudinal direction compressed at a constant rate was proposed. The model began with the hypothesis that the proposed analytical approach could be an alternative methodology to approximate the dynamic local plate buckling response of constituent plates of corrugated core sandwich columns. Prior to the model development, four preliminary finite-element (FE) simulations were conducted to observe the typical dynamic response of the sandwich columns having thin core web plates or thin face sheets. From the simulations, several wrinkles with a regular pattern were generated, and then one of the wrinkles grew excessively to a failure. Accordingly, the proposed model considered an imaginary patch plate on a long plate simulating a face sheet or a core web plate. The size of the patch plate was predefined so as to encompass the major growing wrinkle, and the out-of-plane displacement was calculated till load drop. The verification of the proposed model was followed by comparison with the FE calculations. The model was satisfactory in predicting maximum forces and times-to-failure, but some discrepancies were found when postcritical behavior and plasticity were involved. The sources of the discrepancies were discussed.

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Figures

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Fig. 1

(a) Schematic diagram for the preliminary FE simulations, (b) sideview, and (c) cross section and sandwich geometric parameter notation

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Fig. 2

Considered quasi-static material curve of SS304

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Fig. 3

FE column I: (a) reaction forces per unit width at the front and back ends versus time curves and (b) deformation shapes of sandwich columns at different times; contours are shown for a vertical displacement component normal to the face sheet planes. Times t1, t2, and t3 for ①, ②, and ③ are 533, 1067, and 4000 μs.

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Fig. 4

FE column II: (a) reaction forces per unit width at the front and back ends versus time curves and (b) deformation shapes of sandwich columns at different times; contours are shown for a vertical displacement component normal to the face sheet planes. Times t1, t2, and t3 for ①, ②, and ③ are 1000, 3000, and 9000 μs.

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Fig. 5

FE column III: (a) reaction forces per unit width at the front and back ends versus time curves and (b) deformation shapes of sandwich columns at different times; contours are shown for a vertical displacement component normal to the face sheet planes. Times t1, t2, and t3 for ①, ②, and ③ are 133, 266, and 1067 μs.

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Fig. 6

FE column IV: (a) reaction forces per unit width at the front and back ends versus time curves and (b) deformation shapes of sandwich columns at different times; contours are shown for a vertical displacement component normal to the face sheet planes. Times t1, t2, and t3 for ①, ②, and ③ are 1000, 3333, and 4000 μs.

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Fig. 7

(a) Patch plates on a core web plate of a corrugated core sandwich column, (b) patch plates on a face plate of a corrugated core sandwich column, and (c) boundary conditions of the patch plates

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Fig. 8

Considered material curve of Al6061-T6

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Fig. 9

Boundary conditions of FEA of plates

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Fig. 10

The assigned eigenmode shape superposed for initial curvature imperfections. A repetitive buckling pattern is shown; however, the amplitude of each wrinkle is different, but of the same order. In the dynamic analysis of the plates, the mode shape with a magnitude ξ(LP) is added to the flat plates.

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Fig. 11

FE validation of the analytical model for the Al6061-T6 elastic plate (A: 0.457 mm, W: 22.0 mm, L: 300 mm, ξ(LP) = 10−3 A, and V = 1 m/s): (a) reaction force per unit width and out-of-plane displacement at the midpoint of the patch plate (or failed wrinkle) and (b) and (c) out-of-plane displacement at t = 667 and 866 μs, respectively

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Fig. 12

FE validation of the analytical model for the SS304 elastic plate (A: 0.25 mm, W: 35.35 mm, L: 353 mm, ξ(LP) = 10−3 A, and V = 1 m/s): (a) reaction force per unit width and out-of-plane displacement at the midpoint of the patch plate (or failed wrinkle) and (b) and (c) out-of-plane displacement at t = 433 and 500 μs, respectively

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Fig. 13

FE validation of the analytic model for the Al6061 elastic–plastic plate (A: 0.88, W: 22.0, L: 300, ξ(LP) = 10−2 A, and V = 1 m/s): (a) reaction force per unit width and out-of-plane displacement at the midpoint of the patch plate (or failed wrinkle) and (b) and (c) out-of-plane displacement at t = 1200 and 1534 μs, respectively

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Fig. 14

FE validation of the analytic model for the SS304 elastic–plastic plate (A: 1.0, W: 35.35, L: 353, ξ(LP) = 10−2 A, and V = 1 m/s): (a) reaction force per unit width and out-of-plane displacement at the midpoint of the patch plate (or failed wrinkle) an (b) and (c) out-of-plane displacement at t = 1200 and 2500 μs, respectively

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Fig. 15

Postcritical responses of the Al6061-T6 elastic plates of two different plate thicknesses under V = 0.1 m/s calculated from FEM and the analytical model: (a) A = 0.1 mm and (b) A = 0.457 mm

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