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Research Papers

Wrinkling of Functionally Graded Sandwich Structures Subject to Biaxial and In-Plane Shear Loads

[+] Author and Article Information
Victor Birman

Missouri S&T Global—St. Louis,
Department of Mechanical and Aerospace
Engineering,
Missouri University of Science and Technology,
12837 Flushing Meadows Drive,
St. Louis, MO 63131
e-mail: vbirman@mst.edu

Harold Costa

Department of Mechanical and Aerospace
Engineering,
Missouri University of Science and Technology,
194 Toomey Hall,
Rolla, MO 65409
e-mail: hgcvwf@mst.edu

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received June 13, 2017; final manuscript received October 3, 2017; published online October 20, 2017. Assoc. Editor: George Kardomateas.

J. Appl. Mech 84(12), 121006 (Oct 20, 2017) (10 pages) Paper No: JAM-17-1320; doi: 10.1115/1.4038141 History: Received June 13, 2017; Revised October 03, 2017

Benefits of a functionally graded core increasing wrinkling stability of sandwich panels have been demonstrated in a recent paper (Birman, V., and Vo, N., 2017, “Wrinkling in Sandwich Structures With a Functionally Graded Core,” ASME J. Appl. Mech., 84(2), p. 021002), where a several-fold increase in the wrinkling stress was achieved, without a significant weight penalty, using a stiffer core adjacent to the facings. In this paper, wrinkling is analyzed in case where the facings are subject to biaxial compression and/or in-plane shear loading, and the core is arbitrary graded through the thickness. Two issues addressed are the effect of biaxial or in-plane shear loads on wrinkling stability of panels with both graded and ungraded core, and the verification that functional grading of the core remains an effective tool increasing wrinkling stability under such two-dimensional (2D) loads. As follows from the study, biaxial compression and in-plane shear cause a reduction in the wrinkling stress compared to the case of a uniaxial compression in all grading scenarios. Accordingly, even sandwich panels whose mode of failure under uniaxial compression was global buckling, the loss of strength in the facings or core crimpling may become vulnerable to wrinkling under 2D in-plane loading. It is demonstrated that a functionally graded core with the material distributed to increase the local stiffness in the interface region with the facings is effective in preventing wrinkling under arbitrary in-plane loads compared to the equal weight homogeneous core.

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Figures

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Fig. 1

Sandwich panel subject to biaxial compression (in-plane shear is not shown). The coordinate systems x−y−z and x1−y1−z are oriented along the edges and the wrinkle, respectively. The axis z that is perpendicular to the panel is not shown. The front of the wrinkle is inclined relative to the x-axis by angle θ.

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Fig. 2

Cross section of a sandwich panel with wrinkles in the top facing. Linear and quadratic grading scenarios as well as the case of the equal-weight homogeneous core are shown.

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Fig. 3

The effect of biaxial compression on the wrinkling stress in cases of 10-mm thick and 25-mm thick cores with a linear mass density grading through the thickness

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Fig. 4

The angle of orientation of the wrinkling wave relative to the y-axis in cases of 10-mm thick and 25-mm thick cores with a linear mass density grading through the thickness

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Fig. 5

The effect of combined uniaxial compression and in-plane shear on the wrinkling stress in case of a 10-mm thick core with a linear mass density grading through the thickness

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Fig. 6

The angle of orientation of the wrinkling wave relative to the y-axis under uniaxial compression and in-plane shear in case of a 10-mm thick core with a linear mass density grading through the thickness

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Fig. 7

The effect of combined biaxial compression and in-plane shear on the wrinkling stress for panels with various facing materials and 10-mm thick cores with a linear mass density grading through the thickness

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Fig. 8

The effect of biaxial compression on the wrinkling stress in cases of 10-mm thick and 25-mm thick cores with a quadratic mass density grading through the thickness

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Fig. 9

The effect of uniaxial compression and in-plane shear on the wrinkling stress in case of a 10-mm thick core with a quadratic mass density grading through the thickness

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Fig. 10

The effect of combined biaxial compression and in-plane shear on the wrinkling stress for panels with various facing materials and a quadratic mass density grading of a 10-mm core through the thickness

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Fig. 11

The effect of biaxial compression on the wrinkling stress in sandwich panels with a homogeneous (“ungraded”) core and with the linear and quadratic variations of the mass density of a 10-mm core through the thickness. The weight of the core in all three panels is equal.

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Fig. 12

The effect of in-plane shear on the wrinkling stress in sandwich panels with a homogeneous (“ungraded”) core and with the linear and quadratic variations of the mass density of 10-mm and 25-mm thick cores through the thickness. The facing material is glass/epoxy. The weight of the core in all three panels is equal.

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Fig. 13

Effect of grading and a combination of biaxial and in-plane shear loading on the wrinkling stress in sandwich panels with glass/epoxy facings and homogeneous, linearly graded and quadratically graded 10-mm thick cores

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Fig. 14

Effect of grading and a combination of biaxial and in-plane shear loading on the wrinkling stress in sandwich panels with AS 3501 graphite/epoxy facings and homogeneous, linearly graded and quadratically graded 25-mm thick cores

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