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Research Papers

Wrinkling in Sandwich Structures With a Functionally Graded Core

[+] Author and Article Information
Victor Birman

Department of Mechanical and
Aerospace Engineering,
Missouri S&T Global—St. Louis,
Missouri University of Science and Technology,
12837 Flushing Meadows Drive,
St. Louis, MO 63131

Nam Vo

Department of Mechanical and
Aerospace Engineering,
Missouri University of Science and Technology,
Centennial Hall,
300 W 12th Street,
Rolla, MO 65409

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received July 7, 2016; final manuscript received October 10, 2016; published online November 7, 2016. Assoc. Editor: Dr. George Kardomateas.

J. Appl. Mech 84(2), 021002 (Nov 07, 2016) (8 pages) Paper No: JAM-16-1344; doi: 10.1115/1.4034990 History: Received July 07, 2016; Revised October 10, 2016

This paper illustrates the effectiveness of a functionally graded core in preventing wrinkling in sandwich structures. The problem is solved for piecewise and continuous through-the-thickness core stiffness variations. The analysis is extended to account for the effect of temperature on wrinkling of a sandwich beam with a functionally graded core. The applicability of the developed theory is demonstrated for foam cores where the stiffness is an analytical function of the mass density. In this case, a desirable variation of the stiffness can be achieved by varying the mass density through the thickness of the core. Numerical examples demonstrate that wrinkling stability of a facing can significantly be increased using a piecewise graded core. The best results are achieved locating the layers with a higher mass density adjacent to the facing. A significant increase in the wrinkling stress can eliminate wrinkling as a possible mode of failure, without noticeably increasing the weight of the structure. In the case of a uniform temperature applied in addition to compression, wrinkling in a sandwich beam with a functionally graded core is affected both by its grading as well as by the effect of temperature on the facing and core properties. Although even a moderately elevated temperature may significantly lower the wrinkling stress, the advantage of a graded core over the homogeneous counterpart is conserved.

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Figures

Grahic Jump Location
Fig. 1

The facing of a sandwich structure supported by a functionally graded core. The wrinkling stress is increased by using stiffer outer layers: ρ1>ρ2>ρ3.

Grahic Jump Location
Fig. 2

Effect of variations in the thickness of a functionally graded core on the wrinkling stress. The mass density of the core layers are ρ1=0.35ρ,  ρ2=0.15ρ, and ρ3=0.10ρ, the thicknesses of layers 1 and 2 are equal to each other.

Grahic Jump Location
Fig. 3

Effect of variations in the thickness of intermediate layer 2 in a functionally graded core on the wrinkling stress. The thickness of outermost layer 1 is t1=tf. The mass density of the core layers are ρ1=0.35ρ,  ρ2=0.15ρ,  and ρ3=0.10ρ. The thickness of layer 2 varies from tf  (2 mm) to 4tf  (8 mm).

Grahic Jump Location
Fig. 4

Effect of variations in the thickness of outermost layer 1 in a functionally graded core on the wrinkling stress. The thickness of intermediate layer 2 is t2=tf. The mass density of the core layers are ρ1=0.35ρ,  ρ2=0.15ρ,  andρ3=0.10ρ. The thickness of layer 1 varies from tf  (2mm) to 4tf(8 mm).

Grahic Jump Location
Fig. 5

Effect of variations in the mass density of intermediate layer 2 in a functionally graded core on the wrinkling stress. The mass density of the core layers are ρ1=0.35ρ,ρ3≤ρ2≤ρ1,  and ρ3=0.10ρ, the thicknesses of layers 1 and 2 are equal to t1=t2=tf.

Grahic Jump Location
Fig. 6

Effect of variations in the mass density of intermediate layer 2 in a functionally graded core on the wrinkling stress. The mass density of the core layers are ρ1=0.35ρ,ρ3≤ρ2≤ρ1, and ρ3=0.10ρ, the thicknesses of layers 1 and 2 are equal to t1=t2=4tf.

Grahic Jump Location
Fig. 7

Effect of variations in the mass density of outermost layer 1 in a functionally graded core on the wrinkling stress. The mass density of the core layers are ρ2≤ρ1≤0.35ρ,ρ2=0.20ρ,  and ρ3=0.10ρ, the thicknesses of layers 1 and 2 are equal to t1=t2=tf.

Grahic Jump Location
Fig. 8

Effect of variations in the mass density of outermost layer 1 in a functionally graded core on the wrinkling stress. The mass density of the core layers are ρ2≤ρ1≤0.35ρ,ρ2=0.20ρ,  and ρ3=0.10ρ, the thicknesses of layers 1 and 2 are equal to t1=t2=4tf.

Grahic Jump Location
Fig. 9

Failure envelopes for mass densities of layers 1 and 2 necessary to increase the wrinkling stress by a factor of 2.0 compared to a homogeneous core of mass density ρ3=0.1ρ=120  kg/m3. The thicknesses of layers 1 and 2 are equal to t1=t2=4tf.

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