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TECHNICAL PAPERS

Hierarchical Corrugated Core Sandwich Panel Concepts

[+] Author and Article Information
Gregory W. Kooistra1

Department of Materials Science and Engineering,  University of Virginia, 116 Engineer's Way, Charlottesville, VA 22904gkooistra@watsonfurniture.com

Vikram Deshpande

Engineering Department,  Cambridge University, Trumpington Street, Cambridge CB2 1PZ, UK

Haydn N. G. Wadley

Department of Materials Science and Engineering,  University of Virginia, 116 Engineer's Way, Charlottesville, VA 22904

1

Author to whom correspondence should be addressed.

J. Appl. Mech 74(2), 259-268 (Sep 20, 2005) (10 pages) doi:10.1115/1.2198243 History: Received May 12, 2005; Revised September 20, 2005

The transverse compression and shear collapse mechanisms of a second order, hierarchical corrugated truss structure have been analyzed. The two competing collapse modes of a first order corrugated truss are elastic buckling or plastic yielding of the truss members. In second order trusses, elastic buckling and yielding of the larger and smaller struts, shear buckling of the larger struts, and wrinkling of the face sheets of the larger struts have been identified as the six competing modes of failure. Analytical expressions for the compressive and shear collapse strengths in each of these modes are derived and used to construct collapse mechanism maps for second order trusses. The maps are useful for selecting the geometries of second order trusses that maximize the collapse strength for a given mass. The optimization reveals that second order trusses made from structural alloys have significantly higher compressive and shear collapse strengths than their equivalent mass first order counterparts for relative densities less than about 5%. A simple sheet metal folding and dip brazing method of fabrication has been used to manufacture a prototype second order truss with a relative density of about 2%. The experimental investigation confirmed the analytical strength predictions of the second order truss, and demonstrate that its strength is about ten times greater than that of a first order truss of the same relative density.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Sketches of (a) the first and (b) the second order corrugated cores sandwiched between two rigid face sheets

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Figure 10

(a) Compressive and (b) shear failure mechanism maps for the ω=ω1=70deg second order corrugated core with l1∕l=0.03. The arrows trace the path of the optimum designs that maximize the strengths for a given relative density. The yield strain of the solid material is taken to be εY=0.002.

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Figure 11

Comparison between the (a) compressive and (b) shear strengths of the fully optimized second order and first order corrugated cores. Results are shown for three selected values of the corrugation angle ω=ω1 and the yield strain of the solid material is taken to be εY=0.002.

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Figure 12

The geometries of the fully optimized ω=ω1=70deg second order corrugated core. The geometries that maximize the compressive (red lines) and shear (black lines) strengths are included.

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Figure 13

Comparison between the compressive strengths of competing sandwich core topologies for the solid material yield strains (a) εY=0.002 and (b) εY=0.02

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Figure 2

Schematic drawings of the failure modes in the second order corrugated core (a) plastic yielding of the larger struts, (b) Euler buckling of the larger struts, (c) shear buckling of the larger struts, (d) elastic wrinkling of the larger strut face sheets, (e) yielding of the smaller struts, and (f) Euler buckling of the smaller struts

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Figure 3

Failure mechanism map for Al6061-T6 (εY=0.004) second order corrugated core with l1∕l=0.04, ω1=45deg. The solid circle marks the geometry tested in this study. The arrows trace the path of the optimum designs that maximize the compressive strength σp for a given relative density ρ¯.

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Figure 4

Photographs of the as-manufactured (a) first and (b) second order corrugated cores. In this study the manufactured cores are comprised of a single unit cell.

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Figure 5

Uniaxial tensile response of the Al-6061-T6

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Figure 6

Measured compressive nominal stress versus nominal strain responses of the ρ¯≈0.02 first and second order corrugated cores

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Figure 7

Photographs showing the failure modes of (a) second (ε≈0.007) and (b) first (ε≈0.20) order corrugated cores

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Figure 8

Collapse mechanism maps for the compressive failure of the ω=ω1=45deg second order core with (a) l1∕l=0.01 and (b) l1∕l=0.03. The arrows trace the path of the optimum designs that maximize the compressive strength σp for a given relative density ρ¯. The yield strain of the solid material is taken to be εY=0.002.

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Figure 9

(a) Comparison between the normalized compressive strengths of the optimized ω=ω1=45deg second order corrugated cores and the ω=45deg first order core. The yield strain of the solid material is taken to be εY=0.002. (b) The corresponding geometries of the fully optimized second order core.

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