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Research Papers

Analysis of Sandwich Beams With a Compliant Core and With In-Plane Rigidity—Extended High-Order Sandwich Panel Theory Versus Elasticity

[+] Author and Article Information
Catherine N. Phan, George A. Kardomateas

 School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0150

Yeoshua Frostig

 Faculty of Civil and Environmental Engineering, Department of Structural Engineering andConstruction Management, Technion Israel Institute of Technology, Haifa 32 000, Israel

J. Appl. Mech 79(4), 041001 (May 08, 2012) (11 pages) doi:10.1115/1.4005550 History: Received June 27, 2010; Revised September 29, 2011; Posted January 31, 2012; Published May 08, 2012; Online May 08, 2012

A new one-dimensional high-order theory for orthotropic elastic sandwich beams is formulated. This new theory is an extension of the high-order sandwich panel theory (HSAPT) and includes the in-plane rigidity of the core. In this theory, in which the compressibility of the soft core in the transverse direction is also considered, the displacement field of the core has the same functional structure as in the high-order sandwich panel theory. Hence, the transverse displacement in the core is of second order in the transverse coordinate and the in-plane displacements are of third order in the transverse coordinate. The novelty of this theory is that it allows for three generalized coordinates in the core (the axial and transverse displacements at the centroid of the core and the rotation at the centroid of the core) instead of just one (midpoint transverse displacement) commonly adopted in other available theories. It is proven, by comparison to the elasticity solution, that this approach results in superior accuracy, especially for the cases of stiffer cores, for which cases the other available sandwich computational models cannot predict correctly the stress fields involved. Thus, this theory, referred to as the “extended high-order sandwich panel theory” (EHSAPT), can be used with any combinations of core and face sheets and not only the very “soft” cores that the other theories demand. The theory is derived so that all core/face sheet displacement continuity conditions are fulfilled. The governing equations as well as the boundary conditions are derived via a variational principle. The solution procedure is outlined and numerical results for the simply supported case of transverse distributed loading are produced for several typical sandwich configurations. These results are compared with the corresponding ones from the elasticity solution. Furthermore, the results using the classical sandwich model without shear, the first-order shear, and the earlier HSAPT are also presented for completeness. The comparison among these numerical results shows that the solution from the current theory is very close to that of the elasticity in terms of both the displacements and stress or strains, especially the shear stress distributions in the core for a wide range of cores. Finally, it should be noted that the theory is formulated for sandwich panels with a generally asymmetric geometric layout.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 7

Through-thickness distribution in the core of the transverse shear stress, τxz, at z=a/10 for the case of isotropic aluminum alloy faces and a wide range of isotropic cores

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Figure 1

Definition of the sandwich configuration

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Figure 2

Transverse displacement, w, at the top, z=c+f, for the case of graphite/epoxy faces and glass phenolic honeycomb core

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Figure 3

Through-thickness distribution in the core of the axial stress, σxx, at x=a/2 for the case of graphite/epoxy faces and glass phenolic honeycomb core

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Figure 4

(a) Through-thickness distribution in the core of the transverse normal stress, σzz, at x=a/2 for the case of E-glass/polyester faces and balsa wood core. (b) Through-thickness distribution in the core of the transverse normal strain, εzz, at x=a/2 for the case of E-glass/polyester faces and balsa wood core.

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Figure 5

Through-thickness distribution in the core of the transverse shear stress, τxz, at x=a/10 for the case of graphite/epoxy faces and glass phenolic honeycomb

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Figure 6

Through-thickness distribution in the core of the transverse shear stress, τxz, at x=a/10 for the case of E-glass/polyester faces and balsa wood core

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