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Review Articles

A Survey With Numerical Assessment of Classical and Refined Theories for the Analysis of Sandwich Plates

[+] Author and Article Information
E. Carrera1

Aeronautics and Space Engineering Department, Politecnico di Torino, Turin 10129, Italyerasmo.carrera@polito.it

S. Brischetto

Aeronautics and Space Engineering Department, Politecnico di Torino, Turin 10129, Italy

1

Corresponding author.

Appl. Mech. Rev 62(1), 010803 (Dec 16, 2008) (17 pages) doi:10.1115/1.3013824 History: Received January 23, 2008; Revised June 20, 2008; Published December 16, 2008

A large variety of plate theories are described and assessed in the present work to evaluate the bending and vibration of sandwich structures. A brief survey of available works is first given. Such a survey includes significant review papers and latest developments on sandwich structure modelings. The kinematics of classical, higher order, zigzag, layerwise, and mixed theories is described. An exhaustive numerical assessment of the whole theories is provided in the case of closed form solutions of simply supported panels made of orthotropic layers. Reference is made to the unified formulation that has recently been introduced by the first author for a plate/shell analysis. Attention has been given to displacements, stresses (both in-plane and out-of-plane components), and the free vibration response. Only simply supported orthotropic panels loaded by a transverse distribution of bisinusoidal pressure have been analyzed. Five benchmark problems are treated. The accuracy of the plate theories is established with respect to the length-to-thickness-ratio (LTR) geometrical parameters and to the face-to-core-stiffness-ratio (FCSR) mechanical parameters. Two main sources of error are outlined, which are related to LTR and FCSR, respectively. It has been concluded that higher order theories (HOTs) can be conveniently used to reduce the error due to LTR in thick plate cases. But HOTs are not effective in increasing the accuracy of the classical theory analysis whenever the error is caused by increasing FCSR values; layerwise analysis becomes mandatory in this case.

Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Geometry and notations of the considered plate

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Figure 2

Displacements and transverse stresses in the case of classical lamination theory

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Figure 3

Displacements and transverse stresses in the case of first order shear deformation theory

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Figure 4

Displacements and transverse stresses in the case of ED2

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Figure 5

Displacements and transverse stresses in the case of EDZ1

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Figure 6

Displacements and transverse stresses in the case of LD3

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Figure 7

Displacements and transverse stresses in the case of LM2

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Figure 8

Displacements and transverse stresses in the case of EM2

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Figure 9

Benchmark 1. Sandwich plate with a core in Nomex. Static analysis. σxx versus z. Comparison between 3D solutions and classical theories. a∕h=4 on the left. a∕h=100 on the right.

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Figure 10

Benchmark 1. Sandwich plate with a core in Nomex. Static analysis. σxz versus z. Comparison between 3D solutions and classical theories. a∕h=4 on the left. a∕h=100 on the right.

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Figure 11

Benchmark 1. Sandwich plate with a core in Nomex. Static analysis. σxz versus z. Comparison between 3D solutions, HOT theories, and HOT theories with MZZF. a∕h=4 on the left. a∕h=100 on the right.

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Figure 12

Sandwich plate with a core in Nomex. Static analysis. σxz versus z. Comparison between 3D solutions, LW models, and HOT theories with MZZF. a∕h=4 on the left. a∕h=100 on the right.

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Figure 13

In-plane stress evaluation Benchmark 1 (left) and Benchmark 2 (right). Sandwich plate with a core in Nomex. Static analysis. σxx versus z. Comparison between 3D solutions, HOT, and LW theories. Thin plate case a∕h=100.

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Figure 14

In-plane stress evaluations. Benchmark 4 (left) versus Benchmark 5 (right). σxx versus z. Comparison between 3D solutions, HOT, and LW theories. Thick plate case a∕h=4.

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Figure 15

Benchmark 5. Sandwich plate with high reduced core stiffness. Static analysis. σxz versus z. Comparison between 3D solutions, HOT, and LW theories. a∕h=4 on the left. a∕h=100 on the right.

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Figure 16

Comparison Benchmark 1 and Benchmark 5. Sandwich plate with a core in Nomex (on the top) and with high reduced core stiffness (on the bottom). ED2 theory. a∕h=100. Static case.

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Figure 17

Comparison of Benchmark 1 and Benchmark 5. Sandwich plate with a core in Nomex (on the top) and with high reduced core stiffness (on the bottom). LD2 theory. a∕h=100. Static case.

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