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Research Papers

Hybrid Transformation to a Generalized Reissner–Mindlin Theory for Composite Plates

[+] Author and Article Information
Chang-Yong Lee

Assistant Professor
Department of Mechanical Engineering,
Pukyong National University,
Busan 608-739, South Korea
e-mail: bravenlee@pknu.ac.kr

Dewey H. Hodges

Professor
The Daniel Guggenheim
School of Aerospace Engineering,
Georgia Institute of Technology,
Atlanta, Georgia 30332-0150
e-mail: dhodges@gatech.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received March 24, 2015; final manuscript received May 27, 2015; published online June 19, 2015. Assoc. Editor: Taher Saif.

J. Appl. Mech 82(9), 091005 (Sep 01, 2015) (7 pages) Paper No: JAM-15-1161; doi: 10.1115/1.4030740 History: Received March 24, 2015; Revised May 27, 2015; Online June 19, 2015

An asymptotic theory of composite plates is constructed using the variational asymptotic method. To maximize simplicity and promote efficiency of the developed model, a transformation procedure is required to establish a mathematical link between an asymptotically correct energy functional derived herein and a simpler engineering model, such as a generalized Reissner–Mindlin model. Without relaxing the warping constraints and performing “smart minimization” or optimization procedures introduced in previous work, a different approach is suggested in this paper. To eliminate all partial derivatives of the 2D generalized strains in the asymptotically correct energy functional, a hybrid transformation procedure is systematically carried out by involving modified equilibrium and compatibility equations, and solving a system of linear algebraic equations via the pseudo-inverse method. Equivalent constitutive laws for the generalized Reissner–Mindlin plate model are then estimated. Several examples as a preliminary validation are used to demonstrate the capability and accuracy of this new model.

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References

Figures

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Fig. 1

Schematic of plate deformation

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Fig. 2

Distribution of σ13 versus the through-thickness coordinate for [15 deg/−15 deg]

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Fig. 3

Distribution of σ33 versus the through-thickness coordinate for [15 deg/−15 deg]

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Fig. 4

Distribution of σ13 versus the through-thickness coordinate for [30 deg/−30 deg/−30 deg/30 deg]

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Fig. 5

Distribution of σ33 versus the through-thickness coordinate for [30 deg/−30 deg/−30 deg/30 deg]

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Fig. 6

Distribution of σ13 versus the through-thickness coordinate for [30 deg/−30 deg/−30 deg/30 deg]

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