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Research Papers

Correspondence Relations Between Deflection, Buckling Load, and Frequencies of Thin Functionally Graded Material Plates and Those of Corresponding Homogeneous Plates

[+] Author and Article Information
Shi-Rong Li

Department of Civil Engineering,
Yangzhou University,
Yangzhou, Jiangsu 225127, China;
Department of Biomedical
Engineering and Mechanics,
Virginia Polytechnic Institute and
State University,
Blacksburg, VA 24061

Xuan Wang

School of Hydraulic,
Energy and Power Engineering,
Yangzhou University,
Yangzhou, Jiangsu 225127, China

Romesh C. Batra

Fellow ASME
Department of Biomedical
Engineering and Mechanics,
Virginia Polytechnic Institute and
State University,
Blacksburg, VA 24061

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received April 21, 2015; final manuscript received July 27, 2015; published online August 21, 2015. Assoc. Editor: Glaucio H. Paulino.

J. Appl. Mech 82(11), 111006 (Aug 21, 2015) (8 pages) Paper No: JAM-15-1206; doi: 10.1115/1.4031186 History: Received April 21, 2015; Revised July 27, 2015

Based on the classical plate theory (CPT), we derive scaling factors between solutions of bending, buckling and free vibration of isotropic functionally graded material (FGM) thin plates and those of the corresponding isotropic homogeneous plates. The effective material properties of the FGM plate are assumed to vary piecewise continuously in the thickness direction except for the Poisson ratio that is taken to be constant. The correspondence relations hold for plates of arbitrary geometry provided that the governing equations and boundary conditions are linear. When the stretching and bending stiffnesses of the FGM plate satisfy a relation, Poisson's ratio is constant and the boundary conditions are such that the in-plane membrane forces vanish, then there exists a physical neutral surface for the FGM plate that is usually different from the plate midsurface. Example problems studied verify the accuracy of scaling factors.

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Grahic Jump Location
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Rectangular plates subjected to in-plane uniformly distributed loads

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