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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November 2015
Research-Article
Correspondence Relations Between Deflection, Buckling Load, and Frequencies of Thin Functionally Graded Material Plates and Those of Corresponding Homogeneous Plates
Shi-Rong Li,
Shi-Rong Li
Department of Civil Engineering,
Yangzhou University,
Yangzhou, Jiangsu 225127, China;
Yangzhou University,
Yangzhou, Jiangsu 225127, China;
Department of Biomedical
Engineering and Mechanics,
Virginia Polytechnic Institute and
State University,
Blacksburg, VA 24061
Engineering and Mechanics,
Virginia Polytechnic Institute and
State University,
Blacksburg, VA 24061
Search for other works by this author on:
Xuan Wang,
Xuan Wang
School of Hydraulic,
Energy and Power Engineering,
Yangzhou University,
Yangzhou, Jiangsu 225127, China
Energy and Power Engineering,
Yangzhou University,
Yangzhou, Jiangsu 225127, China
Search for other works by this author on:
Romesh C. Batra
Romesh C. Batra
Fellow ASME
Department of Biomedical
Engineering and Mechanics,
Virginia Polytechnic Institute and
State University,
Blacksburg, VA 24061
Department of Biomedical
Engineering and Mechanics,
Virginia Polytechnic Institute and
State University,
Blacksburg, VA 24061
Search for other works by this author on:
Shi-Rong Li
Department of Civil Engineering,
Yangzhou University,
Yangzhou, Jiangsu 225127, China;
Yangzhou University,
Yangzhou, Jiangsu 225127, China;
Department of Biomedical
Engineering and Mechanics,
Virginia Polytechnic Institute and
State University,
Blacksburg, VA 24061
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
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
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. Nov 2015, 82(11): 111006 (8 pages)
Published Online: August 21, 2015
Article history
Received:
April 21, 2015
Revised:
July 27, 2015
Citation
Li, S., Wang, X., and Batra, R. C. (August 21, 2015). "Correspondence Relations Between Deflection, Buckling Load, and Frequencies of Thin Functionally Graded Material Plates and Those of Corresponding Homogeneous Plates." ASME. J. Appl. Mech. November 2015; 82(11): 111006. https://doi.org/10.1115/1.4031186
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