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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 476131, 10 pages
Research Article

Analysis of Sigmoid Functionally Graded Material (S-FGM) Nanoscale Plates Using the Nonlocal Elasticity Theory

1Department of Civil Engineering, Gangneung-Wonju National University, 7 Jukheon, Gangneung 210-702, Republic of Korea
2Department of Civil & Railroad Engineering, Daewon University College, 599 Shinwol, Jecheon 390-702, Republic of Korea

Received 13 April 2013; Accepted 16 May 2013

Academic Editor: Abdelouahed Tounsi

Copyright © 2013 Woo-Young Jung and Sung-Cheon Han. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Based on a nonlocal elasticity theory, a model for sigmoid functionally graded material (S-FGM) nanoscale plate with first-order shear deformation is studied. The material properties of S-FGM nanoscale plate are assumed to vary according to sigmoid function (two power law distribution) of the volume fraction of the constituents. Elastic theory of the sigmoid FGM (S-FGM) nanoscale plate is reformulated using the nonlocal differential constitutive relations of Eringen and first-order shear deformation theory. The equations of motion of the nonlocal theories are derived using Hamilton’s principle. The nonlocal elasticity of Eringen has the ability to capture the small scale effect. The solutions of S-FGM nanoscale plate are presented to illustrate the effect of nonlocal theory on bending and vibration response of the S-FGM nanoscale plates. The effects of nonlocal parameters, power law index, aspect ratio, elastic modulus ratio, side-to-thickness ratio, and loading type on bending and vibration response are investigated. Results of the present theory show a good agreement with the reference solutions. These results can be used for evaluating the reliability of size-dependent S-FGM nanoscale plate models developed in the future.