Journal
APPLIED MATHEMATICAL MODELLING
Volume 39, Issue 13, Pages 3814-3845Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2014.12.001
Keywords
Strain gradient elasticity theory; Refined shear deformation theory; Functionally graded microplates; Elastic foundation
Funding
- NSFC [11272131, 11472114]
- Specialized Research Fund for the Doctoral Program of Higher Education of China [20110142110039]
- Fundamental Research Funds for the Central Universities, HUST [2013KXYQ008]
- Doctoral Innovation Fund of Huazhong University of Science and Technology [0118240034]
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Based on the strain gradient elasticity theory and a refined shear deformation theory, an efficient size-dependent plate model is developed to analysis the bending, buckling and free vibration problems of functionally graded microplates resting on elastic foundation. The present model contains four displacement variables only and introduces three material length scale parameters. Besides, it satisfies the stress-free boundary conditions on the top and bottom surfaces of the microplate without using a shear correction factor. The elastic foundation is modeled as two-parameter Winkler-Pasternak foundation. The material properties of the microplate are assumed to vary in the thickness direction and estimated through the classical rule of mixture. By using Hamilton's principle, the equations of motion and boundary conditions are obtained. Closed form solutions are presented for the simply supported microplate. Comparison studies are performed to establish the validity of the derived formulation. The effects of material length scale parameter, material gradient index, elastic foundation, aspect ratio and transverse shear deformation on the bending, buckling and vibration characteristics of the microplate are investigated in detail. (C) 2014 Elsevier Inc. All rights reserved.
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