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International Journal for Multiscale Computational Engineering
Impact-faktor: 1.016 5-jähriger Impact-Faktor: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Druckformat: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2012004062
pages 309-318


H. Farahmand
Department of Mechanical Engineering, Islamic Azad University of Kerman Branch, Kerman, Iran
M. Mohammadi
Young Researchers and Elites Club, Kerman Branch, Islamic Azad University, Kerman, Iran


In this paper, bending analysis of thin functionally graded (FG) rectangular microplates based on the strain gradient theory is presented. Relying on strain gradient theory, flexural microplate theory is utilized to obtain the governing equations for FG flexural microplates, which include higher-order terms. It is assumed that the material properties of FG microplates vary through the thickness according to a power law function. Also, it is supposed that the microplate is simply supported along all edges; hence, the Navier solution is used to find the deflection of the microplate. Finally, based on the obtained closed form solution, effects of length scale parameters, material properties, and dimensions on the static response of flexural microplates are investigated in detail.


  1. Ahmadi, A. R., Farahmand, H., and Arabnejad, S., Static deflection analysis of flexural simply supported sectorial micro-plate using P-version finite element method. DOI: 10.1615/IntJMultCompEng.v9.i2.40

  2. Asghari, M., Rahaeifard, M., Kahrobaiyan, M. H., and Ahmadian, M. T., The modified couple stress functionally graded timoshenko beam formulation. DOI: 10.1016/j.matdes.2010.08.046

  3. Eringen, A. C., Linear theory of micro-polar elasticity. DOI: 10.1007/978-1-4612-0555-5_5

  4. Eringen, A. C., Theory of micro-polar plates. DOI: 10.1007/BF01593891

  5. Farahmand, H. and Arabnejad, S., Developing a novel finite elastic approach in strain gradient theory for microstructures. DOI: 10.1615/IntJMultCompEng.v8.i4.70

  6. Fish, J. and Kuznetsov, S., Computational continua. DOI: 10.1002/nme.2918

  7. Gauthier, R. D. and Jahsman, W. E., A quest for micropolar elastic constants. DOI: 10.1115/1.3423583

  8. Hofstetter, K., Hellmich, C., and Eberhardsteiner, J., Development and experimental validation of a continuum micro-mechanics model for the elasticity of wood. DOI: 10.1016/j.euromechsol.2005.05.006

  9. Javaheri, R. and Eslami, M. R., Buckling of functionally graded plates under in-plane compressive loading. DOI: 10.1016/j.tws.2005.01.002

  10. Ke, L. L. and Wang, Y. S., Size effect on dynamic stability of functionally graded micro-beams based on a modified couple stress theory. DOI: 10.1016/j.compstruct.2010.09.008

  11. Ke, L. L., Wang, Y. S., Yang, J., and Kitipornchai, S., Nonlinear free vibration of size dependent functionally graded micro-beams. DOI: 10.1016/j.ijengsci.2010.12.008

  12. Krishna Reddy, G. V. and Venkatasubramanian, N. K., On the flexural rigidity of a micro-polar elastic cylinder. DOI: 10.1115/1.3424317

  13. Koizumi, M., FGM activities in Japan. DOI: 10.1016/S1359-8368(96)00016-9

  14. Lakes, R. S., The role of gradient effects in the piezoelectricity of bone.

  15. Lakes, R. S., Experimental micro-elasticity of two porous solids. DOI: 10.1016/0020-7683(86)90103-4

  16. Lazopoulos, K. A., On bending of strain elastic micro-plates. DOI: 10.1016/j.mechrescom.2009.05.005

  17. Mindlin, R. D., Micro-structure in linear elasticity. DOI: 10.1007/BF00248490

  18. Mindlin, R. D. and Eshel, N. N., On first strain-gradient theories in linear elasticity. DOI: 10.1016/0020-7683(68)90036-X

  19. Mohammadi, M., Saidi, A. L., and Jomehzadeh, E., A novel analytical approach for buckling analysis of moderately thick functionally graded rectangular plates with two simply supported opposite edges. DOI: 10.1243/09544062JMES1804

  20. Mohammadi, M., Saidi, A. L., and Jomehzadeh, E., Levy solution for buckling analysis of functionally graded rectangular plates. DOI: 10.1007/s10443-009-9100-z

  21. Papargyri-Beskou, S., Giannakopoulos, A. E., and Beskos, D. E., Variational analysis of gradient elastic flexural plates under static loading. DOI: 10.1016/j.ijsolstr.2010.06.003

  22. Papargyri-Beskou, S. and Beskos, D. E., Static, stability and dynamic analysis of gradient elastic flexural Kirchhoff plates. DOI: 10.1007/s00419-007-0166-5

  23. Schijve, J., Note on couple stresses. DOI: 10.1016/0022-5096(66)90042-1

  24. Toupin, R. A., Elasic materials with couple stress. DOI: 10.1007/BF00253945

  25. Yang, J. F. C. and Lakes, R. S. V., Experimental study of micro-polar and couple stress elasticity in compact bone in bending. DOI: 10.1016/0021-9290(82)90040-9

  26. Wang, C. M., Reddy, J. N., and Lee, K. H., Shear Deformable Beams and Plates: Relationship with the Classical Theory.

  27. Wang, B., Zhou, S., Zhao, J., and Chen, X., A size dependent Kirchhoff micro-plate model based on strain gradient elasticity theory. DOI: 10.1016/j.euromechsol.2011.04.001