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Structural Engineering and Mechanics
  Volume 65, Number 5, March10 2018, pages 573-585

Modelling of graded rectangular micro-plates with variable length scale parameters
Reza Aghazadeh, Serkan Dag and Ender Cigeroglu

    This article presents strain gradient elasticity-based procedures for static bending, free vibration and buckling analyses of functionally graded rectangular micro-plates. The developed method allows consideration of smooth spatial variations of length scale parameters of strain gradient elasticity. Governing partial differential equations and boundary conditions are derived by following the variational approach and applying Hamilton\'s principle. Displacement field is expressed in a unified way to produce numerical results in accordance with Kirchhoff, Mindlin, and third order shear deformation theories. All material properties, including the length scale parameters, are assumed to be functions of the plate thickness coordinate in the derivations. Developed equations are solved numerically by means of differential quadrature method. Proposed procedures are verified through comparisons made to the results available in the literature for certain limiting cases. Further numerical results are provided to illustrate the effects of material and geometric parameters on bending, free vibrations, and buckling. The results generated by Kirchhoff and third order shear deformation theories are in very good agreement, whereas Mindlin plate theory slightly overestimates static deflection and underestimates natural frequency. A rise in the length scale parameter ratio, which identifies the degree of spatial variations, leads to a drop in dimensionless maximum deflection, and increases in dimensionless vibration frequency and buckling load. Size effect is shown to play a more significant role as the plate thickness becomes smaller compared to the length scale parameter. Numerical results indicate that consideration of length scale parameter variation is required for accurate modelling of graded rectangular micro-plates.
Key Words
    functionally graded micro-plates; strain gradient elasticity; length scale parameters; bending; free vibrations; buckling
Reza Aghazadeh:
1) Department of Mechanical Engineering, Middle East Technical University, Ankara 06800, Turkey
2) Department of Aeronautical Engineering, University of Turkish Aeronautical Association, Ankara 06790, Turkey
Serkan Dag and Ender Cigeroglu: Department of Mechanical Engineering, Middle East Technical University, Ankara 06800, Turkey

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