Modelling of graded rectangular micro-plates with variable length scale parameters

Date

2018-03-10

Author

Aghazadeh, Reza
Dağ, Serkan
Ciğeroğlu, Ender

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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.

Subject Keywords

Functionally graded micro-plates, Strain gradient elasticity, Length scale parameters, Bending, Free vibrations, Buckling

URI

https://hdl.handle.net/11511/36728

Journal

STRUCTURAL ENGINEERING AND MECHANICS

DOI

https://doi.org/10.12989/sem.2018.65.5.573

Collections

Department of Mechanical Engineering, Article

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Citation Formats

R. Aghazadeh, S. Dağ, and E. Ciğeroğlu, “Modelling of graded rectangular micro-plates with variable length scale parameters,” STRUCTURAL ENGINEERING AND MECHANICS, pp. 573–585, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/36728.