New modeling and analysis methods for micro-plates

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2017
Aghazadeh, Reza
This study presents strain gradient elasticity based procedures for static bending, free vibration and buckling analyses of functionally graded rectangular micro-plates subjected to mechanical and thermal loadings. Mathematically the non-classical modified couple stress and classical elasticity theories are the two special cases of the new model. The methods developed allow taking into account spatial variations of length scale parameters of strain gradient elasticity and modified couple stress theory. Governing partial differential equations and boundary conditions are derived by following variational approaches 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 upon static deflection, vibration frequency, and critical buckling load. Presented numerical results clearly illustrate size effect at micro-scale, impact of length scale parameter variations and influence of initial thermal stresses upon mechanical behavior of functionally graded rectangular micro-plates.

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Citation Formats
R. Aghazadeh, “New modeling and analysis methods for micro-plates,” Ph.D. - Doctoral Program, Middle East Technical University, 2017.