Abstract
In this paper, a size-dependent microscale plate model is developed to describe the bending, buckling and free vibration behaviors of microplates made of functionally graded materials (FGMs). The size effects are captured based on the modified strain gradient theory (MSGT), and the formulation of the paper is on the basis of Mindlin plate theory. The presented model accommodates the models based upon the classical theory (CT) and the modified couple stress theory (MCST) if all or two scale parameters are set to zero, respectively. By using Hamilton's principle, the governing equations and related boundary conditions are derived. The bending, buckling and free vibration problems are considered and are solved through the generalized differential quadrature (GDQ) method. A detailed parametric and comparative study is conducted to evaluate the effects of length scale parameter, material gradient index and aspect ratio predicted by the CT, MCST and MSGT on the deflection, critical buckling load and first natural frequency of the microplate. The numerical results indicate that the model developed herein is significantly size-dependent when the thickness of the microplate is on the order of the material scale parameters.
Highlights
The experiments conducted on the microstructures subjected to different loading conditions have revealed their size–dependent behavior (Nix 1989; Fleck et al 1994; Ma and Clarke 1995; Vardoulakis et al 1998; Stolken and Evans 1998; Chong and Lam 1999; Lam et al 2003; and Colton 2005)
In contrast with the results of the previous figure, it is seen that the couple stress and the strain gradient theories predict the buckling load larger than that of the classical theory and this pattern is more evident for the small length scale
In addition to modified strain gradient theory (MSGT), the numerical results were given for the two other models i.e., classical theory (CT) and modified couple stress theory (MCST) constructed by ignoring all or two scale constants in the present model
Summary
The experiments conducted on the microstructures subjected to different loading conditions have revealed their size–dependent behavior (Nix 1989; Fleck et al 1994; Ma and Clarke 1995; Vardoulakis et al 1998; Stolken and Evans 1998; Chong and Lam 1999; Lam et al 2003; and Colton 2005). Relevant works concerning the applicability of MCST in the analysis of microstructures can be found in (Ma et al (2008); Tsiatas (2009); Kahrobaiyan et al (2010); Ke et al (2011); Jomehzadeh et al (2011); Asghari (2012); Thai and Choi (2013)) In addition to these works, based on the modified couple stress and Kirchhoff plate theories, a size-dependent plate model was developed by Yin et al (2010) for the dynamic analysis of microplate. Kahrobian et al (2012) proposed a non-classical beam model accounting for the size influences in the framework of Euler– Bernoulli beam and strain gradient theories for static and free vibrations analyzes They derived five equivalent length scale parameters in terms of the length scales of material constituents for functionally graded microbeams. The effects of different model parameters on the response of the microplate are investigated
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