Modified strain gradient Reddy rectangular plate model for biaxial buckling and bending analysis of double-coupled piezoelectric polymeric nanocomposite reinforced by FG-SWNT

In this paper, the modified strain gradient (MSG) Reddy rectangular plate theory is extended for biaxial buckling and bending analysis of double-coupled polymeric nanocomposite plates reinforced by functionally graded single-walled boron nitride nanotubes (FG-SWBNNTs) and functionally graded single-walled carbon nanotubes (FG-SWCNTs). Different distribution patterns of BNNTs and SWCNTs including uniform distribution (UD), FG-V, FG-X and FG-O are used. The micromechanical approach is employed to determine the elastic and piezoelectric material properties of the double-coupled nanocomposite rectangular plates. The equilibrium equations are obtained by Hamilton's principle. Then, the critical biaxial buckling load and deflection of the double-coupled nanocomposite plates are derived by Navier's method with simply supported boundary conditions for all edges. A good agreement is observed between the obtained and literature results. Inclusive parametric study is conducted to investigate the effects of material length scale parameters, applied voltage, elastic foundation coefficients, aspect ratio and van der Waals interaction on the dimensionless critical biaxial buckling load and deflection of the double-coupled nanocomposite rectangular plates. The results reveal that the elastic foundation and van der Waals interaction in contrast to applied voltage increase the dimensionless critical biaxial buckling load and vice versa decrease the dimensionless deflection of the double-coupled nanocomposite plates. Influence of the material length scale parameters on the dimensionless critical biaxial buckling load and deflection of the double-coupled nanocomposite plates are insignificant at h/l ≥ 10 for modified couple stress theory (MCST) and MSGT. Also, the effects of volume fraction and various distributions of SWNTs on the shear stress of polymeric nanocomposite Reddy rectangular plates are studied. The obtained results can be useful for micro-electro-mechanical (MEMS) and nano-electro-mechanical (NEMS) systems.