Size‐dependent buckling analysis of functionally graded nanoplate coupled with piezoelectric layers resting on orthotropic foundation based on surface piezo‐elasticity theory

Abstract In this study, a refined plate theory by considering stretching effects extended to investigation of quasi‐3D size‐dependent buckling analysis of a functionally graded simply supported nanoplate integrated with piezoelectric face‐sheets resting on orthotropic foundation by taking into account the surface effects. The power law is used to calculate the material properties in the functionally graded core in which the non‐homogeneous core properties are continuously changing along the thickness. Due to the consideration of functionally graded materials and due to the asymmetry in the distribution of material properties in the core, the middle plane and the neutral plane do not coincide. Hence, to consider a reference plane, the concept of a neutral surface is considered. The kinematics of nanoplate are formulated with nonlocal higher order shear deformation theory based on nonlocal strain gradient theory. Additionally, the surface effect is modeled based on surface piezo‐elasticity theory. To check the accuracy and efficiency of the current model, a comprehensive validation and comparative study has been conducted based on the results obtained and the results found in the previous literature. Finally, a comprehensive study is conducted to investigate the effect of various parameters, including different foundations, residual stress, surface effects, stretching effect, neutral surface, aspect ratio, thickness ratio, nanlocal parameter, length scale parameter, gradient index, and initial voltage, which are examined on critical buckling load of nanoplate in details. It is expected that the results of the current study should be utilized in designing micro/nano‐electro‐mechanical systems components based on smart nanostructures.