Buckling and post-buckling analyses of size-dependent piezoelectric nanoplates

•An increasing nonlocal parameter leads to smaller buckling and post-buckling loads.•The positive/negative electric voltage decreases/increases buckling and post-buckling loads.•A relatively large temperature rise results in slight drops in buckling and post-buckling loads.

This paper attempts to investigate the buckling and post-buckling behaviors of piezoelectric nanoplate based on the nonlocal Mindlin plate model and von Karman geometric nonlinearity. An external electric voltage and a uniform temperature rise are applied on the piezoelectric nanoplate. Both the uniaxial and biaxial mechanical compression forces will be considered in the buckling and post-buckling analysis. By substituting the energy functions into the equation of the minimum total potential energy principle, the governing equations are derived directly, and then discretized through the differential quadrature (DQ) method. The buckling and post-buckling responses of piezoelectric nanoplates are calculated by employing a direct iterative method under different boundary conditions. The numerical results are presented to show the influences of different factors including the nonlocal parameter, electric voltage, and temperature rise on the buckling and post-buckling responses.