Electro-mechanical shear buckling of piezoelectric nanoplate using modified couple stress theory based on simplified first order shear deformation theory

Abstract

• Shear buckling of piezoelectric nanoplate is analyzed based on modified couple stress theory. • Nonlinear equations are found using simplified first order shear deformation theory. • The critical shear load is obtained via closed-form solution with various boundary conditions. • Increasing length scale parameter increases critical shear load. • The effect of external electric voltage on the critical shear load occurring on the piezoelectric nanoplate is insignificant. This paper studies the electro-mechanical shear buckling analysis of piezoelectric nanoplate using modified couple stress theory with various boundary conditions.In order to be taken electric effects into account, an external electric voltage is applied on the piezoelectric nanoplate. The simplified first order shear deformation theory (S-FSDT) has been employed and the governing differential equations have been obtained using Hamilton's principle and nonlinear strains of Von-Karman. The modified couple stress theory has been applied to considering small scale effects. An analytical approach was developing to obtain exact results with various boundary conditions. After all, results have been presented by change in some parameters, such as; aspect ratio, effect of various boundary conditions, electric voltage and length scale parameter influences. At the end, results showed that the effect of external electric voltage on the critical shear load occurring on the piezoelectric nanoplate is insignificant.