Buckling and post-buckling of size-dependent piezoelectric Timoshenko nanobeams subject to thermo-electro-mechanical loadings

Buckling and post-buckling behaviors of piezoelectric nanobeams are investigated by using the nonlocal Timoshenko beam theory and von Karman geometric nonlinearity. The piezoelectric nanobeam is subjected to an axial compression force, an applied voltage and a uniform temperature rise. After constructing the energy functionals, the nonlinear governing equations are derived by using the principle of minimum total potential energy and discretized by using the differential quadrature (DQ) method. A direct iterative method is employed to determine the buckling and post-buckling responses of piezoelectric nanobeams with hinged-hinged, clamped-hinged and clamped-clamped end conditions. Numerical examples are presented to study the influences of the nonlocal parameter, temperature rise and external electric voltage on the size-dependent buckling and post-buckling responses of piezoelectric nanobeams.