Size dependency in nonlinear instability of smart magneto-electro-elastic cylindrical composite nanopanels based upon nonlocal strain gradient elasticity

In the present article, a new size-dependent panel model is established incorporating the both hardening-stiffness and softening-stiffness small scale effects jointly with electrostatics and magnetostatics to study analytically the buckling and postbuckling behavior of smart magneto-electro-elastic (MEE) composite nanopanels under combination of axial compression, external electric and magnetic potentials. To this end, the nonlocal strain gradient elasticity theory in conjunction with the Maxwell equations is applied to the classical panel theory to develop a more comprehensive size-dependent panel model including simultaneously the both nonlocality and strain gradient size dependency. With the aid of the virtual work’s principle, the size-dependent differential equations of the problem are derived. The attained non-classical governing differential equations are solved analytically by means an improved perturbation technique within the framework of the boundary layer theory of shell buckling. Explicit analytical expressions associated with the nonlinear axial stability equilibrium paths of the electromagnetic actuated smart MEE composite nanopanels including nonlocality and strain gradient micro-size dependency are proposed. It is displayed that the nonlocal size effect leads to reduce the buckling stiffness, while the strain gradient size dependency causes to enhance it. Moreover, it is found that by applying a negative electric field as well as positive magnetic field, the influences of the nonlocal and strain gradient size effects on the critical buckling load of an axially loaded MEE composite nanopanel are more significant.