Size effects on nanomechanical behaviors of nanoelectronics devices based on consistent couple-stress theory

• Formulation of Euler–Bernoulli beam model based on consistent couple stress theory and its application for the CNTs.
• Analyzing the deflection of the CNTs under electrostatic actuation using the consistent couple stress theory.
• Presentation of the pull-in voltages for various dimensions and boundary conditions.

The paper presents the size-dependant mechanical behavior of the carbon nanotube-based nano-electromechanical systems using the consistent couple-stress theory. The formulation of the Euler–Bernoulli beam model applied in mechanical modeling of the carbon nanotubes is developed via considering true continuum kinematical displacement and rotation. This is done to solve the indeterminacy of the spherical part of the couple-stress tensor and the appearance of the body couple in the constitutive equation of the force–stress tensor of the original coupe stress theory. The governing equations are solved in order to obtain the size-dependent amount of deflection and pull-in voltages of the carbon nanotubes under electrostatic actuation. The results are provided for various dimensions and boundary conditions. Moreover, the influences of couples-stress theory on the outcomes are scrutinized. The comparison between the results obtained from the classical and couple stress theory reveals that application of the latter leads to a model of the CNT with higher stiffness, smaller deflection and larger pull-in voltages.