Nonlocal effects on curved double-walled carbon nanotubes based on nonlocal theory

Abstract

Curved double-walled carbon nanotubes (CDWCNTs) are crucial components in nanoelectronics, mechanical sensors, and composite materials due to their unique geometry and structural properties. Electron microscopy images have revealed that carbon nanotubes are rarely perfectly straight, often exhibiting curvature or waviness along their length due to inherent geometrical imperfections. The accurate mechanical modeling of these structures is essential, particularly to capture size-dependent effects that classical elasticity theories fail to account for. In this study, a novel analytical framework was introduced for combining the initial value method with the approximate transfer matrix approach to analyze the mechanical behavior of CDWCNTs under anti-plane loading within the framework of nonlocal elasticity theory. The proposed methodology provides an effective and computationally efficient alternative to traditional analytical approaches. By analyzing displacements, rotations, bending moments, and shear forces, substantial deviations were revealed between classical and nonlocal elasticity solutions, particularly as the dimensionless nonlocal parameter \(R/\gamma \) decreased. The results show that nonlocal effects become dominant at smaller size parameters, especially in displacements, rotations, and bending moments, while shear forces remain unaffected. These findings emphasize the critical role of nonlocal effects in accurately predicting nanoscale mechanical responses and offer valuable insights for modeling advanced nanostructures in emerging technologies, such as microelectromechanical systems and nanotechnology. Convergence studies have confirmed the accuracy and stability of the proposed approach, thereby establishing this as a robust tool for modeling nanoscale structures.