Carbon nanotubes (CNTs), owing to their exceptional mechanical, thermal, and electrical properties such as high strength, large elastic modulus, and remarkable chemical stability, have attracted considerable attention in a wide range of applications, including nanosensors, heat transfer systems, and composite reinforcements. Understanding their mechanical behavior, particularly in terms of deformation, vibration, and buckling, plays a crucial role in the design and development of advanced nanostructure-based devices. In this study, the static bending behavior of single-walled carbon nanotubes (SWCNTs) is analyzed using Love’s shell theory in combination with the nonlocal elasticity theory. To more accurately represent nanoscale effects, the nonlocal elasticity approach is employed, which considers the dependence of stress on the strains of neighboring points. The governing equations are derived based on Love’s shell theory, and appropriate boundary conditions are applied. The resulting partial differential equations are solved using the generalized differential quadrature method (GDQM). The effects of various parameters, such as the nonlocal length scale, boundary conditions, geometric dimensions of the nanotube, and the type of applied load, on the bending response are examined.

The numerical results are compared with those obtained from modeling the nanotube using beam theory, and the differences between the two approaches in predicting the bending behavior are evaluated. The findings indicate that nonlocal effects lead to a reduction in the bending stiffness of nanotubes, highlighting the importance of shell theory for accurate modeling of their behavior. The results of the shell model are further compared with those of the beam model, showing that, when nonlocal effects are taken into account, the discrepancy between shell theory and beam theory predictions of deflection increases even for long nanotubes. Therefore, the use of beam theory for modeling nanotube deflection can result in considerable errors. The effect of various parameters and loading on the bending deflection of carbon nanotube is investigated in the numerical results.