Buckling analysis of single-walled carbon nanotubes using the initial value method and approximate transfer matrix based on nonlocal elasticity theory

In this study, a novel method is presented to analyze the buckling behavior of single-walled carbon nanotubes (SWCNTs) using the initial value method (IVM) in conjunction with the approximate transfer matrix, within the framework of nonlocal elasticity theory. The study aims to accurately approximate critical buckling load parameters under various boundary conditions, without encountering high computational requirements. IVM enables the computation of displacements and stress resultants along the entire beam from given initial conditions. The approximate transfer matrix is employed to analyze system states at different points through successive integration of solutions, generating the principal matrix needed for IVM and ensuring systematic and precise results that optimize the accuracy of the analysis. A convergence study confirms the effectiveness and precision of the proposed method, revealing a decrease in the critical buckling load parameters as the nonlocal parameter increases, applicable across all boundary conditions studied (simply supported, clamped–clamped, clamped–simply supported, and clamped-free). These results underscore the need to incorporate nonlocal effects for more accurate nanostructure mechanics predictions. The integration of IVM and the approximate transfer matrix provides a computationally efficient alternative to traditional numerical and semi-analytical methods, aiding researchers and engineers working with SWCNTs and other nanomaterials.