Buckling analysis of nonlocal Timoshenko beams via an efficient semi-analytical approach

This article delves into the buckling analysis of nonlocal Timoshenko beams, focusing on the critical role of size effects in micro- and nanoscale structures. It introduces an efficient semi-analytical approach that combines the Initial Value Method (IVM) with the Approximate Transfer Matrix (ATM) formulation, offering a computationally efficient and numerically robust solution. The study validates this method against exact analytical and Finite Element Method (FEM) results, demonstrating excellent agreement across various boundary conditions. Key topics include the influence of the nonlocal parameter on critical buckling loads, the convergence behavior of the ATM formulation, and the parametric analysis of beam geometry and material properties. The findings highlight the significant reduction in buckling loads due to nonlocal effects, particularly in beams with rigid boundary conditions and lower length-to-diameter ratios. This research provides valuable insights for engineers and scientists working on nanoscale structural design, emphasizing the importance of considering nonlocal effects for accurate and reliable predictions.