Structural analysis of nonlocal nanobeam via FEM using equivalent nonlocal differential model

The publication delves into the structural analysis of nonlocal nanobeams via the finite element method (FEM) using an equivalent nonlocal differential model. It addresses the challenges posed by Eringen’s nonlocal elastic theory, particularly the issues with constitutive boundary conditions. The authors introduce a novel FEM framework that treats these boundary conditions as high-order external loads, significantly simplifying the analysis process. This approach not only ensures a more accurate representation of nonlocal effects but also optimizes computational efficiency. The paper includes detailed derivations of the governing equations, weak formulations, and implementation strategies for static bending, vibration, and buckling analyses. The results are validated through comparisons with exact solutions, demonstrating the framework's accuracy and reliability. This work promises to advance the field of nanoscale structural analysis by offering a practical and efficient tool for engineers and researchers.