A Nonlocal Finite Element Approach for Nanobeams Based on Stress-Driven Model

The manuscript proposes a nonlocal finite element approach for the analysis of the bending behavior of Bernoulli-Euler nanobeams, based on well-posed Stress-Driven nonlocal continuum mechanics. The structural behavior of the nanobeams was investigated using COMSOL Multiphysics® 6.2. The approach is based on a 1D-finite element discrete model where the nonlocal constitutive law is introduced to capture the nonlocal effects characteristic of nanostructures, even though the software employs a classical local constitutive law by default. The proposed approach involves determining an elastic modulus multiplier function, ensuring equivalence between the bending curvature functions of the nonlocal and local models. The reliability and the potentialities of the proposed approach are assessed by comparing the numerical results with both experimental and analytical data available in the current literature. Additionally, the work performs a parametric investigation, presenting and examining the main results across different values of the nonlocal parameter, mesh type, and boundary conditions. This study offers a practical framework for the design of nanostructures using commercially available engineering software.