Nonlocal biaxial buckling analysis of nanoplates with multiple Gaussian defects using the finite difference method

Abstract

In this study, the biaxial buckling behavior of a nanoplate containing defects within the framework of nonlocal elasticity theory was investigated numerically by the finite difference method (FDM). The plate has a square geometry with four simply supported edges (SSSS), and the buckling differential equation was converted to a discrete form using the central difference method. Boundary conditions were imposed via ghost nodes, resulting in an eigenvalue problem. Gaussian-type defects were modeled with the parametric functions that attenuate the Young’s modulus. The effects of defect location, spread, and severity on buckling were thoroughly investigated. The validity of the model was confirmed by comparison with available molecular dynamics (MD) results in the literature. In addition, analyses performed for different nonlocal parameters and the defect scenarios demonstrated the decisive effects of defect location and spread on the buckling behavior. The findings highlighted the significance of defect modeling and the consideration of nonlocal effects in determining the mechanical stability of nanosystems. The proposed method offers a powerful tool for advanced nanoscale structural analysis with accuracy and flexibility.