Nonlocal bending analysis of multi-layered 2D nanostructures with defective interlayer bonds and elastic foundations

Abstract This work presents a comprehensive methodology and formulation for analyzing the bending behavior of multi-layered nanoplates, considering defective interlayer bonding and elastic foundations—areas that have not been sufficiently explored in existing literature. While nanostructures are often treated as single-layer entities in research, it is essential to recognize that they are typically multi-layered in real-world applications. The proposed formulation allows for the creation of defective nanostructures by incorporating interlayer defects within the bonding. The analysis employs the Kirchhoff-Love plate theory in conjunction with Eringen’s nonlocal elasticity (NLE) theory. The multi-layered nanoplate is assumed to be simply supported at all edges and subjected to a uniformly distributed load. The bonding between layers and the elastic foundations of the multilayered nanoplate are modeled at specific points using the Dirac-delta function, which facilitates the introduction of defects in both layer bonding and the elastic foundations. To address this problem, the Galerkin’s method is employed. A computer code has been developed for numerical simulation, introducing randomly oriented defects for both the bonding between layers and within the elastic foundations. As a result, the bending performance of multi-layered nanoplates with these randomly oriented defective elastic foundations and nanostructures is analyzed and discussed across various defect rates. The current formulation is general enough to realistically tackle challenges associated with both pristine and defective two-dimensional multi-layered nanostructures.