A novel modified nonlocal strain gradient theory for comprehensive analysis of functionally graded nanoplates

In this study, a novel theory, called the modified nonlocal strain gradient theory, is established for the analysis of functionally graded nanoplates. This theory integrates the nonlocal effects through classical stress tensors, the deviatoric part of the symmetric couple stress tensor, dilatation gradient and deviatoric stretch gradient tensors. This combination ensures compatibility for investigating a wide range of structures, from nano- to macro-scales. Some comparative studies are performed to establish the precision and reliability of the proposed theory in specific cases. Furthermore, a massive parametric study is organized to illustrate the influence of several coefficients on the bending, free vibration and buckling behaviors of the functionally graded nanoplates. The proposed theory provides a robust theoretical foundation for future investigations into various small-scale structures situated within multi-physical environments. This establishing approach not only enhances the understanding of micro- and nanoscale mechanics but also paves the way for advanced applications in mechanical engineering. © The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature 2024.