Static bending analysis of BDFG nanobeams by nonlocal couple stress theory and nonlocal strain gradient theory

This paper presents analytical solutions for the bending behavior of bi-directional functionally graded (BDFG) micro and nanobeams, wherein the material properties vary along both the thickness and axial directions, following power-law and exponential-law profiles, respectively. This study employs two size-dependent theories, nonlocal modified couple stress theory (NCST) and nonlocal strain gradient theory (NSGT), to account for size effects inherent in nanoscale structures. The governing differential equations are derived using Hamilton's principle, and the Laplace transform technique is utilized for their solution. The study critically compares the size effects captured by NCST and NSGT and assesses the influence of material gradation parameters in both directions. Additionally, the impacts of nonlocal and length scale parameters are thoroughly investigated. The findings indicate that NSGT tends to overestimate size effects compared to NCST. This research enhances the understanding of the mechanical behavior of BDFG nanobeams, offering valuable insights for the design and analysis of nanoscale structures across diverse applications.