Advanced Computational Modeling and Mechanical Behavior Analysis of Multi-Directional Functionally Graded Nanostructures: A Comprehensive Review

This review explores multi-directional functionally graded (MDFG) nanostructures, focusing on their material characteristics, modeling approaches, and mechanical behavior. It starts by classifying different types of functionally graded (FG) materials such as conventional, axial, bi-directional, and tri-directional, and the material distribution models like power-law, exponential, trigonometric, polynomial functions, etc. It also discusses the application of advanced size-dependent theories like Eringen’s nonlocal elasticity, nonlocal strain gradient, modified couple stress, and consistent couple stress theories, which are essential to predict the behavior of structures at small scales. The review covers the mechanical analysis of MDFG nanostructures in nanobeams, nanopipes, nanoplates, and nanoshells and their dynamic and static responses under different loading conditions. The effect of multi-directional material gradation on stiffness, stability and vibration is discussed. Moreover, the review highlights the need for more advanced analytical, semi-analytical, and numerical methods to solve the complex vibration problems of MDFG nanostructures. It is evident that the continued development of these methods is crucial for the design, optimization, and real-world application of MDFG nanostructures in advanced engineering fields like aerospace, biomedicine, and micro/nanoelectromechanical systems (MEMS/NEMS). This study is a reference for researchers and engineers working in the domain of MDFG nanostructures.