Modeling and analysis of bi-directional functionally graded nanob eams base d on nonlocal strain gradient theory

The main goal of this research paper is to present the modeling and analysis of bidirectional functionally graded (BDFG) nanobeams within the framework of the Timoshenko beam theory and nonlocal strain gradient theory. According to the DBFG material model, the material properties of the nanobeams are simultaneously distributed in two different directions (thickness and length directions). Besides, the volume fraction of component material is described by a function that combines the power and exponential distribution rules. The study focuses strongly on understanding the mechanical behavior of the BDFG nanobeams and in calculating important parameters of materials and nonlocal strain gradient coefficients. In addition, equilibrium and stability equations for DBFG nanobeams are systematically formulated to static bending and buckling problems with the corresponding boundary condition. The highlight is the combination of two different technical solutions as Navier solution and the Galerkin technique. In the numerical results section, some specific examples are presented to verify the proposed solution, and thereby, a good agreement is observed. Finally, a detailed investigation is performed, with a particular focus on the influences of material properties, nonlocal parameter on the critical buckling load and transverse deflection of the BDFG nanobeams. (c) 2021 Elsevier Inc. All rights reserved.