Static and stability analysis of nonlocal functionally graded nanobeams

In this paper, the size-dependent static-buckling behavior of functionally graded (FG) nanobeams is investigated on the basis of the nonlocal continuum model. The nonlocal elastic behavior is described by the differential constitutive model of Eringen, which enables the present model to become effective in the analysis and design of nanosensors and nanoactuators. The material properties of FG nanobeams are assumed to vary through the thickness according to the power law. The nanobeam is modeled according to the Euler-Bernoulli beam theory with small deformation and the equilibrium equations are derived using the principle of virtual displacement. The finite element method is used to discretize the model and obtain a numerical approximation of equilibrium equations. The model is validated by comparing the obtained results with benchmark results available in the literature. A good agreement has been obtained. Numerical results addressing the significance of the material distribution profile, nonlocal effect, and boundary conditions on the bending and buckling behavior of nanobeams are presented. It is found out that these parameters are crucial in analyzing behavior of the nanobeams.