NONLINEAR BENDING, BUCKLING AND VIBRATION OF FUNCTIONALLY GRADED NONLOCAL STRAIN GRADIENT NANOBEAMS RESTING ON AN ELASTIC FOUNDATION

This work aims to provide a comprehensive theoretical framework for the nonlinear bending, vibration and buckling of functionally graded (FG) nanobeams resting on an elastic foundation through nonlocal strain gradient theory. To this end, both Timoshenko and Euler-Bernoulli beam theories are considered and the equations of motion are established by Hamilton's principle. The analytical expressions of the nonlinear deflections, frequencies and critical buckling forces of FG nanobeams are presented with closed-form expressions. Comparing the obtained results with those published in the literature shows the accuracy of the current analysis. Finally, the impacts of some effective parameters are thoroughly investigated and discussed.