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.
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