This paper provides the first examination of buckling behavior of axially functionally graded nanobeams. A nonlocal strain gradient theory consisting of two scale parameter is employed for modeling of size-dependent behavior axially functionally graded nanobeam much accurately. This theory takes into account both nonlocal stress field and strain gradient effects on the response of nanostructures. A power-law model is used to describe the distribution of material properties along the axial direction. The axially functionally graded nanobeam is in contact with a non-uniform elastic medium which consists of a Winkler layer with variable stiffness and also a Pasternak layer with constant stiffness. Linear, parabolic and sinusoidal variations of Winkler foundation in longitudinal direction are considered. A Galerkin-based solution technique is implemented to solve the governing equation obtained from Hamilton’s principle. Buckling loads of functionally graded nanobeam are verified with those of previous papers. It is shown that buckling loads of axially functionally graded nanobeams are significantly influenced by power-law index, nonlocal parameter, length scale parameter, type of elastic foundation and boundary conditions.
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