The thermal buckling analysis of nonuniform, nonhomogeneous (functionally
graded-FG) nanobeams is presented here for three boundary conditions using
Euler–Bernoulli’s beam theory. By assuming the temperature-independent
mechanical properties and physical neutral axis of nanobeam material, the rule of
mixture is considered to calculate the effective properties for power-law model.
Euler–Lagrange’s equation is derived from Hamilton’s principle, and the
implementation of size-effect leads to the governing equation for such a nanobeam
model. The generalized differential quadrature (GDQ) method discretises this
equation along with boundary condition. The obtained homogenous system of linear
equations is solved to find the critical buckling temperature for nonuniform FG
nanobeams. Further, the general solutions are proposed, and the eigen equation is
derived to compute the critical temperature for buckling of uniform FG nanobeams
and compare it with those obtained by the adopted numerical method. The
developed analytic approach is accurate and easy to implement and provides
general expressions to find the buckling temperature difference for all modes
of uniform nanobeams. Moreover, the effects of the choice of constituent
materials, homogenisation scheme, nonhomogeneity parameter, nonlocal
parameter, and temperature profile are studied. The effect of the nonlocal
parameter is highly prominent over the other parameters. Also, engineers and
scientists can control the critical temperature of the beam by varying its
nonhomogeneity.
