In this paper, a Levy-type solution based on the modified couple stress theory is
developed to study the buckling behaviors of micro-plates. Based on this theory, length
scale parameter is considered to capture the size effect of rectangular micro-plates.
Minimum potential energy and adjacent-equilibrium criteria are exploited to obtain the
stability equations and corresponding boundary conditions. Different boundary conditions
with two opposite edges simply supported and arbitrary boundary conditions along the other
edges are considered. To illustrate the new model, both uniaxial and biaxial loads are
applied and the critical buckling loads are defined for over a wide range of thickness,
different length scale parameters and various boundary conditions. To show the accuracy of
the formulations, present results are compared with available results in literature for
specific cases and a very good agreement is observed. Results reveal that the critical
buckling load increases as the length scale parameter increases especially when the
thickness of the micro-plates becomes in order of length scale parameter and this effect
is more significant for free boundary condition.