Analytical solutions for the size dependent buckling and postbuckling behavior of functionally graded micro-plates

In this study, the buckling and postbuckling analysis of FG micro-plates under different kinds of traction on the edges is investigated based on the modified couple stress theory. The static equilibrium equations of an FG rectangular micro-plate as well as the boundary conditions are derived using the principle of minimum total potential energy. The analytical solutions are developed for three case studies including: simply supported micro-plates subjected to uniform transverse load and biaxial tractions, clamped-simply supported micro-plates under uniform transverse load and axial traction, and simply supported micro-plates subjected to shear traction. All plate properties except the length scale parameter are assumed to vary through the thickness according to the simple power law. The numerical results present the effects of the aspect ratio, material length scale parameter and power index on the critical values of traction and the curves of static equilibrium paths. Findings indicate that the length scale parameter is the most effective factor on the critical buckling values. Meanwhile, the aspect ratio has the most influence on the forms of the static equilibrium paths.