A Levy-type solution for buckling analysis of micro-plates considering the small length scale

Abstract

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.