An analytical solution for buckling analysis of size-dependent rectangular micro-plates according to the modified strain gradient and couple stress theories

In this study, a size-dependent Kirchhoff plate model is developed for determining the critical buckling loads of rectangular micro-plates. Modified strain gradient theory with three length scale parameters is used. It should be noted that this theory is reduced to modified couple stress theory by setting two length scale parameters to zero. Using the variational approach and the principle of minimum total potential energy, the nonlinear form of the governing equations and all possible boundary conditions are determined. It is assumed that the micro-plate is simply supported on two opposite edges. The stability equations are solved analytically, and the critical buckling loads are obtained based on the modified strain gradient and modified couple stress theories. Also, the effects of length scale parameters, dimensions and loading states on the buckling loads are investigated in detail.