Navier Solution for Buckling Analysis of Size-Dependent Functionally Graded Micro-Plates

In the present paper, buckling analysis of functionally graded rectangular micro-plates, on the basis of strain gradient theory with one length scale parameter is studied. Considering the Kirchhoff plate theory and the principle of minimum total potential energy, governing equations of micro-plate subjected to in-plane loads are extracted. In accordance with functionally graded distribution of material properties through the thickness, higher order governing equation of sixth order is derived. Consequently, the stability equation is solved analytically for simply supported micro-plates and the effects of material properties, micro-structure parameters, dimensions and loading conditions are expounded on the critical buckling load. Developing the strain gradient theory for buckling analysis of micro-plates made of functionally graded material is a significant novelty of the presented study.