Buckling of FG circular/annular Mindlin nanoplates with an internal ring support using nonlocal elasticity

In this paper, the buckling analysis of FG circular/annular nanoplates under uniform in-plane radial compressive load with a concentric internal ring support and elastically restrained edges is studied using an exact analytical approach within the framework of nonlocal Mindlin plate theory. The material properties vary according to a power-law distribution of the volume fraction of the constituents whereas Poison's ratio is set to be constant. In solving this problem, the circular/annular FG nanoplate is first divided into an annular segment and a core circular/annular segment at the location of the internal ring support; accordingly solutions for two segments brought together by using the interfacial conditions. It is observed that an internal ring support can increase the buckling capacity, accordingly this capacity is maximized when the internal ring support is located at an optimal position. Furthermore, the effects of small scales on the maximum buckling load corresponding to the optimal radius of the internal ring support are investigated for various parameters such as radius and thickness of the FG nanoplate, boundary conditions, mode numbers and material properties.