An exact solution of mechanical buckling for functionally graded material bimorph circular plates

Abstract

Presented herein is the exact solution of mechanical buckling response of FGM (Functionally Graded Material) bimorph circular plates, performed under uniform radial compression, by means of the classic theory and the non-linear Von-Karman assumptions, for both simply supported and clamped boundary conditions. Material properties are assumed to be symmetric with respect to the middle surface and are graded in the thickness direction according to a simple power law, in a way that the middle surface is pure metal and the two sides are pure ceramic. Using the energy method the non-linear equilibrium equations are derived and the stability equations have been used, so as to determine the critical buckling pressure, considering the adjacent equilibrium criterion, and finally a closed-form solution has been achieved for it. The effect of different factors, including thickness to radius variation rate of the plate, volumetric percentage of material index, and Poisson's ratio on the critical buckling compression have been investigated for two simply supported and clamped boundary conditions, and the results