An exact solution of thermal stability analysis of bimorph functionally graded annular plates

Abstract

The present study aims to provide an exact solution for thermal buckling of bimorph functionally graded circular plates under uniform thermal loading with regard to von Kármán’s classic theory and non-linear assumptions in clamped-clamped, simple-simple, clamped-simple and simpleclamped support conditions. Martials properties will change in association to the middle surface of symmetric plate and according to the power law in direction of thickness. So that, the middle surface of the annular plate was pure metal and the sides of plate were pure ceramic. Using non-linear equations energy, the equilibrium was determined and the stability equations were employed by the method of equilibrium in vicinity in order to specify the critical temperature of buckling. Finally, a closed solution was obtained. We also measured the impact of varying factors like the rate of thickness to plate radius changes, volume fraction percentile changes of materials, and the ratio of the inner radius to the outer radius over the critical buckling temperature. Then, the results were compared together and with former studies. The findings indicated that for bimorph functionally graded materials, thermal moment does not occur, while buckling critical temperature in bimorph functionally graded materials of annular plates increases as the ratio of thickness to radius increases. Moreover, by increasing the ratio of inner to outer radius in clamped-clamped and clamped-simple support conditions we have an increase in thermal buckling free parameter.