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.Key words: Thermal buckling, annular plates, functionally graded materials, classical theory Resumen El presente estudio tiene por objeto proporcionar una solución exacta para el pandeo térmico de placas bimorfas funcionalmente graduadas circulares bajo carga térmica uniforme con respecto a la teoría clásica de von Kármán y suposiciones no lineales en Condiciones de soporte: empotrado-empotrado, articulado-articulado, empotrado-articulado y articulado-empotrado. Las propiedades de los marciales cambiarán en asociación con la superficie media de la placa simétrica y de acuerdo con la ley de potencia en la dirección del espesor. De manera que la superficie media de la placa anular era de metal puro y los lados de la placa eran de cerámica pura. Utilizando ecuaciones no lineales de energía, se determinó el equilibrio y se emplearon las ecuaciones de estabilidad mediante el método de equilibrio en la vecindad para especificar la temperatura crítica de pandeo. Finalmente, se obtuvo una solución cerrada. También medimos el impacto de factores variables como la tasa de espesor de los cambios en el radio de la placa, los cambios en el percentil de la fracción volumétrica de los materiales y la relación entre el radio interior y el radio exterior sobre la temperatura crítica de pandeo. A continuación, los resultados se compararon entre sí y con estudios anteriores. Los resultados indicaron que para los materiales bimórficos funcionalmente clasificados, no ocurre el momento térmico, mientras que la temp...

Pseudo-spectral method for mechanical buckling analysis of circular plates with variable thickness made of bimorph FGMs

“…In this reference, the numerical solution is based on the dynamic release method and the governing equations are extracted based on the first-order shear deformation theory. Khosravi and colleagues [16,17] presented a precise closed-form solution for the thermal buckling of circular plates made of bimorph FGMs by adopting the first-order shear deformation theory. They evaluated the effects of different factors including the ratio of thickness to the plate radius and the volume fraction index on the critical temperature.…”