Elastic state of functionally graded curved beam on the plane stress state subject to thermal load

Abstract

This study investigates analytical solutions stresses and displacements of the functionally graded cylindrically curved beam subjected to the thermal load in the radial direction. The ends of this curved FGM beam is supposed to be guided in such a way that a displacement in circumferential direction may occur and that the radius of the middle surface remains unchanged. Then, couples act on those ends, giving rise to pure bending condition. It is assumed that the temperature distribution varies as a function of the radial coordinate and is in steady state. The modulus of elasticity varies with the power law through of the thickness of the curved FGM beam. Accordingly, by applying the general mixture law, the thermal expansion, the heat transfer coefficient and the volume fraction varies depending on the power law (except Poisson ratio). The curved FGM beam is assumed to be in plane stress state. Using the von Mises yield criterion, the effects of the values of power law index on the displacement and stresses of the curved beam is discussed. The inner surface of the curved FGM beam is steel and its outer surface is aluminum. At positive and negative temperatures, the effects of the yielding on the curved beam are investigated. It is observed that the starting of the plastic yielding is on the outer surface, inner surface and at the simultaneously on both surfaces.