Radial heating of a thick‐walled cylindrically curved FGM‐panel

Abstract

A cylindrically curved panel in a state of generalized plane strain subject to a radial temperature gradient is discussed by analytical means. The ends of this thick‐walled shell are presupposed 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. The material is power‐law functionally graded, and – based on the rule of mixtures – a coherent dependence of all the material properties (except for Poisson's ratio) on the radial coordinate is taken into account. The stresses occurring for both a positive and a negative temperature gradient are analyzed, and one finds that, depending on the grading exponent, the yield limit according to von Mises may be reached either at the inner surface, the outer surface or at both surfaces simultaneously. Numerical results are provided for a steel/aluminum FGM, and it is shown that by appropriate grading not only a reduction of the couples acting at the supports but in some cases also a considerable reduction of the weight of the panel may be achieved.