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Abstract: We present a technique to tailor materials for functionally graded (FG) linear elastic hollow cylinders and spheres to attain through-the-thickness either a constant hoop (or circumferential) stress or a constant in-plane shear stress. The volume fractions of two phases of a FG material (FGM) are assumed to vary only with the radius and the effective material properties are estimated by using either the rule of mixtures or the Mori–Tanaka scheme; the analysis is applicable to other homogenization methods. For a FG cylinder we find the required radial variation of the volume fractions of constituents to make a linear combination of the radial and the hoop stresses uniform throughout the thickness. The through-the-thickness uniformity of the hoop stress automatically eliminates the stress concentration near the inner surface of a very thick cylinder. The through-the-thickness variations of Young’s moduli obtained with and without considering the variation of Poisson’s ratio are very close to each other for a moderately thick hollow cylinder but are quite different in a very thick hollow cylinder. For an FG sphere the required radial variation of the volume fractions of the two phases to get a constant circumferential stress is similar to that in an FG cylinder. The material tailoring results presented here should help structural engineers and material scientists optimally design hollow cylinders and spheres comprised of inhomogeneous materials. [Copyright &y& Elsevier]

Abstract: The tailoring of elastic moduli in the radial direction is studied to design a fiber-reinforced orthotropic linear elastic rotating disk with constant radial or hoop stress or constant in-plane shear stress. For fibers arranged in concentric circles the axes of material symmetry coincide with the radial and the circumferential directions. However, when fibers are aligned along helices, the orientation of material principal axes varies with the radial coordinate of a point. For a solid disk made of an orthotropic material with Young’s moduli proportional to each other, we give explicit expressions for the required variations of the elastic moduli with the radius to attain a given state of stress. For a rotating annular disk composed of a fiber-reinforced composite with fibers placed along concentric circles, the required radial variation of the volume fraction of fibers is calculated numerically and exhibited graphically. For fibers of known volume fraction laid along helices, the radial variation of the fiber orientation angle is determined. We have also analyzed the material tailoring problem for a disk of variable thickness. Results presented herein should help structural engineers and material scientists optimally design rotating disks composed of radially inhomogeneous materials. [ABSTRACT FROM AUTHOR]