Material tailoring for orthotropic elastic rotating disks

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.