Favorable mechanical properties such as high strength-to-weight ratio, high stiffness-to-weight ratio, low specific weight and high fatigue strength, and stiffness tailoring capabilities have enabled the use of composite materials in turbomachinery, automotive and aviation industries. Recent developments on the applications to rotating tapered structures such as thickness-tapered flywheels and rotors in gas turbines and airplane engines have shown increasing use of continuous fiber-reinforced composite materials. Rotating annular thickness-tapered discs made of orthotropic and fiber-reinforced composite materials have preferential stress state as compared to the uniform-thickness discs made of isotropic materials rotating at the same speed. Therefore, due to their distinct characteristics from uniform-thickness discs and wide range of applications, the design of thickness-tapered rotating discs requires comprehensive research to understand their elastic behavior under different loading and boundary conditions. 
In the present work, the in-plane stress and displacement analyses of rotating annular uniform-thickness and thickness-tapered discs made of orthotropic and fiber-reinforced composite materials are conducted considering different boundary conditions. A computational solution based on the Rayleigh-Ritz method with finite-element-like modification is developed to evaluate the elastic response of rotating annular thickness-tapered discs made of orthotropic materials. Linear taper and Stodola taper profiles are considered in the elastic analysis of thickness-tapered orthotropic discs with the free-free and the clamped-free boundary conditions. The accuracy of the developed formulation for the elastic response of thickness-tapered orthotropic discs is established based on the convergence of the results obtained for the elastic response using the sub-domain-wise application of Rayleigh-Ritz method in terms of the number of divisions of the thickness-tapered disc, to the results obtained using closed-form analytical solutions available in the literature. For rotating annular uniform-thickness and thickness-tapered fiber-reinforced composite discs with the clamped-free boundary condition, the Rayleigh-Ritz method in conjunction with the Classical Laminate Theory in cylindrical coordinate system is used to evaluate the elastic response. The finite element analysis tool ANSYS is used to model the various three-dimensional internal taper configurations of rotating annular thickness-tapered fiber-reinforced composite discs. The results obtained for the elastic response of uniform-thickness and thickness-tapered fiber-reinforced composite discs using the SOLID185 and SHELL181 elements in ANSYS® are used to verify the results obtained for the same using the Rayleigh-Ritz method based on the Classical Laminate Theory in cylindrical coordinate system. Numerical and symbolic calculations to solve the boundary value problem using the Rayleigh-Ritz method are performed using the technical computing language MATLAB®. The effects of degree of orthotropy, taper profile and taper parameter values on the in-plane stress distributions and radial displacement distribution in the rotating annular thickness-tapered discs made of orthotropic materials are observed for the free-free and clamped-free boundary conditions through extensive parametric studies. The influences of fiber orientation, radius ratio, rotational velocity, laminate configuration, ply reduction and internal taper configuration on the elastic response of rotating annular thickness-tapered fiber-reinforced composite discs are thoroughly examined considering the clamped-free boundary condition. For the parametric studies, a wide range of orthotropic materials are chosen and also, the NCT-301 graphite-epoxy prepreg is chosen as a fiber-reinforced composite material. Important design aspects are systematically brought out.