Stress analysis of spinning discs and shells

Abstract

This thesis is concerned with the stress analysis of isotropic and orthotropic spinning discs and shells. The shell geometries considered in this thesis are: spherical shallow shell, conical shell, and cylindrical shell. Closed-form solutions are developed to obtain membrane and bending stresses in orthotropic discs and shells, and results are compared with FEM analysis. Theoretical predictions correspond well with FEM results. The influence of orthotropic ratio and geometrical parameters such as shell radius and apex angle of the cone is discussed. An important issue discussed in this thesis concerns the stress singularity in spinning orthotropic discs and shells when the tangential modulus (Ee) is smaller than the radial modulus (Er). This thesis also examines techniques for optimizing stresses in spinning discs and shells. In the first optimization problem, the orthotropic elastic constants are tailored to achieve uniform strength in a disc of uniform thickness. In the second optimization problem, stress concentration factor for various bore holes in spinning shallow shells is examined for optimizing the shell geometry. Finally, impact response of spinning discs and shallow shells is examined using Laplace and Hankel transforms for different types of impact loading. Analytical results are compared with the predictions of an explicit FEM software for stationary and spinning discs and shallow shells. The effect of centrifugal stiffening and longitudinal inertia on the transient response of spinning shells is also discussed.