Singularity in rotating orthotropic discs and shells

A unified formulation for studying stresses in rotating polarly orthotropic discs, shallow shells and conical shells is presented. The main focus of this paper is on the examination of singularities when tangential modulus of elasticity $(E_{\theta})$ is smaller than the radial modulus $(E_r)$. The order of the singularity is extracted by expressing the solutions in terms of modified bessel function with complex argument. The order of the singularity is shown to be $(\sqrt{E_{\theta}/{E_r-1}})$ in all the three cases studied here. There is no singularity present when $E_{\theta}/E_r \geq 1$. Theoretical results\ud are compared with FEM calculations in all the cases