Free vibration and stability of complete orthotropic circular toroidal shells

Abstract

This study makes contributions in the areas of vibration and stability analysis of complete orthotropic circular toroidal shells. It is conducted in four main parts. A literature survey is first carried out indicating the new and continuing uses of toroidal shells in engineering structures. Secondly, theory is developed for the free vibration analysis of toroidal shells using the differential quadrature method. Numerical results are determined using the method for shells with small bend to cross-section radius ratios, and compared with finite element results. Thirdly, theory is developed using the Rayleigh-Ritz method for the free vibration analysis of toroidal shells having large bend to cross-section radius ratios. A parametric study of such shells including orthotropic and ring-stiffened isotropic ones is conducted using the finite element method. Finally, theory is developed using the Rayleigh-Ritz method for the linearized buckling analysis of toroidal shells with large bend to cross-section radius ratios. Numerical results are found for orthotropic and ring-stiffened isotropic shells using the finite element method. All theoretical work is carried out within the confines of the first-order Sanders-Budiansky shell theory. The work ends with an appropriate set of conclusions.