Buckling Analysis of an Orthotropic Elliptical Toroidal Shell

A theoretical solution is given for the linearized buckling problem of an orthotropic toroidal shell with an elliptical cross-section under external pressure loading. The solution is based on the Sanders-Budiansky shell theory, and makes use of the harmonic differential quadrature method. Theory developed earlier for the buckling of orthotropic shells of revolution, and the vibration of orthotropic elliptical toroidal shells, is incorporated in the present work. Numerical results obtained from the solution are compared with results given in the literature, and good correspondence is generally observed. A parametric study is then conducted, covering a wide range of material and geometric parameters. Regression formulas are derived, indicating the variation of the buckling pressure with the degree of orthotropy of the material. Overall, the study introduces a new tool for the buckling analysis of elliptical toroidal shells, and extends the information available for orthotropic toroidal shells.