Finite-element analysis of an axisymmetric, thin-walled, nonlinear elastic pressurized torus

A finite-element methodology for the static analysis of an axisymmetric, toroidal membrane of initially circular cross section under internal uniform pressure is developed. The torus experiences large elastic deformations and its material behavior is described by a nonlinear elastic constitutive equation. Both incompressible and compressible material cases are considered. Axisymmetric finite elements are employed in the formulation, which is established with the aid of a variational principle. The resulting nonlinear stiffness equations are solved by a highly accurate and efficient least squares method. The accuracy of the finite element method is assessed. Numerical results for the deformational configuration and the developed stresses of a torus as functions of the applied internal pressure are presented in order to illustrate the method and demonstrate its accuracy by comparison with analytical results whenever this is possible.