Stress analysis of a thick-walled cylinder composed of incompressible hyperelastic materials subjected to internal and/or external pressure: analytical and finite element analysis

In this work, the mechanical behaviour of a thick-walled cylindrical pressure vessel composed of an incompressible isotropic non-linearly hyper-elastic material subjected to internal and/or external pressure is investigated. An analytical solution is proposed for the general form of the free strain energy density and different models including Neo-Hookean, Mooney-Rivlin, and Yeoh are employed. An analysis was conducted to determine the extension ratio at the inner and outer radii as well as the stress distribution, in different cases, namely the application of internal pressure only, external pressure only, and internal and external pressure applied simultaneously. In addition, various pressure values are applied to account for different levels of deformation. In order to strengthen the analytical solution, a finite element model of the pressurised vessel was constructed. A very good agreement has been found between the analytical predictions and the numerical results, suggesting the accuracy of the analytical solution. The analytical solution can be used for parametric studies (material or geometrical parameters) and the design/optimisation of a thick-walled cylindrical pressure vessel subjected to internal and/or external pressure. Additionally, it obviates the requirement for many finite element simulations, where computational cost is an important parameter.