Membrane Solutions for Metallic Toroidal Pressure Vessels

Linear membrane solutions can be adopted to analyze the circumferential and meridional stresses and strains in a toroidal pressure vessel (TPV) subjected to internal pressure. This paper brings out the importance and limitations of membrane solutions for TPVs. Further, the linear and the modified linear membrane solutions are discussed in detail with an illustrative example. Analytical solutions are compared with finite element analysis (FEA) results to highlight their accuracies. It is observed from the results that the linear membrane solution fails to predict circumferential stress and the displacements are singular near the apex of TPV. The modified linear membrane theory addressed the limitations of linear membrane theory, and the results are fairly consistent with the FEA results.