Analytical formulation and numerical modelling for multi-shell toroidal pressure vessels

•A novel shell-assembly of toroidal form for fluid containment is proposed.•A formulation is presented for determining the state of stress in the loaded vessel.•An approximate buckling solution is formulated for the middle regions of the toroid. Depending on the required solution, this paper presents results for the state of stress and buckling of a uniformly pressurized elastic toroidal vessel of four segments. In the first part of the paper, a closed-formed stress solution is formulated for the novel shell form, by adopting the membrane solution as the particular solution of the Reissner-Meissner general bending-theory equations, and an approximate bending solution is used to quantify discontinuity effect at the shell junctions. In the second part of the paper, linearized stability equations are formulated and simplified for the segmented toroidal vessel buckling problem. The membrane results obtained in the first part is used to predict the pre-buckling state and the stability equations are approximately solved for the segments in the middle regions of the toroidal vessel, using the Galerkin’s scheme. This leads to an expression for estimating the critical buckling pressures of pressurized isotropic toroids. Numerical results from the proposed methods are presented and compared with those from a finite element method solution.