The vaulted roofs of oil storage tank are usually designed as the shallow spherical shells subjecting to a uniform external pressure, which have been widely observed that these shallow spherical shells undergo various levels of corrosion in their employing conditions. It is important to assess the stability of these local weaken shallow spherical roofs due to corrosion for preventing them from occurring unexpected buckling failure. In this paper, the uniform eroded part of a shallow spherical oil tank vaulted roof is simplified as a shallow spherical shell with elastic supports. Based on the simplification, a general pathway to calculate the critical pressure of eroded shallow spherical shell is proposed. The modified iteration method considering large deflection of the shell is applied to solve the problem of nonlinear stability of the shallow spherical shells, and then the second-order approximate analytical solution is obtained. The critical pressure calculated by this method is consistent with the classical numerical results and nonlinear finite element method, and the calculation errors are less than 10%. It shows that it is feasible to apply the method proposed here.

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