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Abstract

This paper focuses on spherical shells with random geometric imperfections under uniform external pressure. An extensive numerical investigation is performed to calculate the buckling loads of perfect and imperfect spherical shells. To discuss the effects of initial geometric imperfections, a finite element analysis model of the perfect spherical shell is considered to obtain its first 60 modes. Then, the consistent imperfect buckling analysis method is applied to analyze the nonlinear stability of the spherical shells with geometric imperfections. The shapes of the shell in the 1st to 20th eigenmode are considered. A lower buckling load is found corresponding to the 17th eigenmode, which is different from the analysis-derived opinion that the buckling stress is often observed in the 1st eigenmode. Moreover, the random geometric imperfection method is applied to imperfect spherical shells by incorporating random geometric imperfections. The statistical analysis of numerical results from 200 random cases indicates that the calculated ultimate strength can be lowered to 5.58 MPa in this example, which is approximately 87% of the result from the 1st eigenmode. Therefore, it may be concluded that the random geometric imperfection method can be used for analyzing the stability of structures with imperfections to obtain realistic results.

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