Buckling load prediction of an externally pressurized thin spherical shell with localized imperfections

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Abstract
A simple formula for buckling load was derived from the asymptotic analysis of nonlinear behavior of a thin spherical shell. Firstly, two asymptotic cases were studied: the initial post-buckling regime of a perfect structure with small (compared to shell thickness) deflections and equilibrium states with large deflections. Two asymptotic formulae were jointed to obtain the solution for the entire range of deflection amplitude. Then the solution was modified for an imperfect shell. Initial deflections were introduced by only one parameter: the slope of the load–deflection diagram at small pressure. This minimal information was enough to predict the buckling load of the structure with localized imperfections. The suggested asymptotic result was validated by the finite element method and by comparison with experimental data.

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