Abstract
In this paper, equations of bifurcation sets of swallowtail catastrophe, hyperbolic umbilic catastrophe and elliptic umbilic catastrophe are derived by alternative elimination method. The equations of bifurcation sets of elliptic/hyperbolic umbilic catastrophes are applied in imperfection sensitivity analysis of mono-symmetric bimodal interaction problems to determine the worst imperfection directions, the imperfection insensitive domain, the stability load contours and the allowable imperfection territories. Furthermore, new concepts such as imperfection insensitive structure, imperfection full-sensitive structure, passive structural stability control, and multiple objective structural stability optimization are advanced and discussed. Five representative cases of a longitudinally stiffened panel under compression are investigated numerically to demonstrate the application.
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