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Home  >  Transasctions of NAMP VOL2

10. Dynamic Stability of a Spherical Cap Pre-Loaded Statically But Trapped By a Step Load BY A.M Ette and I.U. Udo-Akpan Transactions of NAMP Volume2,(November, 2016), pp91 – 106
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In this investigation, we adopt perturbation method to determine the dynamic buckling load of an imperfect spherical cap pre-statically loaded but later trapped as a step load of infinite loading duration. The displacement is discretized into a pre-buckling symmetric mode, an axisymmetric buckling mode and a non-axisymmetric buckling mode a way of which all are discretized in such that their amplitudes are time-dependent. The relevant parameters are expanded asymptotically, while a two-timing multi-timing procedure is utilized to determine a uniformly valid asymptotic solution of the problem. The dynamic buckling load is determined analytically and is related to the corresponding static buckling load, hence showing that if either of the buckling loads is known, then the other can be evaluated without the labour of repeating the arduous process all over. Specializations of the result are mode on specific limitations of the imperfections.