Dynamic buckling of an imperfect spherical shell under an axial impulse

Analysis of the Dynamic Buckling of a Viscously Damped Spherical Shell Under an Impulse Load

“…Earlier and pioneering investigations seem to have been led by Budiansky and Roth [1], Budiansky [2], Budiansky and Hutchinson [3] and Hutchinson and Budiansky [4], amongst others. Mention must be made of other relevant investigations as in Koteiko and Mania [5], Kolakowski [6,7], Rajanna et al [8], Ozoigbo et al [9] and Ette [10,11]. In a similar study, Ozoigbo and Ette [12], in a perturbation approach investigated the dynamic buckling of a prestatically but viscously damped elastic structures while Mcshane et al [13] made a similar investigation on inclined structures.…”

“…Against this backdrop, we avoid Mathieu-type of instability in this investigation. In the same token, Ette [10,11] earlier investigations of the undamped versions of the same problem had deduced that (a) neglecting any imperfection automatically leads to equally neglecting any coupling effect of the mode that is in the shape of the neglected imperfection with any other mode, (b) it also leads to neglecting the effect of the nonlinearity that is in the shape of the neglected imperfection. Consequently, neglecting both 𝑘 1 𝜀 1 From the hind sight of all these considerations, we shall here retain all the terms in the formulation including the pre-buckling mode and the two imperfection parameters, 𝜀̅ 1 and 𝜀̅ 2 together with all nonlinearities and coupling terms.…”

Static Buckling Analysis of a Quadratic-Cubic Model Structure Using the Phase Plane Method and Method of Asymptotics

“…Much earlier on, Amazigo et al [22] had studied asymptotic analysis of the buckling of imperfect columns on a nonlinear elastic foundation while Qiang et al [23] considered the asymptotic solution of a dynamic buckling problem in elastic columns. Ette [24], on the other hand, used asymptotic expansions to examine the dynamic buckling of a spherical shell under an axial impulse while Ette [25] similarly used analytical methods to study a two-parameter dynamic buckling of a lightly damped spherical cap trapped by a step load. Ette [26] also studied the static buckling of an externally pressurized finite circular cylindrical shell using asymptotic methods.…”