In this paper, we embark on analytical determination of the dynamic buckling of a statically pre-loaded elastic structure subjected to step loading. We first employ a two-timing regular perturbation procedure for asymptotic determination of a uniformly valid expansion of the displacement. The dynamic buckling load is determined nontrivially and is related to the corresponding static load. The dynamic buckling load is studied as a function of various problem parameters: degree of damping, initial imperfection, and static pre-loading.
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