The dynamic buckling global response of a nonlinear, 3-degree-of-freed
om dissipative model under a step loading of infinite duration is thor
oughly discussed. Geometrically imperfect models with symmetric or ant
isymmetric imperfections losing their static stability through a limit
point and an asymmetric bifurcation point, respectively, are consider
ed. Emphasis is given to the combined effect of nonlinearities (geomet
ric and/or material) and damping. Exact, approximate, and lower/upper
bound estimates based on energy criteria for establishing the dynamic
buckling response of such autonomous models without solving the highly
nonlinear initial-value problem are assessed. The reliability and eff
iciency of the proposed readily obtained estimates is illustrated via
numerical simulation, the accuracy of which is checked using energy ba
lanced considerations. Certain interesting byproducts associated with
a postlimit point bifurcation and breakdown of the symmetry of deforma
tion are also revealed.