Energy-based dynamic buckling estimates for autonomous dissipative systems

The dynamic buckling global response of a nonlinear, 3-degree-of-freedom dissipative model under a step loading of infinite duration is thoroughly discussed. Geometrically imperfect models with symmetric or antisymmetric imperfections losing their static stability through a limit point and an asymmetric bifurcation point, respectively, are considered. Emphasis is given to the combined effect of nonlinearities (geometric 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 efficiency of the proposed readily obtained estimates is illustrated via numerical simulation, the accuracy of which is checked using energy balance considerations. Certain interesting byproducts associated with a postlimit point bifurcation and breakdown of the symmetry of deformation are also revealed.