ENERGY-BASED DYNAMIC BUCKLING ESTIMATES FOR AUTONOMOUS DISSIPATIVE SYSTEMS

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.