Criteria for assessing dynamic collapse of elastoplastic structural systems

Criteria are presented for assessing the propensity for dynamic collapse of elastoplastic structural systems. To detect the onset of dynamic collapse, three key concepts are introduced. First, the equations of motion are line arized and time shifted relative to a reference time in a dynamic process. Second, we study the free vibration of the system after the reference time. Third, we use a modal decomposition of the response. We suggest that dynam ic collapse is likely if (1) there exist negative eigenvalues of the Hessia n of the total potential energy and (2) the direction of motion is consiste nt with the loading direction of the elastoplastic material. The direction of motion is determined by using the gradient of total potential energy and the eigenmodes corresponding to the negative eigenvalues. The fidelity of the present criteria is demonstrated through numerical examples for which t he non-linear equations of motion can be integrated exactly. With the prese nt approach, it becomes apparent that p-delta effects, the tangent stiffnes s, the internal resistance, and the direction of unloading all play key rol es in the dynamic collapse of structures. Copyright (C) 2000 John Wiley & S ons, Ltd.