Criteria for assessing dynamic collapse of elastoplastic structural systems

SUMMARY 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 linearized 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 dynamic collapse is likely if (1) there exist negative eigenvalues of the Hessian of the total potential energy and (2) the direction of motion is consistent 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 "delity of the present criteria is demonstrated through numerical examples for which the non-linear equations of motion can be integrated exactly. With the present approach, it becomes apparent that p-delta e!ects, the tangent sti!ness, the internal resistance, and the direction of unloading all play key roles in the dynamic collapse of structures. Copyright ( 2000 John Wiley & Sons, Ltd.