Dynamic response and instability of frame structures

This paper presents a geometrically non-linear dynamic instability analysis for both two- and three-dimensional frames, which may be subjected to fini te rotations. The finite element displacement method based on the beam-colu mn approach is employed to derive the non-linear equations governing the be haviour of plane and spatial frames. A co-rotational formulation combined w ith small deflection beam theory with the inclusion of the effect of axial force is adopted. The governing dynamic equilibrium equations are obtained from the static equations by adding the inertia and damping terms. The impl icit Newmark time integration with the Newton-Raphson (NR) iteration method is employed. Dynamic critical loads are defined by the Budiansky-Roth crit erion. Several numerical examples are illustrated to demonstrate the effect iveness of the present method. (C) 2001 Elsevier Science B.V. All rights re served.