Dynamic response and instability of frame structures Original Research Article

This paper presents a geometrically non-linear dynamic instability analysis for both two- and three-dimensional frames, which may be subjected to finite rotations. The finite element displacement method based on the beam–column approach is employed to derive the non-linear equations governing the behaviour of plane and spatial frames. A co-rotational formulation combined with 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 implicit Newmark time integration with the Newton–Raphson (NR) iteration method is employed. Dynamic critical loads are defined by the Budiansky–Roth criterion. Several numerical examples are illustrated to demonstrate the effectiveness of the present method.