A study on the instability problem for 3D frames

Abstract

Instead of the traditional load-following process, this paper presents large deflection, post-buckling analysis of the threedimensional elastic frame from a dynamic point of view. A co-rotational formulation combined with small deflection beam theory with the inclusion of the effect of axial force is adopted. The pre-buckling analysis employs the constant arc length method together with the modified Newton-Raphson iteration method and the extrapolation technique to improve the convergence behaviour. As the limit state being examined is passed, the previous converged solution is adopted to start the nonlinear dynamic analysis, based on the average acceleration of the Newmark algorithm with a slow rate of load incrementation, to trace the load-deflection path beyond the limit point. As a result, the snap-through problem is overcome without down loading. The efficiency of the damping coefficients on the control of displacement overshooting and vibration, which are the common phenomena using this procedure under conventional structural damping, is also studied and applied to all the numerical examples. This study is demonstrated by application to typical three-dimensional frames which show snap-through behaviour in static analysis with any increment of load after the limit point.