A STUDY ON THE INSTABILITY PROBLEM FOR 3D FRAMES

Instead of the traditional load-following process, this paper presents large deflection, post-buckling analysis of the three-dimensional ela stic frame from a dynamic point of view. A co-rotational formulation c ombined with small deflection beam theory with the inclusion of the ef fect of axial force is adopted. The pre-buckling analysis employs the constant are length method together with the modified Newton-Raphson i teration method and the extrapolation technique to improve the converg ence behaviour. As the limit state being examined is passed, the previ ous converged solution is adopted to start the nonlinear dynamic analy sis, based on the average acceleration of the Newmark algorithm with a slow rate of load incrementation, to trace the load-deflection path b eyond the limit point. As a result, the snap-through problem is overco me 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 d amping, is also studied and applied to all the numerical examples. Thi s study is demonstrated by application to typical three-dimensional fr ames which show snap-through behaviour in static analysis with any inc rement of load after the limit point. (C) 1998 Elsevier Science S.A.