A study on the instability problem for 2D-frames

Abstract

This paper presents large deflection, post-buckling analysis of the two-dimensional 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. An increment iterative method based on the modified Newton-Raphson method and extrapolation techniques for improving the convergence behaviour combined with a constant arc length control method is employed for the solution of the non-linear equilibrium equations before the limit point. A non-linear dynamic analysis based on the average acceleration of the Newmark algorithm with a slow rate of load incrementation is carried out 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 method proposed in this study is demonstrated by typical two-dimensional frames which show snap-through behaviour in static analysis with any increment of load after the limit point.