A Review of the Instability Problem for Frame Structures

This paper presents large deflection, post-buckling analysis of plane and spatial elastic frames 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. A constant arc length method combined with the modified Newton–Raphson iteration method and the extrapolation technique to improve the convergence behaviour are employed to trace the non-linear equilibrium path up to the limit point. The change in the sign of the incremental work done is used to determine the occurrence of a limit point. As the limit state being examined is passed, the previous converged solution is adopted to start the non-linear dynamic analysis based on the average acceleration of the Newmark algorithm with a slow rate of load increment and in order to trace the post-buckling load-deflection path. As a result, the snap through problem is overcome without decreasing the external load. Numerical examples are presented to demonstrate the performance of the method.