Mechanism of buckling development in elastic bars subjected to axial impact

By use of the finite difference method, the non-linear equations governing the elastic dynamic post-buckling deformations are solved for two types of impact buckling problems for straight bars. The initial dynamic buckling mode with a small amplitude parameter, given by the twin-characteristic-parameter solution, is used as the initial condition of the non-linear post-buckling solution. Particular attention is paid to the mechanism of growth and spread of buckling deformation in the bar and the interaction between the axial stress wave and the buckling deformation in the process of impact. It is found that the initial buckling deflection with one half-wave, occurring near the impacted end, spreads forward and develops into the higher mode as the axial stress wave propagates in the bar. The theoretical results are in good agreement with the experimental results reported in the literatures.