Simulation of the vibration response of a column under the post-buckling behavior by particle mechanics method

Movable Cellular Automata (MCA) is a new efficient numerical method in particle mechanics that is different from methods in the traditional continuum mechanics. In this paper MCA is applied to addressing buckling and post-buckling problems in solid mechanics. The simulation of the buckling behavior of a column subjected to a quasi-static loading is presented in this article. The critical buckling loads result obtained by MCA is consistent with the values calculated by the classical mechanics of materials. Under the post-buckling of the column, a lateral vibration of the column is observed, which was considered to be impossible at so low strain rate of over(ε, ̇) = 10^{- 3}. The equilibrium positions of the vibration of the column are continually adjusted to match the curves of deflection of post-buckling. The vibration decays quickly with the buckling deflection increasing. Finally, the deflections of post-buckling increase steadily and the capability of bearing load of the column is slowly reduced.