The asymptotic solution of a dynamic buckling problem in elastic columns

For the dynamic buckling of an elastic column, which is subjected to a longitudinal impact by a rigid body, the form of the axial load is very complicated. The problem may be reduced to discuss the solution of nonlinear partial differential equations. So far, a theoretical solution may not be obtained. In this paper, this dynamic buckling problem of an ideal elastic column with finite length is discussed. By the perturbation method with a small parameter and the variational method, a solution of this problem is given. Finally, numerical computation is carried out, from this, some beneficial conclusions are obtained.