Localization of dynamic buckling patterns of cylindrical shells under axial impact

A symplectic approach is developed within the perspective of stress wave propagation to study theoretically the localization of dynamic buckling of a cylindrical shell subjected to an axial impact. In this analysis, a set of lower-order fundamental equations, the Hamiltonian canonical equations, is presented in dual variables. Subsequently, the critical load and buckling mode are reduced to solving the symplectic eigenvalue and eigensolution, respectively. The result shows that the localization of dynamic buckling patterns in the elastic shell is mainly caused by the relaxation of boundary conditions. With stress wave propagation and no reflection, the corresponding buckling mode deformation should exist near the impact end. This behavior has significant influence on the reduction of dynamic buckling loads. In conclusion, this paper provides some new analytical and numerical rules for dynamic buckling and the new results are useful in the critical design of shell structures against buckling.