Dynamic buckling of imperfection-sensitive shell structures

Structural buckling under dynamic loads may occur at load levels that are less than the corresponding static loads. Presence of local geometric imperfections may induce an early buckling for both static and dynamic loadings. The phenomenon of “dynamic weakening” is studied for a general class of shell structures under a general class of time-dependent loadings. A doubly curved quadrilateral Love-Kirchhoff shell finite element is used. Geometric deviations of the shell middle surface are included within the element formulation by suitably modifying the strain-displacement relations. This is accomplished by retaining additional terms that are quadratic in spatial derivatives of imperfections and displacement components. The nonlinear equations of motion are written in the Lagrangian system and are solved by using an incremental algorithm based on Newmark's generalized operator. The dynamic responses up to buckling are obtained for a perfect spherical cap and an imperfect spherical cap both under external pressure, as well as a complete imperfect sphere under external pressure. Numerical results include the effects of amplitude of imperfection and thickness of shell on the dynamic buckling loads. The formulation is general and can be applied to obtain the dynamic buckling responses of a wide variety of shell structures.