Simulation of shell buckling by implicit dynamics and numerically dissipative schemes

Shell buckling process is studied by implicit structural dynamics time-stepping schemes with numerical dissipation (in the high-frequency range), which fall into the class of Generalized energy-momentum method. In particular, modified Generalized-α, Bossak, HHT, and Newmark's schemes are considered, as well as Energy-momentum conserving scheme, and Energy-decaying scheme with controllable numerical dissipation. We are interested in the assessment of the ability of these schemes to handle complex buckling and post-buckling processes of thin shells (even for cases when path-following methods fail). The schemes are specialized for geometrically exact shell formulation (with only displacement-like degrees of freedom). Computed numerical examples include classical shell buckling problems: snap-through, shell collapse, and buckling of perfect and imperfect cylinder under axial load. The examples illustrate that (high-frequency) numerical dissipation is absolutely necessary for an efficient implicit dynamic simulation of complex shell buckling and post-buckling processes. Since the Energy-momentum conserving scheme does not damp high-frequency oscillations that accompany shell buckling (and thus accumulates large error in the high-frequency range), it is not suitable for the simulation of shell instabilities (the scheme fails to converge for several computed examples). The dynamic results are compared with the static ones that were computed by the path-following method. It turns out that implicit dynamic analysis with (high-frequency) numerical dissipation is considerably more robust and efficient than static analysis for several computed examples, including snap trough problems and buckling of cylinder under axial load.