an:06986389
Zbl 1402.74072
Kreilos, Tobias; Schneider, Tobias M.
Fully localized post-buckling states of cylindrical shells under axial compression
EN
Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 473, No. 2205, Article ID 20170177, 16 p. (2017).
00372223
2017
j
74K25 74G60 74S30
cylinder buckling; shell buckling; edge state; homoclinic snaking
Summary: We compute nonlinear force equilibrium solutions for a clamped thin cylindrical shell under axial compression. The equilibrium solutions are dynamically unstable and located on the stability boundary of the unbuckled state. A fully localized single dimple deformation is identified as the \textit{edge state} -- the attractor for the dynamics restricted to the stability boundary. Under variation of the axial load, the single dimple undergoes homoclinic snaking in the azimuthal direction, creating states with multiple dimples arranged around the central circumference. Once the circumference is completely filled with a ring of dimples, snaking in the axial direction leads to further growth of the dimple pattern. These fully nonlinear solutions embedded in the stability boundary of the unbuckled state constitute critical shape deformations. The solutions may thus be a step towards explaining when the buckling and subsequent collapse of an axially loaded cylinder shell is triggered.