Localizations and mode transition of cylindrical shells with geometrical imperfections under axial compression: Numerical and experimental investigations

Abstract

The bending-dominated post-buckling deformations of cylindrical shells offer valuable opportunities for designing compliant mechanisms in soft materials. A deep understanding of the mechanics behind mode localization and transition phenomena is crucial for tailoring periodic mode shapes in shells. In this study, both finite element and experimental studies are conducted to explain the mechanics of circumferential snaking and mode jump phenomena using strain energy density as a key parameter. The numerical analysis reveals the complex interplay between the geometry and strain energy distribution during the snaking phenomenon. In this process, membrane strain energy stored in the structure is converted into bending strain energy, which is then redistributed to localized geometrical features within the periodic mode shape. Furthermore, the study examines the relationship between bending strain energy evolution and geometric transitions that occur during a mode jump, which leads to a reduction in the circumferential wave number of the shell’s periodic mode shape. Experimental validation is performed on 3D-printed cylindrical shells using a multi-3D Digital Image Correlation (DIC) setup. A methodology based on Sander-Koiter’s kinematics is developed to evaluate the full-field bending strain energy density distributions in the shells. The experimental results align with the numerical simulations, providing valuable insights into the nonlinear post-buckling behavior of cylindrical shells. These findings can be applied to the design of continuous compliant-shell mechanisms in soft robotics paving the way for advanced flexible mechanical systems.