Scaling laws for thin-walled cylindrical shells under uniform lateral free-drop low-velocity impact loading with elastic effects

Scaling laws serve as an important link in relevant physical quantities between scaled models and full-size prototypes, enabling accurate prediction of structural impact behavior. However, conventional scaling methods often fail to accurately predict the impact response of thin-walled cylindrical shells when elastic effects are non-negligible. To address this issue, a refined set of impact scaling laws for thin-walled cylindrical shells is proposed in this study, explicitly accounting for elastic effects that are often neglected in conventional scaling methods. The proposed scaling laws are developed by combining displacement fields, strain-displacement relations, elastic-plastic constitutive equations, and the energy conservation principle through equation and dimensional analysis. Within this scaling framework, geometric distortion is addressed by correcting the mid-surface radius and material distortion is accounted for by correcting the initial impact velocity. Data from a series of impacted thin-walled cylindrical shells, with varying degrees of geometric distortion and materials, are verified numerically and discussed in detail. Numerical results based on temporal evolution and spatial distribution indicate that the proposed impact scaling laws predict the displacement, velocity, energy and stress dynamic responses of the full-size prototype with only a small error. Furthermore, the influence of a dimensionless impact elastic-plastic number on prediction errors is identified. The effectiveness of the scaling framework is further validated across a wide range of elastic deformation proportions, offering a reliable theoretical foundation for the design and implementation of scaled impact experiments involving thin-walled cylindrical shells.