The Effect of Localized Imperfection Geometry on Thin-Shell Buckling: Imperfection Width Controls Stability, Imperfection Direction Governs Spatial Sensitivity

This study investigates the influence of imperfections on the buckling response of an open-section thin-shell structure. Using finite-element simulations, we examine how localized geometric imperfections modify the stability characteristics of an initially perfect shell. The imperfection takes the shape of a single dimple, which has been shown to be the most detrimental imperfection type. A probing methodology is employed to quantify this influence by evaluating the buckling energy barrier, defined as the minimum energy required to trigger a local instability. The findings reveal that the natural buckle width acts as a critical threshold that dictates whether imperfections stabilize or destabilize the structure. When the width of an outward imperfection exceeds this threshold, the dimple effectively alters the buckling behavior, preventing the formation of post-buckling equilibria and thus suppressing the potential for early buckling. This demonstrates that beyond modulating the buckling energy barrier, positive dimples can also serve as a mechanism for increasing the minimum buckling load and thereby act as a stabilizing feature. Conversely, when the imperfection is narrower than the natural buckle width, inward dimples unexpectedly raise the minimum buckling load, stabilizing the shell rather than destabilizing it. However, once the imperfection becomes wider than the natural buckle, this stabilizing effect reverses, and the associated energy barrier decreases, making the structure more prone to premature buckling. Probing across the full shell length further shows that positive imperfections localize the disturbance-sensitive region, making buckle formation spatially deterministic, whereas negative dimples broaden this region and yield a more spatially unpredictable instability response.