Thin-walled structures are not limited to submersibles; they are prevalent in everyday objects like cars and planes. These structures may appear flawless in design but often harbor geometric imperfections post-manufacture, making them vulnerable to buckling under much lower forces than if they were perfect.
Historically, predicting the impact of these imperfections has been challenging. However, Roberto Ballarini, the Thomas and Laura Hsu Professor and department chair of Civil and Environmental Engineering, is advancing our understanding with a new theoretical equation. Published in the Proceedings of the National Academy of Sciences (PNAS), this equation estimates the average buckling strength of a shell by analyzing the imperfections' characteristics through computer simulations.
"We derived equations that allow us to predict the resistance to buckling of structures in terms of the parameters that are involved including the shapes and distribution of their imperfections," reports Ballarini. "Given the parameters that describe the imperfections, the equations we constructed using the results of the simulations "spit out" the average buckling resistance of the structures."
The research, coauthored by doctoral student Zheren Baizhikova and Professor Jia-Liang Le from the University of Minnesota, highlights the complex interactions between localized deformations and imperfections that lead to buckling instabilities.
Ballarini emphasizes the importance of material properties in the integrity of these structures, illustrated by the tragic Titan submersible incident. The submersible's hull, made of a carbon fiber composite, likely suffered from micro-buckling and delamination under compression, which, combined with manufacturing imperfections, contributed to its catastrophic failure.
This new probabilistic model for buckling resistance, derived from extensive simulation and theoretical analysis, not only sheds light on structural failures but also paves the way for designing lighter, more sustainable structures without compromising safety.
Research Report:Uncovering the dual role of dimensionless radius in buckling of spherical shells with random geometric imperfections
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