New effective bending rigidity and structural instability analysis of noncircular cross-section elastic rod model
School of Mechanical Engineering, Tianjin University, 300350, Tianjin, China
2 Tianjin Key Laboratory of Nonlinear Dynamics and Control, 300350, Tianjin, China
Accepted: 7 December 2021
Published online: 20 December 2021
Many flexible settings characterized by long, thin, and twisted structures exist in the natural world. They consistently follow some inherent principles of configuration transition, which are implicitly embodied in their structures. To understand such basic principles, the elastic rod model plays a key role in the mathematical analysis of a structure’s generic instabilities. In this article, we present a novel effective bending rigidity of the noncircular cross-section elastic rod model and an analytical strategy to reveal those inherent conformation principles. First, a transformation parameter indicates the correlation between bending and twisting variables on the cross-section, which converts the original system into a lower order system. Second, the new effective rigidity reflects the conformation information and improves consistency with numerical results. Third, a reduced-form Kirchhoff equation is obtained, which is coherent with the original system but expressed in a more compact form. Finally, bifurcation and stability analyses reveal the trivial and buckling conformations of the rod. These results will benefit further study of conformation analysis for noncircular rod models using analytical methods and possible biological applications under generic instabilities.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2021