We derive the shape equations in terms of Euler angles for a uniform elastic filament with circular cross section but free of spontaneous torsion. We show that in general there are planar curve solutions for a closed rod. We study the boundary conditions (i.e., experimental conditions in a force experiment) to form a helical filament under external force and twisting. We find that to form a helix, the Euler angle must be a constant determined by the spontaneous curvatures. We study the elasticity of a helical filament under different conditions. We find that the extension of a helix under fixed and finite torque may subject to a one-step sharp transition with increasing stretching force. However, we show exactly that there is not jump of extension for a helical filament free of external torque. This behavior is quite different from a uniform elastic rod with circular cross section and spontaneous torsion, and provides another very important reason why one cannot observe the sharp jump of extension for most macroscopic helical springs.
為了持續優化網站功能與使用者體驗,本網站將Cookies分析技術用於網站營運、分析和個人化服務之目的。
若您繼續瀏覽本網站,即表示您同意本網站使用Cookies。