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Static friction models for a rod deforming on a cylinder
Journal of the Mechanics and Physics of Solids ( IF 5.3 ) Pub Date : 2023-01-31 , DOI: 10.1016/j.jmps.2023.105224
R. Shah, G.H.M. van der Heijden

We develop a comprehensive geometrically-exact theory for an end-loaded elastic rod constrained to deform on a cylindrical surface. By viewing the rod-cylinder system as a special case of an elastic braid, we are able to obtain all forces and moments imparted by the deforming rod to the cylinder as well as all contact reactions. This framework allows us to give a complete treatment of static friction consistent with force and moment balance. In addition to the commonly considered model of hard frictionless contact we analyse in detail two friction models in which the rod, possibly with intrinsic curvature, experiences either lateral or tangential friction. As applications of the theory we study buckling of the constrained rod under compressive and torsional loads, finding critical loads to depend on Coulomb-like friction parameters, as well as the tendency of the rod to lift off the cylinder under further loading. Our results are relevant for many engineering and medical applications in which a slender structure winds inside or outside a cylindrical boundary.



中文翻译:

杆在圆柱上变形的静摩擦模型

我们针对受约束在圆柱面上变形的端部加载弹性杆开发了一个全面的几何精确理论。通过将杆-圆柱系统视为弹性编织物的一个特例,我们能够获得变形杆传递给圆柱的所有力和力矩以及所有接触反应。该框架使我们能够对与力和力矩平衡一致的静摩擦进行完整处理。除了通常考虑的硬无摩擦接触模型外,我们还详细分析了两种摩擦模型,其中可能具有固有曲率的杆经历横向或切向摩擦。作为该理论的应用,我们研究了受限杆在压缩和扭转载荷下的屈曲,发现临界载荷取决于类库仑摩擦参数,以及杆在进一步加载下从气缸上抬起的趋势。我们的结果与许多工程和医学应用相关,在这些应用中,细长结构缠绕在圆柱形边界的内部或外部。

更新日期:2023-02-04
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