Abstract:In traditional finite element methods, a common hypothesis is the nodes of an element being fixed with material points, which place restrictions on the description of a system. In this paper, this hypothesis is released and a new kind of rope element with nodes being no longer fixed with either spatial coordinates or material coordinates is presented. The theory of obtaining material velocity and acceleration of a point from the corresponding spatial velocity and acceleration of the point is established. The velocities and accelerations in the principle of virtual power should being material velocities and accelerations respectively is emphasized and applied. According to the feature of a rope-pulley system, its movement can be described by a new group of variables, such as arc-lengths, azimuthal angles and strains of ropes at entrance and exit contacting points. Instead of traditional methods, conditions of contact between rope and pulley are modeled as the material velocity of a point on the contacting rope being equal to the corresponding point on the pulley. By means of the presented methods, some obstacles, such as frequently divergence and high time consuming that resulting from traditional finite element methods can be removed. Motion equation of the rope-pulley system is derived by the principle of virtual power. Arc-length coordinates, positions of contact boundary points, the movement of pulley centers and their body-fixed reference coordinate systems, shape and positions changing of ropes as well as the tension forces in every point of a rope, can be obtained high precisely. The presented method can provide a new theoretical basis for analysis of mechanical systems with ropes and pulleys. The presented theory of using spatial points as describing variables to replace traditional material points is of applicable widely. It can be a reference for theory and application of finite element methods.