Equivalent Stiffness Matrix of Frictional Sliding Cables with Application to Structural Nonlinear Dynamic Analysis

Sliding cables are crucial components in various engineering applications. Traditional analysis methods often model friction by incorporating sliding displacements as additional degrees of freedom. These methods typically rely on explicit time-integration techniques for dynamic analysis due to the challenges of obtaining the stiffness matrix and updating the nodal sliding-stick motions. In this paper, an element-level equivalent stiffness matrix for frictional sliding cables is derived based on the force ratios of sliding subsegments. When the nodal sliding-stick motion changes, the element stiffness matrix can be updated through simple operations of the segment connection and force relation matrices, which represent the distribution of sliding nodes and the force relationships between sliding segments, respectively. This stiffness matrix is applied to dynamic analysis based on the nonlinear Newmark method. The effectiveness and accuracy of the proposed method are validated through benchmark problems. This method marks a significant advancement in the dynamic analysis of frictional sliding cables, offering a more stable and computationally efficient alternative to existing methods.