A novel linear complementarity approach for analysis of sliding cable with frictions

TL;DR

This paper introduces a simple linear complementarity method for analyzing sliding cable systems with frictions, effectively handling complex motion states and enabling further theoretical studies.

Contribution

It develops a novel linear complementarity approach that simplifies analysis and allows for solution existence and uniqueness studies in sliding cable systems with frictions.

Findings

The method accurately captures variegated motion states.

Solution uniqueness is proved, existence remains open.

Numerical examples demonstrate effectiveness and reveal new phenomena.

Abstract

Sliding cable system with frictions is encountered in many engineering applications. Such system is typically characterized by existences of complex and varied motion states of different sliding nodes (pulleys), which leads to significant difficulties for analysis. A very simple but effective linear complementarity approach isdeveloped. Within this approach, the challenging and significant issue of determinations of motion states of sliding nodes, as well as calculations of their sliding lengths, can be handled in a standard linear complementarity formulation, and can be solved using any available efficient solver for linear complementarity problem (LCP). The proposed approach eliminates the need for traditional cumbersome predictor-corrector-based operations. It also opens a way to study the theory problem such as the existence and uniqueness of the solution by using complementarity theories, which is generally absent from existing literature given its complexity. The uniqueness of the solution has been proved in this work, while the existence issue remains open and deserves further investigation. Multi examples involving both static and dynamic analyses are presented to demonstrate the effectiveness of the proposed approach, as well as to reveal some novel phenomenon involved in sliding cable system considering frictions. The results highlight the ability of the method in accurately handling variegated motion states of sliding nodes. The proposed approach, we think, has the potential to be a popular method in dealing with multi-node sliding cable with frictions, given its simplicity and effectiveness.