Sliding cable modeling: A nonlinear complementarity function based framework

•A nonlinear complementarity function framework for sliding cable system analysis is developed.•The searching of sliding nodes and geometric configuration is handed in a unified framework.•Any case differentiation on the motion states is avoided and always the same equation is used.•Numerical examples are given to show its ability in capturing diverse motion states of the nodes. Sliding cables are widespread in engineering applications. The friction between the cable and the sliding components results in the existence of diversified motion states of the contact points, which leads to many difficult problems for traditional analysis methods. This paper proposes an effective and robust nonlinear complementarity function based framework for static and dynamic analyses of sliding cable problems. The core idea is that the involved sliding criterion is expressed by complementarity relationships which can be further reformulated as a set of equation by using the modified Fischer-Burmeister complementarity function. By considering the instrumental sliding lengths as additional degrees of freedom in the finite element model, the sliding nodes searching and the geometric configuration searching in the analysis can be handed in a unified framework. The solution can be obtained by using classical Newton-Raphson scheme with a closed-form expression of tangent matrix. Cumbersome trial and error iterations for sliding node searching in traditional analysis methods are rigorously avoided, and always the same equation is used regardless of whether a particular contact point would be sticking or sliding. This framework is developed mainly for implicit static and dynamic analyses, but can also be integrated into explicit analyses. Some typical examples are presented to illustrate the robustness and versatility of the proposed approach. The result highlight its ability to capture the complex and diverse motion states of the contact points in a rather direct way.