A general framework for sliding cable analysis with elastic catenary equation

Sliding cables are widespread in engineering applications. Most of the existing sliding cable models are developed basing on conventional straight truss element, which is not applicable for many engineering applications where structures possess long-span and large sag effects. To effectively analyze this kind of system, this paper proposes a multi-node sliding catenary cable element. Due to the usage of analytic form of elastic catenary equation, the proposed element has the capability to accurately analyze both very taut and very sagged cables with minimum degrees of freedom. The formulation is developed within both dynamic relaxation approach and fully implicit approach. Effective numerical strategies in the nonlinear iteration, as well as the related tangent matrices are rigorously given. In particular, the multi-loop strategy permits to integrate the very complex nonlinear element into general finite element procedure, without needing to introduce any additional variable in the system. Multiple examples are presented to demonstrate the validity of the proposed framework. The numerical results also emphasize that sliding effects have a significate influence on the mechanical behavior of the catenary cable system, while can be easily addressed by using the methodology developed in this work.