The most of the previous research is based on analytical methods or finite element methods. Recently, in computational mechanics the new concept has been developed which is called Isogeometric Analysis (IGA). So far IGA has been applied in many research areas, among them also in catenary structures. The static catenary analysis employing IGA approach is presented in  where various refinement schemes are investigated and effectiveness and accuracy of IGA is demonstrated on 2D and 3D catenary structures. Dynamics of the deformable catenary structures undergoing large displacement using IGA approach is presented in  proposed isogeometric bending–stabilized cable formulation for statics, dynamics and cable–shell coupling. Thai et al. presented a free vibration analysis of cable structures based on IGA, using different refinement techniques the convergence of obtained natural frequencies is analysed.

The sliding joint is very well investigated using the finite element method, although it is still a complex and unefficient task due to the time consuming search algorithm that identifies the finite element hosting sliding contact. Opposite to the finite element method, only a few research papers exist on the multi-catenary dynamics approach with the sliding joint and IGA. They use intermediate reference coordinates defined at the constraint definition point developed for the absolute nodal coordinate formulation. The constraint equations are added to the equations of motion by applying a vector of Lagrange multipliers. The proposed numerical procedure is applied to the flexible plate and sliding rigid pendulum. Bauer et al. proposed formulation for isogeometric simulation of sliding edge cables in membrane structures. They added an additional term to the virtual work which is based on the penalty approach. The additional degree of freedom is defined in the parameter space.