Multi-catenary isogeometric discretization with the sliding constraint

The purpose of this paper is to present the formulation of isogeometric dynamic analysis with frictionless sliding constraint between two catenaries.The sliding condition at the constraint point is defined employing the augmented Lagrangian method,that specifies unique degree of freedom along sliding catenary.The governing equations for the coupled system are derived in terms of Hamilton’s principle together with sliding constraint form differential algebraic equations of multi-catenary system.Recently developed isogeometric approach is employed to discretize the catenaries what enables us to define the unique degree of freedom of sliding constraint along the whole catenary and thus avoid the process of searching for the sliding point as required in some other discretization techniques,e.g.finite element method.Four numerical examples are provided to validate the proposed method and the results are assessed against the results in the literature.