Three-dimensional nonlinear dynamic analysis of slack cable structures using node Relaxation method

Abstract

Abstract This study proposes a robust technique for large displacement analysis of slack cable structures subjected to dynamic loadings using a novel method, entitled Node Relaxation. Ordinary numerical methods are usually unable to analyze cable structures due to singularities arising from large displacements and rotations following any alteration of the applied loads. When dynamic loads are considered, handling these singularities in numerical analyses becomes even more challenging. In this paper, an effective iterative method is proposed for three-dimensional large-displacement dynamic analysis of structures consisting slack cables as the primary load-bearing system. The cable structure is modeled using a set of nonlinear springs with properties that are constantly updated as the structural form gradually responds to the applied loads. The large changes in the cable forms are captured by considering an impedance relation that is used to determine the displacement magnitude in the directions where the structure does not have an appreciable stiffness. The method is verified against closed-form solution of wave transfer phenomenon. The effectiveness of the method is also demonstrated by solving several numerical examples.