Nonlinear dynamic simulation of cable based structures interacting with sliding objects using the concept of macro element

Abstract This paper presents the formulation of a finite element enclosing a specific internal mechanical equilibrium in order to model cable-based structures in dynamics conditions. It is based on the concept of macro finite element which allows embedding complex mechanical systems solved inside the element boundaries. A significant advantage is to allow an easy implementation within classical commercial codes. The proposed macro finite element describes a cable interacting with a sliding object assimilated to a punctual mass where friction can be accounted for. The dynamic response is described by a model developed within the framework of the DEM (Discrete Element Method) where geometrical nonlinearity (large displacements) is considered. A model combining the proposed macro finite element and a classical linear truss finite element is presented in order to validate its implementation. Finally, illustrative examples are presented. First, a cable yarning system is considered. The effect of friction and of the bending stiffness of the posts on the overall kinematics and force within the system are explored. Then the vulnerability of a cable-stayed bridge to earthquake is explored accounting for guy ropes failure.