Nonlinear static and dynamic analysis of mixed cable elements XIV International Conference on Computational Plasticity. Fundamentals and Applications COMPLAS XIV E. O˜ nate, D.R.J. Owen, D. Peric & M. Chiumenti (Eds) NONLINEAR STATIC AND DYNAMIC ANALYSIS OF MIXED CABLE ELEMENTS MIQUEL CRUSELLS-GIRONA * , FILIP C. FILIPPOU * AND ROBERT L. TAYLOR * * Department of Civil and Environmental Engineering University of California, Berkeley 94720 Berkeley, CA, USA e-mail: miquel.crusells@berkeley.edu Key words: Cables, Mixed FEM, Weak Compatibility, Nonlinear Dynamics Abstract. This paper presents a family of finite elements for the nonlinear static and dynamic analysis of cables based on a mixed variational formulation in curvilinear coor- dinates and finite deformations. This formulation identifies stress measures, in the form of axial forces, and conjugate deformation measures for the nonlinear catenary problem. The continuity requirements lead to two distinct implementations: one with a continuous axial force distribution and one with a discontinuous. Two examples from the literature on nonlinear cable analysis are used to validate the proposed formulation for St Venant- Kirchhoff elastic materials. These studies show that displacements and axial forces are captured with high accuracy for both the static and the dynamic case. 1 INTRODUCTION Cable structures are of great interest in many engineering applications because they offer numerous advantages, such as high ultimate strength, light weight or prestressing capabilities, among others. Nonetheless, a highly nonlinear behavior arises in this type of structures because of their high flexibility. For analyzing cable structures, two families of elements have traditionally been considered: truss elements and catenary elements. For truss elements, the cable is discretized in a series of straight 2-node elements. In this case, the geometric nonlinearity is often accounted for by a corotational formulation, involving the transformation of the node kinematic variables under large displacements. Truss elements suffer from excessive mesh refinement to obtain accurate results, especially when assuming a constant axial force distribution in the element. Moreover, they may exhibit snap-through instabilities at states of nearly singular stiffness. Catenary elements use linear kinematics to discretize the cable into a series of curved elements that satisfy the catenary equation. These elements solve the global balance of linear momentum by explicit integration and assuming linear elasticity [1]. As a result, loads are not adjusted with the cable elongation, so that these elements cannot be ex- tended to nonlinear elasticity or inelasticity. Recently, the authors have proposed a general 896