A COROTATIONAL BEAM ELEMENT TO MODEL SUSPENDED CABLES

Due to their slenderness and inherent flexibility, the dynamic behavior of cables is strongly affected by various non-linearities as geometrical, of the material behavior and stemming from the interaction with the environment. Within this context, an interesting issue is the development of reliable and efficient numerical methods (see the review paper: [1]). In this paper the attention is focused on the mechanical response of the cable model. A corotational formulation was adopted [2], [3], essentially based on the formulation proposed by Oran in [4] and Meek and Tan in [5]. This allows to deal with stress and strain measures that otherwise would result in non-objective formulations for large displacements and rotations. This is particularly useful in view of the introduction of non-linear or inelastic constitutive laws (see the companion paper [6]). The core, in the spirit of “element - independent” corotational formulations [7], is the decomposition of the total motion of the element in a rigid component and in an approximately pure deformation, through the introduction of a moving coordinate system attached to the member itself (local or co-rotated frame). The procedure in [2] takes into account large nodal displacements and rotations, but is limited to small nodal rotations increments; in this paper this limit is critically discussed and removed.