Isogeometric rotation-free bending-stabilized cables: Statics, dynamics, bending strips and coupling with shells

Abstract

An isogeometric cable formulation is derived from a 3D continuum, where large-deformation kinematics and the St. Venant–Kirchhoff constitutive law are assumed. It is also assumed that the cable cross-sections remain circular, planar, and orthogonal to the cable middle curve during the deformation. The cable geometry representation reduces to a curve in 3D space, and, because only displacement degrees of freedom are employed, only membrane and bending effects are accounted for in the modeling. Torsion is neglected and bending is confined to an osculating plane of the curve. In the case structural loading and response are confined to a plane, the formulation is reduced to a 2D Euler–Bernoulli beam of finite thickness. Bending terms also stabilize the cable formulation in the presence of compressive forces. The resulting cable formulation is validated in the regime of linear and nonlinear statics, and nonlinear dynamics. The concept of bending strips is extended to the case of multiple cables, and cable-shell coupling is also investigated. The formulation is presented in sufficient mathematical detail for straightforward computer implementation.