Elastodynamic analysis of low tension cables using a new curved beam element

In this paper, we address and overcome the difficulties associated with the use of the classic cable theory to treat low tension cables by developing a new three-noded locking-free nonlinear curved beam element. Based upon nonlinear generalized curved beam theory, large deformations and rotations in the new element are formulated in terms of Updated Lagrangian framework. Consistently coupled polynomial displacement fields are used to satisfy the membrane locking-free condition and the requirement of being able to recover the inextensible bending modes. Quintic transverse displacement interpolation functions are used to represent the bending deformation of the beam, while the axial and torsional displacement fields are derived by integration of the presumably linear membrane and torsional shear strain fields, which are coupled with the transverse displacement fields. Numerical results are presented to demonstrate the superior accuracy and the high convergence rate of the newly developed curved beam element. The stability and accuracy of the new element are further validated by experiments of an instrumented free-swinging steel cable experiencing slack and low tension. Good agreements in cable position and tension are observed between the experimental results and the finite element predictions.