The design and construction of low tension cable systems require rigorous geometric nonlinear analysis. Current analyses are mostly based on an oversimplified string theory, which treats the cable as a slender tension member only, and the finite difference method. The string theory becomes singular when the tension disappears anywhere in the cable. To avoid the problem of singularity, the beam theory is required to model the low tension cables with a stable and accurate numerical time integration algorithm.

In this work, an accurate and computationally efficient three-noded curved beam element is developed for the three-dimensional analysis of large displacement and rotation. Consistently coupled polynomial interpolations of element displacement fields are used to eliminate membrane locking and ensure faster convergence rate. Due to its efficiency and reliability, the Predictor-Corrector time integration scheme with a Newmark time stepping algorithm is adopted to solve the equation of motion of low tension cables. A computer program for nonlinear elastodynamic analysis of low tension cables with the newly developed curved beam element is developed by the author using FORTRAN-95 programming language. Numerical results involving quasistatic and dynamic examples are presented to demonstrate the superior accuracy and the high convergence rate of the newly developed curved beam element. The program is further validated by experiments involving an instrumented free swinging steel cable. High speed imaging and strain gauge bridges are used to record the time histories of the cable position and tension. Good agreements in cable position and tension are observed between the experimental results and the finite element predictions. Finally, the developed computer program is applied to a typical low tension cable system involving aerial refuelling hose and drogue. The numerical predictions are compared with existing simulations. It has been shown that the newly developed curved beam element and the computer program are accurate and stable, and capable of providing an robust alternative to existing commercial codes in analysis of aerial refuelling. These newly developed codes should provide designers with a powerful tool for treating low tension cable problems, especially for the snap or slack cables.