Numerical integration algorithms and constraint formulations for an ALE-ANCF cable element

In this study, the Absolute Nodal Coordinate Formulation (ANCF) is examined in the framework of the Arbitrary Lagrangian-Eulerian (ALE) formulation for cable simulation. The objective is to determine the stability, efficiency, and accuracy in different frequency domains for two different numerical time integration methods. The methods being compared are the Runge- Kutta method RK4, and the Generalized-������ method. For simulations where the lower frequency domain is of interest, the Generalized-������ method is stable, accurate and can be used with large time-steps; while where the high frequency domains is of interest, the RK4 procedure can be a more efficient method. The penalty method, the Lagrange multiplier method and linear coupling are tested as constraint methods for connecting ALE-ANCF cable elements. For RK4, the penalty constraint method highly affects the maximum time-step, which again affects the total solution time. For the Generalized-method, the constraint methods all provide accurate results, and they have similar solution time. ALE-ANCF cable elements can be connected by different constraint techniques without impeding the ability to exhibit large deformations.

Automated summary

In this study, the stability, efficiency, and accuracy of the Absolute Nodal Coordinate Formulation (ANCF) in the Arbitrary Lagrangian-Eulerian (ALE) formulation for cable simulation were examined. The Runge-Kutta method RK4 and the Generalized-������ method were compared in different frequency domains. The results showed that the Generalized-������ method is stable and accurate for low frequency simulations with large time-steps, while the RK4 method is more efficient for high frequency simulations. Different constraint techniques can be used to connect ALE-ANCF cable elements without affecting their ability to exhibit large deformations.