Efficient semi-implicit numerical integration of ANCF and ALE-ANCF cable models with holonomic constraints

In this paper, a method for integrating the equations of motion for Absolute Nodal Coordinate Formulation cable models using the Arbitrary Lagrangian–Eulerian framework is described. The proposed semi-implicit method, based on a linearization of the generalized forces, eliminates the need for iterative solution methods required by implicit integrators and incorporates rigid holonomic constraints. Both the constraint forces and the generalized accelerations can be obtained in a single step using a linear solver greatly improving the computational efficiency. Four semi-implicit integrators are derived based on popular implicit methods. The paper examines the suitability of the four semi-implicit integrators for real-time cable simulations through three benchmark studies, comparing both the accuracy and computation speed of the method with the fully implicit Newmark method. The efficiency of the method is demonstrated by obtaining stable real-time simulations in each scenario considered.