A Study on Model Simplification Method for ANCF Based on an Improved Local Linearization Approach

The Absolute Nodal Coordinate Formulation (ANCF) is extensively utilized in the field of flexible multibody dynamics because it offers a constant mass matrix and inherently eliminates Coriolis forces. However, ANCF requires the computation of complex nonlinear elastic internal forces at each time step, which imposes a significant computational burden. To alleviate this burden, researchers have developed local linearization (LL) methods, but these suffer from error accumulation and rely on displacement-based update criteria that are inefficient for systems with large rigid-body motion. This paper proposes an improved local linearization (I-LL) method to address these issues. Two key enhancements are introduced: (1) the update criterion for the tangent stiffness matrix is modified from displacement-based to elastic strain-based, enabling more accurate and size-independent updates; (2) accurate elastic internal force calculations are inserted within the local linearization iteration cycle to mitigate error accumulation. The accuracy and effectiveness of the I-LL algorithm are demonstrated through two numerical examples.