A Study on a Simplified Thermo-Mechanical Coupling Model Based on the Improved Local Linearization Method

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 and thermal deformation forces at each time step, which imposes a significant computational burden. To alleviate this burden, researchers have developed local linearization (LL) methods. The local linearization method constructs constant elastic and thermal stiffness matrices within a small range by means of Taylor expansion, effectively reducing the number of stiffness matrix updates. But the method suffers from error accumulation and relies 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 elastic and thermal stiffness matrices is modified from displacement-based to total strain-based, enabling more accurate and size-independent updates; (2) accurate elastic or thermal deformation force calculations are inserted within the local linearization iteration cycle to mitigate error accumulation. These two improvements reduce the number of calculations of the nonlinear internal forces and, at the same time, lessen the error accumulation in the simplified model. The accuracy and effectiveness of the I-LL algorithm are demonstrated through three numerical examples.