A Projection-Free Sparse Model Order Reduction Method for Thermomechanical Multibody Dynamics

Thermomechanical coupling effects significantly influence the dynamic response of flexible multibody systems operating in thermal environments. Accurate simulation using conventional projection-based reduced-order models remains challenging due to strong nonlinearity and the time-varying nature of thermal fields. This work proposes a projection-free sparse-solving framework for thermomechanical coupling dynamics. The elastic and thermal fields are represented using sparse POD coefficients, and the governing equations are directly sampled online without Galerkin projection. The sparse coefficients are recovered via l1 norm optimization at each time step. To ensure stable recovery under thermal-mechanical coupling, a unit-norm tight frame-based preconditioner is introduced to reduce the coherence of the underdetermined system matrix. The proposed method is validated through three numerical examples. Results show that the method maintains stable accuracy over long-time simulations, reduces computational time by over 40%, and exhibits improved robustness compared with the discrete empirical interpolation method in thermomechanical coupling problems. The adaptive basis selection capability and the necessity of unit norm tight frame preconditioning are confirmed. The method offers an efficient and reliable alternative for thermomechanical multibody dynamics simulation.