POD-L order reduction of flexible multi-body system dynamics based on ANCF planar triangular element

Abstract

Although various reduced-order models (ROM) have been developed for the dynamics of multibody systems modeled based on the Absolute Nodal Coordinate Formulation (ANCF), there still remain issues concerning the efficiency of model reduction. The traditional Proper Orthogonal Decomposition (POD) method can effectively reduce the dimensionality of the ANCF dynamic equations, but it necessitates mapping the generalized nodal coordinates back to their original dimension at each time step to calculate the nonlinear terms of the elastic internal forces. This leads to limited time savings in equation solving despite the dimensionality reduction achieved by the POD method. To enhance the efficiency of equation solving using the POD method, this study proposes the POD-L model reduction approach. Firstly, we apply POD to the collected snapshot matrix and retain dominant POD modes to construct a linear basis. Next, leveraging local linearization, we approximate the system stiffness matrix as constant within a limited displacement range. And iteratively obtain the elastic internal forces using the improved local linearization method, reducing error accumulation. The computed forces are then incorporated into the dynamic equations, which are projected onto the linear basis to reduce their dimensionality. The POD-L approach not only significantly reduces the dimensionality of ANCF dynamic equations and simplifies the computation of nonlinear elastic internal forces, but also reduces the error accumulation associated with the local linearization approach. It demonstrates good accuracy in prolonged simulations. It is well suited for ANCF dynamics problems involving planar triangular element modeling. The effectiveness and accuracy of the POD-L method are validated through three numerical examples.