1. Data-free Non-intrusive Model Reduction for Nonlinear Finite Element Models via Spectral Submanifolds
- Author
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Li, Mingwu, Thurnher, Thomas, Xu, Zhenwei, and Jain, Shobhit
- Subjects
Mathematics - Numerical Analysis ,Computer Science - Computational Engineering, Finance, and Science ,Mathematics - Dynamical Systems - Abstract
The theory of spectral submanifolds (SSMs) has emerged as a powerful tool for constructing rigorous, low-dimensional reduced-order models (ROMs) of high-dimensional nonlinear mechanical systems. A direct computation of SSMs requires explicit knowledge of nonlinear coefficients in the equations of motion, which limits their applicability to generic finite-element (FE) solvers. Here, we propose a non-intrusive algorithm for the computation of the SSMs and the associated ROMs up to arbitrary polynomial orders. This non-intrusive algorithm only requires system nonlinearity as a black box and hence, enables SSM-based model reduction via generic finite-element software. Our expressions and algorithms are valid for systems with up to cubic-order nonlinearities, including velocity-dependent nonlinear terms, asymmetric damping, and stiffness matrices, and hence work for a large class of mechanics problems. We demonstrate the effectiveness of the proposed non-intrusive approach over a variety of FE examples of increasing complexity, including a micro-resonator FE model containing more than a million degrees of freedom.
- Published
- 2024