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arXiv · 2409.10126

Data-free Non-intrusive Model Reduction for Nonlinear Finite Element Models via Spectral Submanifolds

Mingwu Li·Thomas Thurnher·Zhenwei Xu·Shobhit Jain
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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.

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Mingwu Li, Thomas Thurnher, Zhenwei Xu, Shobhit Jain. 2024-09-16. Data-free Non-intrusive Model Reduction for Nonlinear Finite Element Models via Spectral Submanifolds. https://doi.org/10.1016/j.cma.2024.117590

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