Work

Data-free non-intrusive model reduction for nonlinear finite element models via spectral submanifolds

Year: 2024

Type: article

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.

Source: Computer Methods in Applied Mechanics and Engineering

DOI: 10.1016/j.cma.2024.117590

Authors: Mingwu Li, Thomas Thurnher, Zhenwei Xu, Shobhit Jain

Institutions: Southern University of Science and Technology, ETH Zurich, Institute of Mechanical Systems, Delft University of Technology

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,660

Funders: MathWorks, National Natural Science Foundation of China, Science, Technology and Innovation Commission of Shenzhen Municipality, Shenzhen Science and Technology Innovation Program