Data-Assisted Non-Intrusive Model Reduction for Forced Nonlinear Finite Elements Models

TL;DR

This paper introduces a data-driven method to construct spectral submanifold-based reduced models from unforced finite element simulations, enabling accurate prediction of forced responses without costly forced simulations.

Contribution

It develops a novel approach for building SSM-based reduced models directly from FE data, bypassing the need for explicit nonlinearities in commercial FE solvers.

Findings

Accurately predicts forced responses in complex FE models.

Reduces computational cost significantly for large-scale problems.

Effective even with internal resonances and quasi-periodic forcing.

Abstract

Spectral submanifolds (SSMs) have emerged as accurate and predictive model reduction tools for dynamical systems defined either by equations or data sets. While finite-elements (FE) models belong to the equation-based class of problems, their implementations in commercial solvers do not generally provide information on the nonlinearities required for the analytical construction of SSMs. Here, we overcome this limitation by developing a data-driven construction of SSM-reduced models from a small number of unforced FE simulations. We then use these models to predict the forced response of the FE model without performing any costly forced simulation. This approach yields accurate forced response predictions even in the presence of internal resonances or quasi-periodic forcing, as we illustrate on several FE models. Our examples range from simple structures, such as beams and shells, to more complex geometries, such as a micro-resonator model containing more than a million degrees of freedom. In the latter case, our algorithm predicts accurate forced response curves in a small fraction of the time it takes to verify just a few points on those curves by simulating the full forced-response.