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

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.

References in corpus (10)

• Data-Driven Modeling and Prediction of Non-Linearizable Dynamics via Spectral Submanifolds
• A Quadratic Manifold for Model Order Reduction of Nonlinear Structural Dynamics
• How to Compute Invariant Manifolds and their Reduced Dynamics in High-Dimensional Finite-Element Models
• Automated Computation of Autonomous Spectral Submanifolds for Nonlinear Modal Analysis
• Nonlinear analysis of forced mechanical systems with internal resonance using spectral submanifolds, Part I: Periodic response and forced response curve
• Exact Nonlinear Model Reduction for a von Karman beam: Slow-Fast Decomposition and Spectral Submanifolds
• Nonlinear analysis of forced mechanical systems with internal resonance using spectral submanifolds, Part II: Bifurcation and quasi-periodic response
• Data-driven Nonlinear Model Reduction to Spectral Submanifolds in Mechanical Systems
• Nonlinear model identification and spectral submanifolds for multi-degree-of-freedom mechanical vibrations
• Nonlinear Model Reduction to Fractional and Mixed-Mode Spectral Submanifolds

Cited by in corpus (1)

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