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| Original language | English |
|---|---|
| Publication status | E-pub ahead of print - 22 Dec 2019 |
Abstract
Keywords
- math.NA, cs.NA
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2019.
Research output: Working paper/Preprint › Preprint
}
TY - UNPB
T1 - A Framework for Data-Driven Computational Dynamics Based on Nonlinear Optimization
AU - Gebhardt, Cristian Guillermo
AU - Steinbach, Marc Christian
AU - Schillinger, Dominik
AU - Rolfes, Raimund
N1 - arXiv admin note: substantial text overlap with arXiv:1910.12736
PY - 2019/12/22
Y1 - 2019/12/22
N2 - In this article, we present an extension of the formulation recently developed by the authors (A Framework for Data-Driven Computational Mechanics Based on Nonlinear Optimization, arXiv:1910.12736 [math.NA]) to the structural dynamics setting. Inspired by a structure-preserving family of variational integrators, our new formulation relies on a discrete balance equation that establishes the dynamic equilibrium. From this point of departure, we first derive an "exact" discrete-continuous nonlinear optimization problem that works directly with data sets. We then develop this formulation further into an "approximate" nonlinear optimization problem that relies on a general constitutive model. This underlying model can be identified from a data set in an offline phase. To showcase the advantages of our framework, we specialize our methodology to the case of a geometrically exact beam formulation that makes use of all elements of our approach. We investigate three numerical examples of increasing difficulty that demonstrate the excellent computational behavior of the proposed framework and motivate future research in this direction.
AB - In this article, we present an extension of the formulation recently developed by the authors (A Framework for Data-Driven Computational Mechanics Based on Nonlinear Optimization, arXiv:1910.12736 [math.NA]) to the structural dynamics setting. Inspired by a structure-preserving family of variational integrators, our new formulation relies on a discrete balance equation that establishes the dynamic equilibrium. From this point of departure, we first derive an "exact" discrete-continuous nonlinear optimization problem that works directly with data sets. We then develop this formulation further into an "approximate" nonlinear optimization problem that relies on a general constitutive model. This underlying model can be identified from a data set in an offline phase. To showcase the advantages of our framework, we specialize our methodology to the case of a geometrically exact beam formulation that makes use of all elements of our approach. We investigate three numerical examples of increasing difficulty that demonstrate the excellent computational behavior of the proposed framework and motivate future research in this direction.
KW - math.NA
KW - cs.NA
M3 - Preprint
BT - A Framework for Data-Driven Computational Dynamics Based on Nonlinear Optimization
ER -