Details
| Original language | English |
|---|---|
| Pages (from-to) | 5447-5468 |
| Number of pages | 22 |
| Journal | International Journal for Numerical Methods in Engineering |
| Volume | 121 |
| Issue number | 24 |
| Early online date | 13 May 2020 |
| Publication status | Published - 11 Nov 2020 |
Abstract
In this article, we present an extension of the formulation recently developed by the authors 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.
Keywords
- data-driven structural dynamics, finite elements, geometrically exact beams, nonlinear optimization problem, structure-preserving time integration
ASJC Scopus subject areas
- Mathematics(all)
- Numerical Analysis
- Engineering(all)
- Mathematics(all)
- Applied Mathematics
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In: International Journal for Numerical Methods in Engineering, Vol. 121, No. 24, 11.11.2020, p. 5447-5468.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A framework for data-driven structural analysis in general elasticity based on nonlinear optimization
T2 - The dynamic case
AU - Gebhardt, Cristian Guillermo
AU - Steinbach, Marc Christian
AU - Schillinger, Dominik
AU - Rolfes, Raimund
N1 - Funding Information: Deutsche Forschungsgemeinschaft, "ENERGIZE", GE 2773/3‐1 and RO 706/20‐1 and Emmy Noether Award, SCH 1249/2‐1; European Research Council, "ImageToSim”, Action No. 759001; Niedersächsisches Ministerium für Wissenschaft und Kultur, "ventus efficiens", FKZ ZN3024 Funding information Funding Information: C. G. Gebhardt and R. Rolfes gratefully acknowledge the financial support of the Lower Saxony Ministry of Science and Culture (research project , FKZ ZN3024) and the German Research Foundation (research project ENERGIZE, GE 2773/3‐1 – RO 706/20‐1) that enabled this work. D. Schillinger acknowledges support from the German Research Foundation through the DFG Emmy Noether Award SCH 1249/2‐1, and from the European Research Council via the ERC Starting Grant “ImageToSim” (Action No. 759001). ventus efficiens
PY - 2020/11/11
Y1 - 2020/11/11
N2 - In this article, we present an extension of the formulation recently developed by the authors 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 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 - data-driven structural dynamics
KW - finite elements
KW - geometrically exact beams
KW - nonlinear optimization problem
KW - structure-preserving time integration
UR - http://www.scopus.com/inward/record.url?scp=85091170728&partnerID=8YFLogxK
U2 - 10.1002/nme.6389
DO - 10.1002/nme.6389
M3 - Article
AN - SCOPUS:85091170728
VL - 121
SP - 5447
EP - 5468
JO - International Journal for Numerical Methods in Engineering
JF - International Journal for Numerical Methods in Engineering
SN - 0029-5981
IS - 24
ER -