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 -