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A framework for data‐driven structural analysis in general elasticity based on nonlinear optimization: The dynamic case

 
: Gebhardt, C.G.; Steinbach, M.C.; Schillinger, D.; Rolfes, R.

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Volltext ()

International journal for numerical methods in engineering 121 (2020), Nr.24, S.5447-5468
ISSN: 0029-5981
European Commission EC
759001; ImageToSim
Multiscale Imaging-through-analysis Methods for Autonomous Patient-specific Simulation Workflows
Englisch
Zeitschriftenaufsatz, Elektronische Publikation
Fraunhofer IWES ()

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.

: http://publica.fraunhofer.de/dokumente/N-634538.html