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A framework for data‐driven structural analysis in general elasticity based on nonlinear optimization: The dynamic case
Author(s) -
Gebhardt Cristian Guillermo,
Steinbach Marc Christian,
Schillinger Dominik,
Rolfes Raimund
Publication year - 2020
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6389
Subject(s) - nonlinear system , mathematical optimization , computer science , extension (predicate logic) , nonlinear elasticity , optimization problem , mathematics , dynamic problem , physics , quantum mechanics , programming language
Summary 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.