A Framework for Data-Driven Computational Dynamics Based on Nonlinear Optimization

Abstract

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.

On an objective, geometrically exact coupling element for a director-based multi-body finite element framework

“…It is important to note that other deformation measures can also be used, provided that they satisfy the necessary properties. As discussed in [27,28,30,31], the Green-Lagrange strain tensor can be decomposed into two work-conjugate strain vectors of axial strains and curvatures. This is also applied to the deformation measure of the coupling element, leading to…”