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

TL;DR

This paper extends a data-driven nonlinear optimization framework to structural dynamics, enabling direct use of data sets for modeling and simulation, demonstrated through a geometrically exact beam example with promising computational results.

Contribution

It introduces a novel data-driven dynamic modeling approach based on nonlinear optimization, incorporating both exact and approximate formulations, and applies it to structural beam problems.

Findings

Effective computational performance demonstrated in numerical examples

Framework accommodates data-driven constitutive modeling

Potential for future research in data-based structural dynamics

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.