A Data-Driven Solving Strategy Based on a Greedy Optimization Algorithm for the Analysis of Nonlinear Beam Structures

Jul 16, 2026

Uploaded by Theodore

Data-driven computational mechanics (DDCM) enables structural analysis by using constitutive stress–strain data directly, avoiding ad-hoc material models and information loss. This work extends GO-ADM, combining a greedy optimization algorithm with the alternating direction method (ADM), to geometrically exact director-based nonlinear beams. Nonlinear initialization relies on conventional finite element results under a prescribed constitutive model, yielding discrete stress–strain fields as potential artificial datasets. A penalty formulation weakly enforces thermomechanical consistency, improving global optimality versus standard ADM for examined structures.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages39

Reading Time1 h 38 min

AccessFree to download

Introduction

Data-driven computational mechanics (DDCM)

Direct DDCM and discrete-continuous optimization

Alternating direction methods (ADM/ADMM)

Variants and applications of DDCM

Highlights A data-driven solving strategy based on a greedy optimization algorithm for the analysis of nonlinear beam structures Thi-Hoa Nguyen, Bruno A. Roccia, Cristian G. Gebhardt • We extend our data-driven solving strategy GO-ADM to the structural analysis of geometrically exact beams formulated using director-based kinematics. • We initialize the data for nonlinear systems with results obtained from a conventional finite element analysis of the same structure, performed using a prescribed constitutive model. • We propose a penalty formulation to weakly enforce the thermomechanical consistency constraint in the discrete solution. • We numerically illustrate via single-and multi-member structures that the proposed solving strategy GO-ADM yields a generally improved approximation of the globally optimal solution. arXiv :2607 . 1040 1v 1 [ cs .CE] 11 Jul 2026 A data-driven solving strategy based on a greedy optimization algorithm for the analysis of nonlinear beam structures Thi-Hoa Nguyena,∗ , Bruno A. Rocciaa , Cristian G. Gebhardta a Geophysical Institute and Bergen Offshore Wind Centre, University of Bergen, Norway Abstract In the last decade, data-driven computational mechanics (DDCM) has emerged as a novel paradigm in computational mechanics, enabling the direct use of constitutive data – such as stress-strain pairs obtained from experiments, without relying on ad-hoc material models and thereby avoiding information loss. In this work, we extend our data-driven solving strategy GO-ADM, which combines a greedy optimization algorithm with the alternating direction method (ADM), to the structural analysis of geometrically exact beams formulated using director-based kinematics. We discuss a data initialization strategy for nonlinear systems based on a conventional finite element analysis of the same structure using a prescribed constitutive model. The resulting discrete stress and strain fields, possibly obtained under multiple loading scenarios, may also be employed as artificial datasets for the subsequent data-driven computations. Furthermore, we investigate the thermomechanical consistency of both the dataset and the discrete solution, and propose a weak enforcement of this consistency in the latter via a penalty approach. Numerical examples involving single-and multi-member structures demonstrate that the proposed penalty term leads to thermomechanically consistent discrete stress and strain fields. Moreover, for the studied examples, the solving strategy GO-ADM yields a generally improved approximation of the globally optimal solution compared to the standard ADM-based direct solver. Keywords: Geometrically exact beam, Data-driven computational mechanics, Alternating direction method, Discrete-continuous nonlinear optimization problems, Greedy optimization, Static structural analysis 1. Introduction Over the last decade, data-driven computational mechanics (DDCM) has developed into an alternative computational framework that replaces the explicit constitutive relation with the direct use of experimental or synthetic material data. In its original form [1], also known as the direct DDCM, the method seeks stress and strain pairs from a given dataset which are closest to those satisfying equilibrium, compatibility, and prescribed boundary or initial conditions [1, 2] . This is essentially an optimization problem in which the objective is to minimize the distance between the ∗ Corresponding author Email addresses: [hoa.nguyen@uib.no](hoa.nguyen@uib.no) (Thi-Hoa Nguyen ), bruno.roccia@uib.no (Bruno A. Roccia), [cristian.gebhardt@uib.no](cristian.gebhardt@uib.no) (Cristian G. Gebhardt) discrete material data and the continuous field variables, known as a discrete-continuous optimization problem. The solution strategy originally proposed in [1] is an alternating iterative procedure in which admissible mechanical states and nearest material data points are updated successively. This procedur

FAQs

What problem does GO-ADM address in nonlinear beam structural analysis?

GO-ADM targets structural analysis of geometrically exact nonlinear beams by extending a data-driven solving strategy that leverages constitutive data while solving a discrete-continuous nonlinear optimization problem.

How is data initialized for the nonlinear systems?

Initialization uses results from a conventional finite element analysis of the same structure with a prescribed constitutive model, producing discrete stress and strain fields.

How does the proposed method handle thermomechanical consistency?

A penalty formulation weakly enforces thermomechanical consistency in the discrete solution, leading to discrete stress–strain fields consistent with thermomechanical requirements.

Jul 16, 2026

Uploaded by Theodore