Journal Article

Nonlinear dynamic analysis of shear- and torsion-free rods using isogeometric discretization and outlier removal

Hiemstra, René R, Schillinger, Dominik, Roccia, Bruno Antonio, Gebhardt, Cristian Guillermo, Nguyen, Hoa Thi

2025

Overview

In this paper, we present a discrete formulation of nonlinear shear- and torsion-free rods introduced by Gebhardt and Romero (Acta Mechanica 232(10):3825–3847, 2021) that uses isogeometric discretization and robust time integration. Omitting the director as an independent variable field, we reduce the number of degrees of freedom and obtain discrete solutions in multiple copies of the Euclidean space \\(\\left( \\mathbb {R}^3\\right) \\), which is larger than the corresponding multiple copies of the manifold \\(\\left( \\mathbb {R}^3 x S^2\\right) \\) obtained with standard Hermite finite elements. For implicit time integration, we choose the same integration scheme as Gebhardt and Romero in (2021) that is a hybrid form of the midpoint and the trapezoidal rules. In addition, we apply a recently introduced approach for outlier removal by Hiemstra et al. (Comput Methods Appl Mech Eng 387:114115, 2021) that reduces high-frequency content in the response without affecting the accuracy, ensuring robustness of our nonlinear discrete formulation. We illustrate the efficiency of our nonlinear discrete formulation for static and transient rods under different loading conditions, demonstrating good accuracy in space, time and the frequency domain. Our numerical example coincides with a relevant application case, the simulation of mooring lines.

• Publisher: Springer,Springer Berlin Heidelberg,Springer Nature B.V
• Subject: Accuracy / Classical and Continuum Physics / Computational Science and Engineering / Data analysis / Discretization / Engineering / Euclidean geometry / Euclidean space / Independent variables / Nonlinear dynamics / Nonlinear response / Original Paper / Rods / Theoretical and Applied Mechanics / Time integration