Goal oriented error estimation in multi-scale shell element finite element problems

Bonney, Matt; Evans, Richard; Rouse, James; Jones, Arthur; Kerfriden, Pierre; Hamadi, Maxime

doi:10.1186/s40323-021-00189-2

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Goal oriented error estimation in multi-scale shell element finite element problems

Matt Bonney

, Richard Evans, James Rouse

, Arthur Jones, Pierre Kerfriden, Maxime Hamadi

Advanced Modeling and Simulation in Engineering Sciences, Volume: 8, Issue: 1

Swansea University Author: Matt Bonney

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DOI (Published version): 10.1186/s40323-021-00189-2

Abstract

A major challenge with modern aircraft design is the occurrence of structural features of varied length scales. Structural stiffness can be accurately represented using homogenisation, however aspects such as the onset of failure may require information on more refined length scale for both metallic...

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Published in:	Advanced Modeling and Simulation in Engineering Sciences
ISSN:	2213-7467
Published:	Springer Science and Business Media LLC 2021
Online Access:	Check full text
URI:	https://cronfa.swan.ac.uk/Record/cronfa65025

first_indexed	2024-01-02T15:36:44Z
last_indexed	2024-11-25T14:15:13Z
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This work considers the errors encountered in the coarse global models due to the mesh size and how these are propagated into detailed local sub-models. The error is calculated by a goal oriented error estimator, formulated by solving dual problems and Zienkiewicz-Zhu smooth field recovery. Specifically, the novel concept of this work is applying the goal oriented error estimator to shell elements and propagating this error field into the continuum sub-model. This methodology is tested on a simplified aluminium beam section with four different local feature designs, thereby illustrating the sensitivity to various local features with a common global setting. The simulations show that when the feature models only contained holes on the flange section, there was little sensitivity of the von Mises stress to the design modifications. However, when holes were added to the webbing section, there were large stress concentrations that predicted yielding. Despite this increase in nominal stress, the maximum error does not significantly change. However, the error field does change near the holes. A Monte Carlo simulation utilising marginal distributions is performed to show the robustness of the multi-scale analysis to uncertainty in the global error estimation as would be expected in experimental measurements. 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spelling	2024-01-02T15:38:18.3943198 v2 65025 2023-11-21 Goal oriented error estimation in multi-scale shell element finite element problems 323110cf11dcec3e8183228a4b33e06d 0000-0002-1499-0848 Matt Bonney Matt Bonney true false 2023-11-21 ACEM A major challenge with modern aircraft design is the occurrence of structural features of varied length scales. Structural stiffness can be accurately represented using homogenisation, however aspects such as the onset of failure may require information on more refined length scale for both metallic and composite components. This work considers the errors encountered in the coarse global models due to the mesh size and how these are propagated into detailed local sub-models. The error is calculated by a goal oriented error estimator, formulated by solving dual problems and Zienkiewicz-Zhu smooth field recovery. Specifically, the novel concept of this work is applying the goal oriented error estimator to shell elements and propagating this error field into the continuum sub-model. This methodology is tested on a simplified aluminium beam section with four different local feature designs, thereby illustrating the sensitivity to various local features with a common global setting. The simulations show that when the feature models only contained holes on the flange section, there was little sensitivity of the von Mises stress to the design modifications. However, when holes were added to the webbing section, there were large stress concentrations that predicted yielding. Despite this increase in nominal stress, the maximum error does not significantly change. However, the error field does change near the holes. A Monte Carlo simulation utilising marginal distributions is performed to show the robustness of the multi-scale analysis to uncertainty in the global error estimation as would be expected in experimental measurements. This shows a trade-off between Saint-Venant’s principle of the applied loading and stress concentrations on the feature model when investigating the response variance. Journal Article Advanced Modeling and Simulation in Engineering Sciences 8 1 Springer Science and Business Media LLC 2213-7467 Goal orientated error estimation, Shell elements, Multi-scale finite element,Zienkiewicz-Zhu recovery 18 2 2021 2021-02-18 10.1186/s40323-021-00189-2 http://dx.doi.org/10.1186/s40323-021-00189-2 COLLEGE NANME Aerospace, Civil, Electrical, and Mechanical Engineering COLLEGE CODE ACEM Swansea University This project is funded by the Clean Sky 2 Joint Undertaking under the European Union’s Horizon 2020 research and innovation program under grant agreement No 754581. 2024-01-02T15:38:18.3943198 2023-11-21T09:15:48.9128978 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering Matt Bonney 0000-0002-1499-0848 1 Richard Evans 2 James Rouse 0000-0003-1568-9122 3 Arthur Jones 4 Pierre Kerfriden 5 Maxime Hamadi 6 65025__29341__02f6d35f37ae4280b6bf38b2cc854aa3.pdf 65025.VOR.pdf 2024-01-02T15:37:27.6496525 Output 6241629 application/pdf Version of Record true © The Author(s) 2021. Distributed under the terms of a Creative Commons Attribution 4.0 International License (CC BY 4.0). true eng https://creativecommons.org/licenses/by/4.0/
title	Goal oriented error estimation in multi-scale shell element finite element problems
spellingShingle	Goal oriented error estimation in multi-scale shell element finite element problems Matt Bonney
title_short	Goal oriented error estimation in multi-scale shell element finite element problems
title_full	Goal oriented error estimation in multi-scale shell element finite element problems
title_fullStr	Goal oriented error estimation in multi-scale shell element finite element problems
title_full_unstemmed	Goal oriented error estimation in multi-scale shell element finite element problems
title_sort	Goal oriented error estimation in multi-scale shell element finite element problems
author_id_str_mv	323110cf11dcec3e8183228a4b33e06d
author_id_fullname_str_mv	323110cf11dcec3e8183228a4b33e06d_***_Matt Bonney
author	Matt Bonney
author2	Matt Bonney Richard Evans James Rouse Arthur Jones Pierre Kerfriden Maxime Hamadi
format	Journal article
container_title	Advanced Modeling and Simulation in Engineering Sciences
container_volume	8
container_issue	1
publishDate	2021
institution	Swansea University
issn	2213-7467
doi_str_mv	10.1186/s40323-021-00189-2
publisher	Springer Science and Business Media LLC
college_str	Faculty of Science and Engineering
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hierarchy_top_title	Faculty of Science and Engineering
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department_str	School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering
url	http://dx.doi.org/10.1186/s40323-021-00189-2
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description	A major challenge with modern aircraft design is the occurrence of structural features of varied length scales. Structural stiffness can be accurately represented using homogenisation, however aspects such as the onset of failure may require information on more refined length scale for both metallic and composite components. This work considers the errors encountered in the coarse global models due to the mesh size and how these are propagated into detailed local sub-models. The error is calculated by a goal oriented error estimator, formulated by solving dual problems and Zienkiewicz-Zhu smooth field recovery. Specifically, the novel concept of this work is applying the goal oriented error estimator to shell elements and propagating this error field into the continuum sub-model. This methodology is tested on a simplified aluminium beam section with four different local feature designs, thereby illustrating the sensitivity to various local features with a common global setting. The simulations show that when the feature models only contained holes on the flange section, there was little sensitivity of the von Mises stress to the design modifications. However, when holes were added to the webbing section, there were large stress concentrations that predicted yielding. Despite this increase in nominal stress, the maximum error does not significantly change. However, the error field does change near the holes. A Monte Carlo simulation utilising marginal distributions is performed to show the robustness of the multi-scale analysis to uncertainty in the global error estimation as would be expected in experimental measurements. This shows a trade-off between Saint-Venant’s principle of the applied loading and stress concentrations on the feature model when investigating the response variance.
published_date	2021-02-18T20:35:31Z
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score	11.048042

Goal oriented error estimation in multi-scale shell element finite element problems

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