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A new stabilisation approach for level-set based topology optimisation of hyperelastic materials

Rogelio Ortigosa, Jesús Martínez-Frutos, Antonio Gil Orcid Logo, David Herrero-Pérez

Structural and Multidisciplinary Optimization

Swansea University Author: Antonio Gil Orcid Logo

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DOI (Published version): 10.1007/s00158-019-02324-5

Abstract

This paper introduces a novel computational approach for level-set based topology optimisation of hyperelastic materials at large strains. This, to date, is considered an unresolved open problem in topology optimisation due to its extremely challenging nature. Two computational strategies have been...

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Published in: Structural and Multidisciplinary Optimization
ISSN: 1615-147X 1615-1488
Published: 2019
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URI: https://cronfa.swan.ac.uk/Record/cronfa50908
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spelling 2019-07-23T09:38:08.2992239 v2 50908 2019-06-24 A new stabilisation approach for level-set based topology optimisation of hyperelastic materials 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false 2019-06-24 CIVL This paper introduces a novel computational approach for level-set based topology optimisation of hyperelastic materials at large strains. This, to date, is considered an unresolved open problem in topology optimisation due to its extremely challenging nature. Two computational strategies have been proposed to address this problem. The first strategy resorts to an arc-length in the pre-buckling region of intermediate topology optimisation (TO) iterations where numerical difficulties arise (associated with nucleation, disconnected elements, etc.), and is then continued by a novel regularisation technique in the post-buckling region. In the second strategy, the regularisation technique is used for the entire loading process at each TO iteration. The success of both rests on the combination of three distinct key ingredients. First, the nonlinear equilibrium equations of motion are solved in a consistent incrementally linearised fashion by splitting the design load into a number of load increments. Second, the resulting linearised tangent elasticity tensor is stabilised (regularised) in order to prevent its loss of positive definiteness and, thus, avoid the loss of convexity of the discrete tangent operator. Third, and with the purpose of avoiding excessive numerical stabilisation, a scalar degradation function is applied on the regularised linearised elasticity tensor, based on a novel regularisation indicator field. The robustness and applicability of this new methodological approach are thoroughly demonstrated through an ample spectrum of challenging numerical examples, ranging from benchmark two-dimensional (plane stress) examples to larger scale three-dimensional applications. Crucially, the performance of all the designs has been tested at a post-processing stage without adding any source of artificial stiffness. Specifically, an arc-length Newton-Raphson method has been employed in conjunction with a ratio of the material parameters for void and solid regions of 10− 12. Journal Article Structural and Multidisciplinary Optimization 1615-147X 1615-1488 Topology optimisation, Level-set, Nonlinear elasticity, Polyconvexity 31 12 2019 2019-12-31 10.1007/s00158-019-02324-5 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2019-07-23T09:38:08.2992239 2019-06-24T11:20:41.9022079 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Rogelio Ortigosa 1 Jesús Martínez-Frutos 2 Antonio Gil 0000-0001-7753-1414 3 David Herrero-Pérez 4 0050908-24062019112433.pdf ortigosa2019.pdf 2019-06-24T11:24:33.8070000 Output 8514275 application/pdf Accepted Manuscript true 2020-07-09T00:00:00.0000000 false eng
title A new stabilisation approach for level-set based topology optimisation of hyperelastic materials
spellingShingle A new stabilisation approach for level-set based topology optimisation of hyperelastic materials
Antonio Gil
title_short A new stabilisation approach for level-set based topology optimisation of hyperelastic materials
title_full A new stabilisation approach for level-set based topology optimisation of hyperelastic materials
title_fullStr A new stabilisation approach for level-set based topology optimisation of hyperelastic materials
title_full_unstemmed A new stabilisation approach for level-set based topology optimisation of hyperelastic materials
title_sort A new stabilisation approach for level-set based topology optimisation of hyperelastic materials
author_id_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2
author_id_fullname_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio Gil
author Antonio Gil
author2 Rogelio Ortigosa
Jesús Martínez-Frutos
Antonio Gil
David Herrero-Pérez
format Journal article
container_title Structural and Multidisciplinary Optimization
publishDate 2019
institution Swansea University
issn 1615-147X
1615-1488
doi_str_mv 10.1007/s00158-019-02324-5
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering
document_store_str 1
active_str 0
description This paper introduces a novel computational approach for level-set based topology optimisation of hyperelastic materials at large strains. This, to date, is considered an unresolved open problem in topology optimisation due to its extremely challenging nature. Two computational strategies have been proposed to address this problem. The first strategy resorts to an arc-length in the pre-buckling region of intermediate topology optimisation (TO) iterations where numerical difficulties arise (associated with nucleation, disconnected elements, etc.), and is then continued by a novel regularisation technique in the post-buckling region. In the second strategy, the regularisation technique is used for the entire loading process at each TO iteration. The success of both rests on the combination of three distinct key ingredients. First, the nonlinear equilibrium equations of motion are solved in a consistent incrementally linearised fashion by splitting the design load into a number of load increments. Second, the resulting linearised tangent elasticity tensor is stabilised (regularised) in order to prevent its loss of positive definiteness and, thus, avoid the loss of convexity of the discrete tangent operator. Third, and with the purpose of avoiding excessive numerical stabilisation, a scalar degradation function is applied on the regularised linearised elasticity tensor, based on a novel regularisation indicator field. The robustness and applicability of this new methodological approach are thoroughly demonstrated through an ample spectrum of challenging numerical examples, ranging from benchmark two-dimensional (plane stress) examples to larger scale three-dimensional applications. Crucially, the performance of all the designs has been tested at a post-processing stage without adding any source of artificial stiffness. Specifically, an arc-length Newton-Raphson method has been employed in conjunction with a ratio of the material parameters for void and solid regions of 10− 12.
published_date 2019-12-31T04:02:36Z
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score 11.037144

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