Symmetry of solutions in discrete and continuous structural topology optimization

J. N. Richardson; S. Adriaenssens; Ph Bouillard; R. Filomeno Coelho

Symmetry of solutions in discrete and continuous structural topology optimization

J. N. Richardson, S. Adriaenssens, Ph Bouillard, R. Filomeno Coelho

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

In this paper symmetry and asymmetry of optimal solutions in symmetric structural topology optimization problems are investigated, based on the choice of variables. A group theory approach is used to formally define the symmetry of the structural problems. This approach allows the set of symmetric structures to be described and related to the entire search space. It is shown that, given a symmetric problem with continuous variables, an optimal symmetric solution (if any) necessarily exists. However, it is shown that this does not hold for the discrete case. Finally a number of examples are investigated to demonstrate the findings of the research.

Original language	English (US)
Title of host publication	Proceedings of the 11th International Conference on Computational Structures Technology, CST 2012
Publisher	Civil-Comp Press
Volume	99
ISBN (Print)	9781905088546
State	Published - 2012
Event	11th International Conference on Computational Structures Technology, CST 2012 - Dubrovnik, Croatia Duration: Sep 4 2012 → Sep 7 2012

Other

Other	11th International Conference on Computational Structures Technology, CST 2012
Country/Territory	Croatia
City	Dubrovnik
Period	9/4/12 → 9/7/12

All Science Journal Classification (ASJC) codes

Environmental Engineering
Civil and Structural Engineering
Computational Theory and Mathematics
Artificial Intelligence

Keywords

Asymmetric topology
Group theory
Structural topology optimization
Symmetric topology
Symmetry operation
Truss topology optimization

Cite this

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title = "Symmetry of solutions in discrete and continuous structural topology optimization",

abstract = "In this paper symmetry and asymmetry of optimal solutions in symmetric structural topology optimization problems are investigated, based on the choice of variables. A group theory approach is used to formally define the symmetry of the structural problems. This approach allows the set of symmetric structures to be described and related to the entire search space. It is shown that, given a symmetric problem with continuous variables, an optimal symmetric solution (if any) necessarily exists. However, it is shown that this does not hold for the discrete case. Finally a number of examples are investigated to demonstrate the findings of the research.",

keywords = "Asymmetric topology, Group theory, Structural topology optimization, Symmetric topology, Symmetry operation, Truss topology optimization",

author = "Richardson, {J. N.} and S. Adriaenssens and Ph Bouillard and {Filomeno Coelho}, R.",

year = "2012",

language = "English (US)",

isbn = "9781905088546",

volume = "99",

booktitle = "Proceedings of the 11th International Conference on Computational Structures Technology, CST 2012",

publisher = "Civil-Comp Press",

address = "United Kingdom",

note = "11th International Conference on Computational Structures Technology, CST 2012 ; Conference date: 04-09-2012 Through 07-09-2012",

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Richardson, JN, Adriaenssens, S, Bouillard, P & Filomeno Coelho, R 2012, Symmetry of solutions in discrete and continuous structural topology optimization. in Proceedings of the 11th International Conference on Computational Structures Technology, CST 2012. vol. 99, Civil-Comp Press, 11th International Conference on Computational Structures Technology, CST 2012, Dubrovnik, Croatia, 9/4/12.

TY - GEN

T1 - Symmetry of solutions in discrete and continuous structural topology optimization

AU - Richardson, J. N.

AU - Adriaenssens, S.

AU - Bouillard, Ph

AU - Filomeno Coelho, R.

PY - 2012

Y1 - 2012

N2 - In this paper symmetry and asymmetry of optimal solutions in symmetric structural topology optimization problems are investigated, based on the choice of variables. A group theory approach is used to formally define the symmetry of the structural problems. This approach allows the set of symmetric structures to be described and related to the entire search space. It is shown that, given a symmetric problem with continuous variables, an optimal symmetric solution (if any) necessarily exists. However, it is shown that this does not hold for the discrete case. Finally a number of examples are investigated to demonstrate the findings of the research.

AB - In this paper symmetry and asymmetry of optimal solutions in symmetric structural topology optimization problems are investigated, based on the choice of variables. A group theory approach is used to formally define the symmetry of the structural problems. This approach allows the set of symmetric structures to be described and related to the entire search space. It is shown that, given a symmetric problem with continuous variables, an optimal symmetric solution (if any) necessarily exists. However, it is shown that this does not hold for the discrete case. Finally a number of examples are investigated to demonstrate the findings of the research.

KW - Asymmetric topology

KW - Group theory

KW - Structural topology optimization

KW - Symmetric topology

KW - Symmetry operation

KW - Truss topology optimization

UR - http://www.scopus.com/inward/record.url?scp=84893908934&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84893908934&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84893908934

SN - 9781905088546

VL - 99

BT - Proceedings of the 11th International Conference on Computational Structures Technology, CST 2012

PB - Civil-Comp Press

T2 - 11th International Conference on Computational Structures Technology, CST 2012

Y2 - 4 September 2012 through 7 September 2012

ER -

Symmetry of solutions in discrete and continuous structural topology optimization

Abstract

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Keywords

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