article

On the implementation and effectiveness of morphological close-open and open-close filters for topology optimization

Authors:

Mattias Schevenels,

Ole SigmundAuthors Info & Claims

Structural and Multidisciplinary Optimization, Volume 54, Issue 1

Pages 15 - 21

https://doi.org/10.1007/s00158-015-1393-y

Published: 01 July 2016 Publication History

Abstract

This note reconsiders the morphological close-open and open-close filters for topology optimization introduced in an earlier paper (Sigmund Struct Multidiscip Optim 33(4---5):401---424 (2007)). Close-open and open-close filters are defined as the sequential application of four dilation or erosion filters. In the original paper, these filters were proposed in order to provide length scale control in both the solid and the void phase. However, it was concluded that the filters were not useful in practice due to the computational cost of the sensitivity analysis. In this note, it is shown that the computational cost is much lower if the sensitivity analysis for each erosion or dilation step is performed sequentially. Unfortunately, it is also found that the close-open and open-close filters do not have the expected effect in terms of length scale control: each close or open operation ruins the effect of the preceding filters, resulting in a design with a minimum length scale in either the solid phase or the void phase, but not both.

References

[1]

Andreassen E, Clausen A, Schevenels M, Lazarov B, Sigmund O (2011) Efficient topology optimization in MATLAB using 88 lines of code. Struct Multidiscip Optim 43:1-16.

Digital Library

[2]

Bendsøe M (1989) Optimal shape design as a material distribution problem. Struct Multidiscip Optim 1(4):193-202.

[3]

Bourdin B (2001) Filters in topology optimization. Int J Numer Methods Eng 50(9):2143-2158.

[4]

Bovik A (2009) The essential guide to image processing. Academic Press.

[5]

Bruns T, Tortorelli D (2001) Topology optimization of non-linear elastic structures and compliant mechanisms. Comput Methods Appl Mech Eng 190(26-27):3443-3459.

[6]

Díaz A, Sigmund O (1995) Checkerboard patterns in layout optimization. Structural Optimization 10(1):40-45.

[7]

Guest J, Prevost J, Belytschko T (2004) Achieving minimum length scale in topology optimization using nodal design variables and projection functions. Int J Numer Methods Eng 61(2):238-254.

[8]

Jog C, Haber R (1996) Stability of finite element models for distributed-parameter optimization and topology design. Comput Methods Appl Mech Eng 130(3-4):203-226.

[9]

Kreisselmeier G, Steinhauser R (1983) Application of vector performance optimization to a robust-control loop design for a fighter aircraft. Int J Control 37(2):251-284.

[10]

Lazarov BS, Sigmund O (2011) Filters in topology optimization based on helmholtz-type differential equations. Int J Numer Methods Eng 86(6):765-781.

[11]

Pratt W (1991) Digital image processing. Wiley.

[12]

Sigmund O (1994) Design of material structures using topology optimization. PhD thesis, Department of Solid Mechanics, Technical University of Denmark.

[13]

Sigmund O (1997) On the design of compliant mechanisms using topology optimization. Mech Struct Mach 25(4):493- 524.

[14]

Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multidiscip Optim 33(4-5):401- 424.

[15]

Sigmund O (2009) Manufacturing tolerant topology optimization. Acta Mech Sinica 25(2):227-239.

[16]

Sigmund O, Petersson J (1998) Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Structural Optimization 16(1):68-75.

[17]

Svanberg K (1987) The method of moving asymptotes - a new method for structural optimization. Int J Numer Methods Eng 24(2):359- 373.

[18]

Wadbro E, Hägg L (2015) On quasi-arithmetic mean based filters and their fast evaluation for large-scale topology optimization. Structural and Multidisciplinary Optimization Published online.

[19]

Wang F, Lazarov B, Sigmund O (2011) On projection methods, convergence and robust formulations in topology optimization. Struct Multidiscip Optim 43(6):767-784.

Digital Library

[20]

Xu S, Cai Y, Cheng G (2010) Volume preserving nonlinear density filter based on Heaviside functions. Struct Multidiscip Optim 41(4):495-505.

[21]

Zhou M, Rozvany G (1991) The COC algorithm, part II: Topological, geometrical and generalized shape optimization. Comput Methods Appl Mech Eng 89(1-3):309-336.

[22]

Zhou M, Lazarov B, Wang F, Sigmund O (2015) Minimum length scale in topology optimization by geometric constraints. Comput Methods Appl Mech Eng 293:266-282.

Cited By

Mommeyer CLombaert GSchevenels MSigmund O(2024)Taylor series approximations for faster robust topology optimizationStructural and Multidisciplinary Optimization10.1007/s00158-024-03890-z67:10Online publication date: 16-Oct-2024
https://dl.acm.org/doi/10.1007/s00158-024-03890-z
Noack MKühhorn AKober MFirl M(2021)A new stress-based topology optimization approach for finding flexible structuresStructural and Multidisciplinary Optimization10.1007/s00158-021-02960-w64:4(1997-2007)Online publication date: 1-Oct-2021
https://dl.acm.org/doi/10.1007/s00158-021-02960-w
Dong YLiu XSong THe S(2021)Topology optimization for structure with multi-gradient materialsStructural and Multidisciplinary Optimization10.1007/s00158-020-02749-363:3(1151-1167)Online publication date: 1-Mar-2021
https://dl.acm.org/doi/10.1007/s00158-020-02749-3
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cover image Structural and Multidisciplinary Optimization

Structural and Multidisciplinary Optimization Volume 54, Issue 1

July 2016

185 pages

ISSN:1615-147X

Issue’s Table of Contents

Copyright © Copyright © 2016 Springer-Verlag Berlin Heidelberg.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 July 2016

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Cited By

Mommeyer CLombaert GSchevenels MSigmund O(2024)Taylor series approximations for faster robust topology optimizationStructural and Multidisciplinary Optimization10.1007/s00158-024-03890-z67:10Online publication date: 16-Oct-2024
https://dl.acm.org/doi/10.1007/s00158-024-03890-z
Noack MKühhorn AKober MFirl M(2021)A new stress-based topology optimization approach for finding flexible structuresStructural and Multidisciplinary Optimization10.1007/s00158-021-02960-w64:4(1997-2007)Online publication date: 1-Oct-2021
https://dl.acm.org/doi/10.1007/s00158-021-02960-w
Dong YLiu XSong THe S(2021)Topology optimization for structure with multi-gradient materialsStructural and Multidisciplinary Optimization10.1007/s00158-020-02749-363:3(1151-1167)Online publication date: 1-Mar-2021
https://dl.acm.org/doi/10.1007/s00158-020-02749-3
Pellens JLombaert GLazarov BSchevenels M(2019)Combined length scale and overhang angle control in minimum compliance topology optimization for additive manufacturingStructural and Multidisciplinary Optimization10.1007/s00158-018-2168-z59:6(2005-2022)Online publication date: 1-Jun-2019
https://dl.acm.org/doi/10.1007/s00158-018-2168-z
Niu BWadbro E(2019)On equal-width length-scale control in topology optimizationStructural and Multidisciplinary Optimization10.1007/s00158-018-2131-z59:4(1321-1334)Online publication date: 17-May-2019
https://dl.acm.org/doi/10.1007/s00158-018-2131-z
Hägg LWadbro E(2018)On minimum length scale control in density based topology optimizationStructural and Multidisciplinary Optimization10.1007/s00158-018-1944-058:3(1015-1032)Online publication date: 27-Dec-2018
https://dl.acm.org/doi/10.1007/s00158-018-1944-0
Hassan EWadbro EHägg LBerggren M(2018)Topology optimization of compact wideband coaxial-to-waveguide transitions with minimum-size controlStructural and Multidisciplinary Optimization10.1007/s00158-017-1844-857:4(1765-1777)Online publication date: 27-Dec-2018
https://dl.acm.org/doi/10.1007/s00158-017-1844-8

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