Skip to main content
SpringerLink
Log in

A new method based on adaptive volume constraint and stress penalty for stress-constrained topology optimization

  • RESEARCH PAPER
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

This paper focuses on the stress-constrained topology optimization of minimizing the structural volume and compliance. A new method based on adaptive volume constraint and stress penalty is proposed. According to this method, the stress-constrained volume and compliance minimization topology optimization problem is transformed into two simple and related problems: a stress-penalty-based compliance minimization problem and a volume-decision problem. In the former problem, stress penalty is conducted and used to control the local stress level of the structure. To solve this problem, the parametric level set method with the compactly supported radial basis functions is adopted. Meanwhile, an adaptive adjusting scheme of the stress penalty factor is used to improve the control of the local stress level. To solve the volume-decision problem, a combination scheme of the interval search and local search is proposed. Numerical examples are used to test the proposed method. Results show the lightweight design, which meets the stress constraint and whose compliance is simultaneously optimized, can be obtained by the proposed method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25

Similar content being viewed by others

References

  • Allaire G, Jouve F, Toader AM (2004) Structural optimization using sensitivity analysis and a level-set method. J Comput Phys 194:363–393

    Article  MathSciNet  MATH  Google Scholar 

  • Bendsøe MP (1995) Optimization of structural topology, shape and material. Springer, Berlin Heidelberg

  • Bendsøe MP, Sigmund O (2003) Topology optimization: theory, methods and applications, 2nd edn. Springer, Berlin

    MATH  Google Scholar 

  • Bruggi M (2008) On an alternative approach to stress constraints relaxation in topology optimization. Struct Multidiscip Optim 36:125–141

    Article  MathSciNet  MATH  Google Scholar 

  • Bruggi M, Venini P (2008) A mixed FEM approach to stress-constrained topology optimization. Int J Numer Methods Eng 73:1693–1714

    Article  MathSciNet  MATH  Google Scholar 

  • Cheng GD, Guo X (1997) ε-Relaxed approach in structural topology optimization. Struct Optim 13:258–266

    Article  Google Scholar 

  • Choi KK, Kim NH (2005) Structural sensitivity analysis and optimization. Springer, New York

  • Collet M, Bruggi M, Duysinx P (2016) Topology optimization for minimum weight with compliance and simplified nominal stress constraints for fatigue resistance. Struct Multidiscip Optim 55:1–17

  • De Leon DM, Alexandersen J, Fonseca JSO, Sigmund O (2015) Stress-constrained topology optimization for compliant mechanism design. Struct Multidiscip Optim 52:929–943

    Article  MathSciNet  Google Scholar 

  • Deaton JD, Grandhi RV (2014) A survey of structural and multidisciplinary continuum topology optimization: post 2000. Struct Multidiscip Optim 49:1–38

    Article  MathSciNet  Google Scholar 

  • Duysinx P, Bendsøe MP (1998) Topology optimization of continuum structures with local stress constraints. Int J Numer Methods Eng 43:1453–1478

    Article  MathSciNet  MATH  Google Scholar 

  • Duysinx P, Sigmund O (1998) New developments in handling stress constraints in optimal material distribution. In: Proceedings of the 7th AIAA/USAF/NASA/ISSMO symposium on multidisciplinary analysis and optimization, St. Louis, Missouri 1501–1509

  • Guilherme CEM, Fonseca JSO (2007) Topology optimization of continuum structures with epsilon-relaxed stress constraints. In: Alves M, da Costa Mattos H (eds) International symposium on solid mechanics, mechanics of solids in Brazil, vol 1. Brazilian Society of Mechanical Sciences in Engineering 239–250

  • Guo X, Zhang WS, Wang MY, Wei P (2011) Stress-related topology optimization via level set approach. Comput Methods Appl Mech Eng 200:3439–3452

    Article  MathSciNet  MATH  Google Scholar 

  • Guo X, Zhang W, Zhong W (2014) Stress-related topology optimization of continuum structures involving multi-phase materials. Comput Methods Appl Mech Eng 268:632–655

    Article  MathSciNet  MATH  Google Scholar 

  • Guo X, Zhang W, Zhang J, Yuan J (2016) Explicit structural topology optimization based on moving morphable components (MMC) with curved skeletons. Comput Methods Appl Mech Eng 310:711–748

    Article  MathSciNet  Google Scholar 

  • Haug EJ, Choi KK, Komkov V (1986) Design sensitivity analysis of structural systems. Academic Press, London

  • Holmberg E, Torstenfelt B, Klarbring A (2013) Stress constrained topology optimization. Struct Multidiscip Optim 48:33–47

    Article  MathSciNet  MATH  Google Scholar 

  • Jeong SH, Yoon GH, Takezawa A, Choi DH (2014) Development of a novel phase-field method for local stress-based shape and topology optimization. Comput Struct 132:84–98

    Article  Google Scholar 

  • Jr Emmendoerfer H, Fancello EA (2014) A level set approach for topology optimization with local stress constraints. Int J Numer Methods Eng 99:129–156

    Article  MathSciNet  MATH  Google Scholar 

  • Kaw AK, Kalu EE, Duc N (2011) Numerical Methods with Applications. University of South Florida, Textbooks Collection 11. http://scholarcommons.usf.edu/oa_textbooks/11

  • Kiyono CY, Vatanabe SL, Silva ECN, Reddy JN (2016) A new multi- p-norm, formulation approach for stress-based topology optimization design. Compos Struct 156:10–19

    Article  Google Scholar 

  • Lee K, Ahn K, Yoo J (2016) A novel P-norm correction method for lightweight topology optimization under maximum stress constraints. Comput Struct 171:18–30

    Article  Google Scholar 

  • Lin CY, Sheu FM (2009) Adaptive volume constraint algorithm for stress limit-based topology optimization. Comput Aided Des 41:685–694

    Article  Google Scholar 

  • Liu Z, Korvink JG (2008) Adaptive moving mesh level set method for structure topology optimization. Eng Optim 40:529–558

    Article  MathSciNet  Google Scholar 

  • Lopes CG, Novotny AA (2016) Topology design of compliant mechanisms with stress constraints based on the topological derivative concept. Struct Multidiscip Optim 54:737–746

    Article  MathSciNet  Google Scholar 

  • Luo Z, Tong L, Wang MY, Wang S (2007) Shape and topology optimization of compliant mechanisms using a parameterization level set method. J Comput Phys 227:680–705

    Article  MathSciNet  MATH  Google Scholar 

  • Luo Z, Wang MY, Wang S, Wei P (2008) A level set-based parameterization method for structural shape and topology optimization. Int J Numer Methods Eng 76:1–26

    Article  MathSciNet  MATH  Google Scholar 

  • Luo Y, Wang MY, Kang Z (2013) An enhanced aggregation method for topology optimization with local stress constraints. Comput Methods Appl Mech Eng 254:31–41

    Article  MathSciNet  MATH  Google Scholar 

  • París J, Navarrina F, Colominas I, Casteleiro M (2010) Block aggregation of stress constraints in topology optimization of structures. Adv Eng Softw 41:433–441

    Article  MATH  Google Scholar 

  • Pedersen P (2000) On optimal shapes in materials and structures. Struct Multidiscip Optim 19:169–182

    Article  Google Scholar 

  • Pereira JT, Fancello EA, Barcellos CS (2004) Topology optimization of continuum structures with material failure constraints. Struct Multidiscip Optim 26:50–66

    Article  MathSciNet  MATH  Google Scholar 

  • Qiu GY, Li XS (2010) A note on the derivation of global stress constraints. Struct Multidiscip Optim 40:625–628

    Article  MathSciNet  MATH  Google Scholar 

  • Rong JH, Xiao TT, Yu LH, Rong XP, Xie YJ (2016) Continuum structural topological optimizations with stress constraints based on an active constraint technique. Int J Numer Methods Eng 108:326–360

    Article  MathSciNet  Google Scholar 

  • Sigmund O (2001) A 99 line topology optimization code written in Matlab. Struct Multidiscip Optim 21:120–127

    Article  Google Scholar 

  • Silva GAD, Cardoso EL (2017) Stress-based topology optimization of continuum structures under uncertainties. Comput Methods Appl Mech Eng 313:647–672

    Article  MathSciNet  Google Scholar 

  • Verbart A, Langelaar M, Keulen FV (2016) Damage approach: a new method for topology optimization with local stress constraints. Struct Multidiscip Optim 53:1081–1098

    Article  MathSciNet  Google Scholar 

  • Wang MY, Wang X (2004) PDE-driven level sets, shape sensitivity and curvature flow for structural topology optimization. Comput Model Eng Sci 6:373–395

    MATH  Google Scholar 

  • Wang MY, Wang X, Guo D (2003) A level set method for structural topology optimization. Comput Methods Appl Mech Eng 192:227–246

    Article  MathSciNet  MATH  Google Scholar 

  • Wang Y, Luo Z, Kang Z, Zhang N (2015) A multi-material level set-based topology and shape optimization method. Comput Methods Appl Mech Eng 283:1570–1586

    Article  MathSciNet  Google Scholar 

  • Wendland H (1995) Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree. Adv Comput Math 4:389–396

    Article  MathSciNet  MATH  Google Scholar 

  • Xia Q, Shi T, Liu S, Wang MY (2012) A level set solution to the stress-based structural shape and topology optimization. Comput Struct 90–91:55–64

    Article  Google Scholar 

  • Yang RJ, Chen CJ (1996) Stress-based topology optimization. Struct Multidiscip Optim 12:98–105

    Article  Google Scholar 

  • Yoon GH (2014) Stress-based topology optimization method for steady-state fluid–structure interaction problems. Comput Methods Appl Mech Eng 278:499–523

    Article  MathSciNet  Google Scholar 

  • Zhang W, Yuan J, Zhang J, Guo X (2015) A new topology optimization approach based on moving Morphable components (MMC) and the ersatz material model. Struct Multidiscip Optim 53:1243–1260

    Article  MathSciNet  Google Scholar 

Download references

Funding

This research was supported by the National Basic Scientific Research Program of China [grant number JCKY2016110C012]; and the National Natural Science Foundation of China [grant numbers 51675196 51421062].

Author information

Authors and Affiliations

  1. State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, 430074, China

    Sheng Chu, Liang Gao, Mi Xiao, Hao Li & Xin Gui

  2. School of Mechanical and Mechatronic Engineering, The University of Technology Sydney, 15 Broadway, Ultimo, NSW, 2007, Australia

    Zhen Luo

Authors
  1. Sheng Chu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Liang Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mi Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zhen Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Hao Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Xin Gui
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mi Xiao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chu, S., Gao, L., Xiao, M. et al. A new method based on adaptive volume constraint and stress penalty for stress-constrained topology optimization. Struct Multidisc Optim 57, 1163–1185 (2018). https://doi.org/10.1007/s00158-017-1803-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-017-1803-4

Keywords

Search

Navigation