Skip to main content
SpringerLink
Log in

Topology design of binary structures subjected to design-dependent thermal expansion and fluid pressure loads

  • Research Paper
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

The future perspective of using topology optimization to solve challenging design-dependent physics problems motivates the creation of methods with clear structural boundaries and well-defined volume. This paper develops the topology optimization of binary structures (TOBS) method to include design-dependent fluid pressure and constant thermal expansion loads. Topology design in thermoelastic and fluid pressure problems have been only handled separately up to date. To the authors’ best knowledge, this is the first work to consider both type of loads simultaneously within a structural topology optimization framework. The TOBS method uses discrete design variables, sensitivity filtering, and formal mathematical programming (integer linear optimization) to achieve convergent and mesh-independent solutions. The discrete nature of the method presents attractive features when dealing with design-dependent body and surface loads. In this paper, we use the structural mean compliance and volume as functions for optimization. The sensitivity analysis is carried out using the adjoint and semi-analytical methods. Numerous examples are shown to design novel structural designs which perform well under the applied fluid pressure and thermal loads. The observed computational times signify the practicability of integer programming for structural optimization problems.

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
Fig. 26

Similar content being viewed by others

References

  • Ansola Loyola R, Querin OM, Garaigordobil Jiménez A, Alonso Gordoa C (2018) A sequential element rejection and admission (sera) topology optimization code written in matlab. Struct Multidiscip Optim 58 (3):1297–1310. https://doi.org/10.1007/s00158-018-1939-x

    Article  MathSciNet  Google Scholar 

  • Beckers M (1999) Topology optimization using a dual method with discrete variables. Struct Multidiscip Optim 17:14–24

    Article  Google Scholar 

  • Brezzi F, Fortin M (1991) Mixed and hybrid finite element methods. Springer, Berlin

    Book  Google Scholar 

  • Bruyneel M, Duysinx P (2005) Note on topology optmization of continuum structures including self-weight. Struct Multidiscip Optim 29:245–256

    Article  Google Scholar 

  • Deaton JD, Grandhi RV (2013) Stiffening of restrained thermal structures via topology optimization. Struct Multidiscip Optim 48(4):731–745

    Article  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 

  • Deng S, Suresh K (2017) Stress constrained thermo-elastic topology optimization with varying temperature fields via augmented topological sensivitity based level-set. Struct Multidiscip Optim 56(6):1413–1427

    Article  MathSciNet  Google Scholar 

  • Emmendoerfer H, Fancello EA, Silva ECN (2018) Level set topology optimization for design-dependent pressure load problems. Int J Numer Methods Eng 115(7):825–848

    Article  MathSciNet  Google Scholar 

  • Gao T, Zhang W (2010) Topology optimization involving thermo-elastic stress loads. Struct Multidiscip Optim 42(5):725–738

    Article  MathSciNet  Google Scholar 

  • Giusti SM, Mroz Z, Novotny AA, Sokolowski J (2017) Topology design of thermomechanical actuators. Struct Multidiscip Optim 55:1575–1587

    Article  MathSciNet  Google Scholar 

  • Hammer VB, Olhoff N (2000) Topology optimization of continuum structures subjected to pressure loading. Struct Multidiscip Optim 19:85–92

    Article  Google Scholar 

  • Huang X, Xie YM (2007) Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite Elem Anal Des 43:1039–1049

    Article  Google Scholar 

  • Jenkins N, Maute K (2016) An immersed boundary approach for shape and topology optimization of stationary fluid-structure interaction problems. Struct Multidiscip Optim 54:119–1208

    Article  MathSciNet  Google Scholar 

  • Li Q, Steven GP, Xie YM (2001) Thermoelastic topology optimization for problems with varying temperature fields. J Therm Stress 24(4):347–366

    Article  Google Scholar 

  • Liang Y, Cheng G (2019) Topology optimization via sequential integer programming and canonical relaxation algorithm. Comput Methods Appl Mech Eng 348:64–96. https://doi.org/10.1016/j.cma.2018.10.050

    Article  MathSciNet  MATH  Google Scholar 

  • Lundgaard C, Alexandersen J, Zhou M, Andreasen C, Sigmund O (2018) Revisiting density-based topology optimization for fluid-structure-interaction problems. Struct Multidiscip Optim 58:969–995

    Article  MathSciNet  Google Scholar 

  • Paul WH (2009) Logic and integer programming, International Series in Operations Research and Management Science, vol 130, 1st edn. Springer, USA. https://doi.org/10.1007/978-0-387-92280-5

    Google Scholar 

  • Pedersen P, Pedersen NL (2010) Strength optimized designs of thermoelastic structures. Struct Multidiscip Optim 42(5):681– 691

    Article  Google Scholar 

  • Picelli R, Vicente WM, Pavanello R (2015) Bi-directional evolutionary structural optimization for design-dependent fluid pressure loading problems. Eng Optim 47(10):1324–1342

    Article  MathSciNet  Google Scholar 

  • Picelli R, van Dijk R, Vicente WM, Pavanello R, Langelaar M, van Keulen F (2017a) Topology optimization for submerged buoyant structures. Eng Optimiz 49(1):1–21

    Article  MathSciNet  Google Scholar 

  • Picelli R, Vicente WM, Pavanello R (2017b) Evolutionary topology optimization for structural compliance minimization considering design-dependent fsi loads. Finite Elem Anal Des 135:44– 55

    Article  Google Scholar 

  • Picelli R, Townsend S, Brampton C, Norato J, Kim HA (2018) Stress-based shape and topology optimization with the level set method. Comput Methods Appl Mech Eng 329:1–23

    Article  MathSciNet  Google Scholar 

  • Picelli R, Neofytou A, Kim HA (2019) Topology optimization for design-dependent hydrostatic pressure loading via the level-set method. Struct Multidiscip Optim 60:1313–1326

    Article  MathSciNet  Google Scholar 

  • Shu L, Wang MY, Ma Z (2014) Level set based topology optimization of vibrating structures for coupled acoustic-structural dynamics. Comput Struct 132:34–42

    Article  Google Scholar 

  • Sigmund O, Clausen PM (2007) Topology optimization using a mixed formulation: an alternative way to solve pressure load problems. Comput Methods Appl Mech Eng 196:1874–1889

    Article  MathSciNet  Google Scholar 

  • Sivapuram R, Picelli R (2018) Topology optimization of binary structures using integer linear programming. Finite Elem Anal Des 139:49–61

    Article  MathSciNet  Google Scholar 

  • Sivapuram R, Picelli R, Xie YM (2018) Topology optimization of binary microstructures involving various non-volume constraints. Comput Mater Sci 154:405–425. https://doi.org/10.1016/j.commatsci.2018.08.008

    Article  Google Scholar 

  • Svanberg K, Werne M (2006) Topology optimization by sequential integer linear programming. Springer, The Netherlands

    Book  Google Scholar 

  • Takallozadeh M, Yoon GH (2017) Development of pareto topology optimization considering thermal loads. Comput Methods Appl Mech Eng 317:554–579

    Article  MathSciNet  Google Scholar 

  • Vicente WM, Picelli R, Pavanello R, Xie YM (2015) Topology optimization of frequency responses of fluid-structure interaction systems. Finite Elem Anal Des 98:1–13

    Article  Google Scholar 

  • Wang C, Zhao M, Ge T (2016) Structural topology optimization with design-dependent pressure loads. Struct Multidiscip Optim 53:1005–1018

    Article  MathSciNet  Google Scholar 

  • Xia Q, Wang MY (2008) Topology optimization of thermoelastic structures using level set method. Comput Mech 42(6):837

    Article  Google Scholar 

  • Xu B, Huang X, Xie YM (2016) Concurrent topological design of composite thermoelastic macrostructure and microstructure with multi-phase material for maximum stiffness. Compos Struct 150:84–102

    Article  Google Scholar 

  • Yamada T, Izui K, Nishiwaki S, Takezawa A (2010) A topology optimization method based on the level set method incorporating a ficticious interface energy. Comput Methods Appl Mech Eng 199:2876–2891

    Article  Google Scholar 

  • Yoon GH (2010) Topology optimization for stationary fluid-structure interaction problems using a new monolithic formulation. Int J Numer Meth Eng 82:591–616

    Article  Google Scholar 

  • Yoon GH, Jensen JS, Sigmund O (2007) Topology optimization of acoustic-structure problems using a mixed finite element formulation. Int J Numer Meth Eng 70:1049–1075

    Article  MathSciNet  Google Scholar 

Download references

Funding

Renato Picelli would like to thank the support of São Paulo Research Foundation (FAPESP), grants 2018/05797-8 and 2019/01685-3.

Author information

Author notes

    Authors and Affiliations

    1. Structural Engineering Department, University of California, San Diego, 9500 Gilman Drive, San Diego, CA, 92093, USA

      Raghavendra Sivapuram

    2. Department of Mining and Petroleum Engineering, University of São Paulo, Praça Narciso de Andrade, Vila Mathias, Santos - SP, 11013-560, Brazil

      Renato Picelli

    Authors
    1. Raghavendra Sivapuram
      View author publications

      You can also search for this author in PubMed Google Scholar

    2. Renato Picelli
      View author publications

      You can also search for this author in PubMed Google Scholar

    Corresponding author

    Correspondence to Raghavendra Sivapuram.

    Ethics declarations

    Conflict of interests

    The authors declare that they have no conflict of interest.

    Additional information

    Responsible Editor: Ji-Hong Zhu

    Publisher’s note

    Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

    Replication of results

    A MATLAB code intended to reproduce the results presented here is available as supplementary material of this paper. More information on the data underpinning the results are available upon request by e-mail at rpicelli@usp.br. An online repository with a demonstration code of the TOBS methods is available at https://github.com/renatopicelli/tobs.

    Both the authors have equally contributed to this work.

    Rights and permissions

    Reprints and permissions

    About this article

    Check for updates. Verify currency and authenticity via CrossMark

    Cite this article

    Sivapuram, R., Picelli, R. Topology design of binary structures subjected to design-dependent thermal expansion and fluid pressure loads. Struct Multidisc Optim 61, 1877–1895 (2020). https://doi.org/10.1007/s00158-019-02443-z

    Download citation

    • Received:

    • Revised:

    • Accepted:

    • Published:

    • Issue Date:

    • DOI: https://doi.org/10.1007/s00158-019-02443-z

    Keywords

    Search

    Navigation