Skip to main content
SpringerLink
Log in

Robust Topology Optimization with Loading Magnitude and Direction Uncertainty

  • Conference paper
  • First Online:
Advances in Mechanical Design (ICMD 2017)

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 55))

Included in the following conference series:

  • 3746 Accesses

Abstract

The robust topology optimization approach with uncertainties of loading magnitude and direction is investigated for continuum structures. The input loadings with uncertain magnitude and direction are decomposed using the second order Taylor series expansions, and then the response of statistical response of compliance is calculated using perturbation analysis method. The robust topology problem with minimize the compliance is solved using the modified SIMP (Solid Isotropic Material with Penalization) algorithm. The efficiency of the proposed methodology is verified using the examples of cantilever beam.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Savsani VJ, Tejani GG, Patel VK. Truss topology optimization with static and dynamic constraints using modified subpopulation teaching–learning-based optimization. Eng Optim. 2016;48(11):1990–2006.

    Article  MathSciNet  Google Scholar 

  2. Park J, Sutrandhar A. A multi-resolution method for 3D multi-material topology optimization. Comput Methods Appl Mech Eng. 2015;285:571–86.

    Article  MathSciNet  Google Scholar 

  3. Vicente WM, Picelli R, Pavanello R, et al. Topology optimization of frequency responses of fluid–structure interaction systems. Finite Element Anal Design. 2015;98:1–13.

    Article  Google Scholar 

  4. Ramirez-Gil FJ, Silva ECN, Montealegre-Rubio W. Topology optimization design of 3D electrothermomechanical actuators by using GPU as a co-processor. Comput Methods Appl Mech Eng. 2016;302:44–69.

    Article  MathSciNet  Google Scholar 

  5. Kim BJ, Yun DK, Lee SH, et al. Topology optimization of industrial robots for system-level stiffness maximization by using part-level metamodels. Struct Multidiscip Optim. 2016;54(4):1061–71.

    Article  Google Scholar 

  6. Coelho PG, Guedes JM, Rodrigues HC. Multiscale topology optimization of bi-material laminated composite structures. Compos Struct. 2015;132:495–505.

    Article  Google Scholar 

  7. Smith CJ, Gilbert M, Todd I, et al. Application of layout optimization to the design of additively manufactured metallic components. Struct Multidiscip Optim. 2016;54(5):1297–313.

    Article  MathSciNet  Google Scholar 

  8. Kogiso N. Robust topology optimization for compliant mechanisms considering uncertainty of applied loads. J Adv Mech Design Syst Manuf. 2008;2(1):96–107.

    Article  Google Scholar 

  9. Guest JK, Igusa A. Structural optimization under uncertain loads and nodal locations. Comput Methods Appl Mech Eng. 2008;198(1):116–24.

    Article  MATH  MathSciNet  Google Scholar 

  10. Dunning PD, Kim HA, Mullineux G. Introducing loading uncertainty in topology optimization. AIAA J. 2011;49(4):760–8.

    Article  Google Scholar 

  11. Dunning PD, Kim HA. Robust topology optimization: minimization of expected and variance of compliance. AIAA J. 2013;51(11):2656–64.

    Article  Google Scholar 

  12. Csebfalvi A. Structural optimization under uncertainty in loading directions: benchmark results. Adv Eng Softw. 2016;000:1–11.

    Google Scholar 

  13. Zhao J, Wang C. Robust topology optimization under loading uncertainty based on linear elastic theory and orthogonal diagonalization of symmetric matrices. Comput Methods Appl Mech Eng. 2014;273:204–18.

    Article  MATH  MathSciNet  Google Scholar 

  14. Bendsoe MP, Sigmund O. Topology optimization: theory, methods, and applications. Berlin: Springer Science & Business Media; 2013.

    MATH  Google Scholar 

  15. Svanberg K. The method of moving asymptotes—A new method for structural optimization. Int J Numer Meth Eng. 1987;24:359–73.

    Article  MATH  MathSciNet  Google Scholar 

  16. Andreassen E, Clausen A, Schevenels M, et al. Efficient topology optimization in MATLAB using 88 lines of code. Struct Multidiscip Optim. 2011;43(1):1–16.

    Article  MATH  Google Scholar 

  17. Richatdson JN, Coelho RF, Adriaenssens S. A unified stochastic framework for robust topology optimization of continuum and truss-like structures. Eng Optim. 2016;48(2):334–50.

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China under grant [number No. 51505421, 51375451, U1610112], and Open Project Program of the State Key Lab of CAD&CG under grant [number: A1716].

Author information

Authors and Affiliations

  1. Key Laboratory of E&M, Zhejiang University of Technology, 310014, Hangzhou, China

    Xiang Peng, Jianxiang Wang, Jiquan Li & Shaofei Jiang

  2. School of Mechanical Engineering, Tongji University, 201804, Shanghai, China

    Wanghui Bu

  3. School of Traffic and Transportation Engineering, Central South University, Changsha, 410027, China

    Bing Yi

  4. CRRC Hangzhou CO., LTD, Hangzhou, 310014, China

    Sihang Zhou

Authors
  1. Xiang Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jianxiang Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jiquan Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shaofei Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Wanghui Bu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Bing Yi
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Sihang Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shaofei Jiang .

Editor information

Editors and Affiliations

  1. Zhejiang University, Hangzhou, China

    Jianrong Tan

  2. Shanghai Jiao Tong University , Shanghai, China

    Feng Gao

  3. Beijing Institution of Technology, Beijing, China

    Changle Xiang

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Peng, X. et al. (2018). Robust Topology Optimization with Loading Magnitude and Direction Uncertainty. In: Tan, J., Gao, F., Xiang, C. (eds) Advances in Mechanical Design. ICMD 2017. Mechanisms and Machine Science, vol 55. Springer, Singapore. https://doi.org/10.1007/978-981-10-6553-8_31

Download citation

  • DOI: https://doi.org/10.1007/978-981-10-6553-8_31

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-6552-1

  • Online ISBN: 978-981-10-6553-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation