Skip to main content

Advertisement

SpringerLink
Log in

A hybrid Fox and Kirsch’s reduced basis method for structural static reanalysis

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

Abstract

Fox and Kirsch’s static reanalysis methods are reviewed firstly, and then a new hybrid Fox and Kirsch’s reduced basis method is presented for structural static reanalysis in this paper. Reduced basis vectors are derived from Neumann series expansion about multiple initial structures, which is a universal format of reduced basis. The hybrid method combines the merits of Fox’s polynomial fitting reanalysis and Kirsch’s combined approximations reanalysis and has the advantage of global-local approximation. Error evaluation of the approximations is given and the number of algebraic operations is also discussed. The reanalysis accuracy and efficiency are tested by four numerical examples. For the large modification, the hybrid method generally has higher accuracy than Kirsch’s method at the same computational cost. Moreover, the hybrid method does accelerate the process of structural optimization using genetic algorithm and slightly affect the accuracy of the optimal solutions.

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

Similar content being viewed by others

References

  • Amir O, Kirsch U, Sheinman I (2008) Efficient non-linear reanalysis of skeletal structures using combined approximations. Int J Numer Methods Eng 73(9):1328–1346

    Article  MATH  Google Scholar 

  • Amir O, Bendsøe MP, Sigmund O (2009) Approximate reanalysis in topology optimization. Int J Numer Methods Eng 78(12):1474–1491

    Article  MATH  Google Scholar 

  • Barthelemy JM, Haftka RT (1993) Approximation concepts for optimum structural design-a review. Struct Multidisc Optim 5(3):129–144

    Google Scholar 

  • Bogomolny M (2010) Topology optimization for free vibrations using combined approximations. Int J Numer Methods Eng 82(5):617–636

    MATH  Google Scholar 

  • Chen SH, Yang XW (2000) Extended Kirsch combined method for eigenvalue reanalysis. AIAA J 38(5):927–930

    Article  Google Scholar 

  • Fox RL, Miura H (1971) An approximate analysis technique for design calculations. AIAA J 90(1):171–179

    Google Scholar 

  • Rozvany GIN (2009) A critical review of established methods of structural topology optimization. Struct Multidisc Optim 37(3):217–237

    Article  MathSciNet  Google Scholar 

  • Kirsch U (2000) Combined approximations–a general reanalysis approach for structural optimization. Struct Multidisc Optim 20(2):97–106

    Article  Google Scholar 

  • Kirsch U (2003) A unified reanalysis approach for structural analysis, design, and optimization. Struct Multidisc Optim 25(2):67–85

    Article  MathSciNet  Google Scholar 

  • Kirsch U (2010) Reanalysis and sensitivity reanalysis by combined approximations. Struct Multidisc Optim 40(1–6):1–15

    Article  MathSciNet  Google Scholar 

  • Kirsch U, Bogomolni M (2004) Procedures for approximate eigenproblem reanalysis of structures. Int J Numer Methods Eng 60(12):1969–1986

    Article  MATH  Google Scholar 

  • Kirsch U, Papalambros PY (2001) Structural reanalysis for topological modifications–a unified approach. Struct Multidisc Optim 21(5):333–344

    Article  Google Scholar 

  • Kirsch U, Bogomolni M, Sheinman I (2006) Nonlinear dynamic reanalysis of structures by combined approximations. Int J Eng Sci 195(33–36):4420–4432

    MATH  Google Scholar 

  • Leu LJ, Huang CW (2000) Reanalysis-based optimal design of trusses. Int J Numer Methods Eng 49(8):1007–1028

    Article  MATH  Google Scholar 

  • Noor AK (1994) Recent advances and applications of reduction methods. Appl Mech Rev 47(5):125–146

    Article  Google Scholar 

  • Venkataraman S, Haftka RT (2004) Structural optimization complexity: what has Moore’s law done for us? Struct Multidisc Optim 28(6):375–387

    Article  Google Scholar 

  • Xu T, Zuo WJ, Xu TS, Li RC (2010) An adaptive reanalysis method for genetic algorithm with application to fast truss optimization. Acta Mech Sin 26(2):225–234

    Article  MathSciNet  Google Scholar 

  • Zuo WJ, Xu T, Zhang H, Xu TS (2011) Fast structural optimization with frequency constraints by genetic algorithm using eigenvalue reanalysis methods. Struct Multidisc Optim 43(6):799–810

    Article  Google Scholar 

  • Zuo WJ, Li WW, Xu T, Xuan SY, Na JX (2012) A complete development process of finite element software for body-in-white structure with semi-rigid beams in.NET framework. Adv Eng Softw 45(1):261–271

    Google Scholar 

Download references

Acknowledgments

Authors acknowledge financial support from the Plan for Scientific and Technological Development of Jilin Province (No. 201101030), the Fundamental Research Funds for the Central Universities and the Graduate Innovation Fund of Jilin University (No.20111056). Many valuable comments from the referees are also acknowledged.

Author information

Authors and Affiliations

  1. College of Mechanical Science and Engineering, Jilin University, Changchun, 130025, People’s Republic of China

    Wenjie Zuo, Zhenglei Yu, Shijia Zhao & Wei Zhang

Authors
  1. Wenjie Zuo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhenglei Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shijia Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wei Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wenjie Zuo.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zuo, W., Yu, Z., Zhao, S. et al. A hybrid Fox and Kirsch’s reduced basis method for structural static reanalysis. Struct Multidisc Optim 46, 261–272 (2012). https://doi.org/10.1007/s00158-012-0758-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-012-0758-8

Keywords

Search

Navigation