Skip to main content
SpringerLink
Log in

Analytical and numerical solutions for a reliability-based benchmark example

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

Abstract

The aim of this elementary reliability-based truss topology example is to serve as a benchmark for checking on the validity, accuracy and convergence of FE-based numerical topology optimization methods. The above problem has been solved analytically by using an extension of the optimal layout theory (Prager and Rozvany) and the solution has been verified numerically by a first order reliability approach (FORM) combined with a material distribution method (SIMP).

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

Similar content being viewed by others

References

  • Allaire G, Kohn RV (1993) Explicit bounds on elastic energy of a two-phase composite in two space dimensions. Q Appl Math 51:675–699

    MathSciNet  MATH  Google Scholar 

  • Bendsoe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1:193–202

    Article  Google Scholar 

  • Bendsoe MP, Haber RB (1993) The Michell layout problem as a low volume fraction limit of the perforated plate topology optimization problem: an asymptotic study. Struct Optim 6:263–267

    Article  Google Scholar 

  • Lee T, Kwak B (1987) A reliability-based optimal design using advanced first order second moment method. Mechan Struct Mach 15:523–542

    Article  Google Scholar 

  • Maute K, Frangopol DM (2003) Reliability-based design of MEMS mechanisms by topology optimization. Comput Struct 81:813–824

    Article  Google Scholar 

  • Prager W, Rozvany GIN (1977) Optimization of the structural geometry. In: Bednarek AR, Cesari L (eds) Dynamical systems (proc int conf Gainsville, Florida). Academic Press, New York, pp 265–293

    Google Scholar 

  • Rozvany GIN (1992) Optimal layout theory: analytical solutions for elastic structures with several with several deflection constraints and load conditions. Struct Optim 4:247–249

    Article  Google Scholar 

  • Rozvany GIN (2008a) Exact analytical solutions for benchmark problems in probabilistic topology optimization. In: Herskovits J (ed) Proc EngOpt 2008, int conf, Rio de Janeiro

  • Rozvany GIN (2008b) Analytical benchmarks in topology optimization—including probabilistic design. In: Proc 12th AIAA/ISSMO multidisciplinary analysis and optimization conference, Victoria, BC, Canada

  • Rozvany GIN, Olhoff N, Bendsoe MP, Ong TG, Szeto WT (1985) Least-weight design of perforated elastic plates. DCAMM Report No 306, Techn Univ Denmark, Lyngby

  • Rozvany GIN, Olhoff N, Bendsoe MP, Ong TG, Szeto WT (1987) Least-weight design of perforated elastic plates I, II. Int J Solids Struct 23:521–536, 537–550

    Article  MATH  Google Scholar 

  • Rozvany GIN, Zhou M, Birker T (1993) Why multi-load topology designs based on orthogonal microstructures are in general non-optimal. Struct Optim 6:200–204

    Article  Google Scholar 

  • Sigmund O, Petersson J (1998) Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct Optim 16:68–75

    Article  Google Scholar 

  • Silva M, Tortorelli D, Norato J, Ha C, Bae H-R (2010) Component and system reliability-based topology optimization using a single-loop method. Struct Multidisc Optim 41:87–106

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Tu J, Choi K, Park Y (1999) A new study on reliability based design optimization. ASME J Mech Des 121:557–564

    Article  Google Scholar 

  • Zhou M, Rozvany GIN (1991) The COC algorithm, Part II: topological, geometrical and generalized shape optimization. Comput Methods Appl Mech Eng 89:309–336

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department Structural Mechanics, Budapest University, of Technology and Economics, Müegyetem rkpt. 3, Kmf. 35, 1521, Budapest, Hungary

    George I. N. Rozvany

  2. Department of Aerospace Engineering Sciences, University of Colorado, Boulder, CO, USA

    Kurt Maute

Authors
  1. George I. N. Rozvany
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kurt Maute
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to George I. N. Rozvany.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rozvany, G.I.N., Maute, K. Analytical and numerical solutions for a reliability-based benchmark example. Struct Multidisc Optim 43, 745–753 (2011). https://doi.org/10.1007/s00158-011-0637-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-011-0637-8

Keywords

Search

Navigation