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Optimization and Engineering

, Volume 20, Issue 1, pp 215–249 | Cite as

Towards a lifecycle oriented design of infrastructure by mathematical optimization

  • T. Kufner
  • G. Leugering
  • A. Martin
  • J. Medgenberg
  • J. Schelbert
  • L. Schewe
  • M. StinglEmail author
  • C. Strohmeyer
  • M. Walther
Research Article
  • 31 Downloads

Abstract

Today’s infrastructures are mainly designed heuristically using state-of-the-art simulation software and engineering approaches. However, due to complexity, only part of the restrictions and costs that show up during the lifecycle can be taken into account. In this paper, we focus on a typical and important class of infrastructure problems, the design of high-pressure steam pipes in power plants, and describe a holistic approach taking all design, physical, and technical constraints and the costs over the full lifecycle into account. The problem leads to a large-scale mixed-integer optimization problem with partial differential equation (PDE) constraints which will be addressed hierarchically. The hierarchy consists of a combinatorial and a PDE-constrained optimization problem. The final design is evaluated with respect to damage, using beam models that are nonlinear with respect to kinematics as well as constitutive law. We demonstrate the success of our approach on a real-world instance from our industrial partner Bilfinger SE.

Keywords

Structural optimization Lifecycle oriented design Mixed integer nonlinear programming 

Notes

Acknowledgements

We thank Bilfinger SE for their valuable cooperation and acknowledge support from the BMBF (Grant 03MS637A).

References

  1. Achtziger W, Stolpe M (2007a) Global optimization of truss topology with discrete bar areas—part II: implementation and numerical results. Comput Optim Appl 44(2):315.  https://doi.org/10.1007/s10589-007-9152-7. ISSN: 1573-2894zbMATHGoogle Scholar
  2. Achtziger W, Stolpe M (2007b) Truss topology optimization with discrete design variables—guaranteed global optimality and benchmark examples. Struct Multidiscip Optim 34(1):1–20.  https://doi.org/10.1007/s00158-006-0074-2. ISSN: 1615-1488MathSciNetzbMATHGoogle Scholar
  3. Achtziger W, Stolpe M (2008) Global optimization of truss topology with discrete bar areas—part I: theory of relaxed problems. Comput Optim Appl 40(2):247–280.  https://doi.org/10.1007/s10589-007-9138-5 MathSciNetzbMATHGoogle Scholar
  4. Aldwaik M, Adeli H (2014) Advances in optimization of highrise building structures. Struct Multidiscip Optim 50(6):899–919Google Scholar
  5. Altenbach H, Kolarow G, Naumenko K (1999) Solutions of Creep—damage problems for beams and plates using Ritz and FE method. Technische Mechanik 19(4):249–258Google Scholar
  6. Beasley JE (1989) An SST-based algorithm for the Steiner problem in graphs. Networks 19(1):1–16.  https://doi.org/10.1002/net.3230190102. ISSN: 1097-0037MathSciNetzbMATHGoogle Scholar
  7. Beghini LL, Beghini A, Katz N, Baker WF, Paulino GH (2014) Connecting architecture and engineering through structural topology optimization. Eng Struct 59:716–726.  https://doi.org/10.1016/j.engstruct.2013.10.032. ISSN: 0141-0296Google Scholar
  8. Bendsøe MP, Sigmund O (2003) Topology optimization: theory, method and applications, 2nd edn. Springer, New YorkzbMATHGoogle Scholar
  9. Biondini F (2013) Frontier technologies for infrastructures engineering: structures and infrastructures book series. Struct Infrastruct Eng 9(7):733–734.  https://doi.org/10.1080/15732479.2012.726406 Google Scholar
  10. Burry J, Burry M (2010) The new mathematics of architecture. Thames & Hudson Ltd, LondonzbMATHGoogle Scholar
  11. Chopra S, Rao MR (1994) The Steiner tree problem I: formulations, compositions and extension of facets. Math Program 64(1–3):209–229.  https://doi.org/10.1007/BF01582573 MathSciNetzbMATHGoogle Scholar
  12. Cowper GR (1966) The shear coefficient in Timoshenko’s beam theory. J Appl Mech 33(2):335–340zbMATHGoogle Scholar
  13. DIN (2014) Metallische industrielle Rohrleitungen—Teil 3: Konstruktion und BerechnungGoogle Scholar
  14. Dorn WS, Gomory RE, Greenberg HJ (1964) Automatic design of optimal structures. Journal de Mecanique 3(1):25–52Google Scholar
  15. Frangopol DM, Dong Y, Sabatino S (2017) Bridge life-cycle performance and cost: analysis, prediction, optimisation and decision-making. Struct Infrastruct Eng 13(10):1239–1257.  https://doi.org/10.1080/15732479.2016.1267772 Google Scholar
  16. Geoffrion AM (1972) Generalized benders decomposition. J Optim Theory Appl 10(4):237–260.  https://doi.org/10.1007/BF00934810 MathSciNetzbMATHGoogle Scholar
  17. Gill PE, Murray W, Saunders MA (2002) SNOPT: an SQP algorithm for large-scale constrained optimization. SIAM J Optim 12(1):979–1006.  https://doi.org/10.1137/S1052623499350013 MathSciNetzbMATHGoogle Scholar
  18. Gruttmann F, Sauer R, Wagner W (2000) Theory and numerics of three-dimensional beams with elastoplastic material behaviour. Int J Numer Methods Biomed Eng 48(12):1675–1702zbMATHGoogle Scholar
  19. Hirota M, Kanno Y (2015) Optimal design of periodic frame structures with negative thermal expansion via mixed integer programming. Optim Eng 16(4):767–809.  https://doi.org/10.1007/s11081-015-9276-z. ISSN: 1573-2924MathSciNetzbMATHGoogle Scholar
  20. Ibrahimbegovic A (1997) On the choice of finite rotation parameters. Comput Methods Appl Mech Eng 149:49–71MathSciNetzbMATHGoogle Scholar
  21. Ito T (1999) A genetic algorithm approach to piping route path planning. J Intell Manuf 10(1):103–114Google Scholar
  22. Jones JP (1966) Thermoelastic vibrations of a beam. J Acoust Soc Am 39(3):542–548zbMATHGoogle Scholar
  23. Kanno Y (2013) Topology optimization of tensegrity structures under compliance constraint: a mixed integer linear programming approach. Optim Eng 14(1):61–96.  https://doi.org/10.1007/s11081-011-9172-0. ISSN: 1573-2924MathSciNetzbMATHGoogle Scholar
  24. Kingman JJ, Tsavdaridis K, Toropov V (2015) Applications of topology optimisation in structural engineering: high-rise buildings & steel components. Jordan J Civ Eng 9(3):335–357. ISSN: 1993-0461Google Scholar
  25. Kufner T, Leugering G, Semmler J, Strohmeyer C, Stingl M (2016) Simulation and structural optimization of large 3D Timoshenko beam networks. ESAIM: Math Model Numer Anal (To appear)Google Scholar
  26. Langnese J, Leugering G, Schmidt E (1994) Modeling, analysis and control of dynamic elastic multi-link structures. Springer, New YorkGoogle Scholar
  27. Liu Q, Wang C (2010) Pipe-assembly approach for aero-engines by modified particle swarm optimization. Assem Autom 30(4):365–377Google Scholar
  28. Mata P, Oller S, Barbat AH (2007) Static analysis of beam structures under nonlinear geometric and constitutive behavior. Comput Methods Appl Mech Eng 196(45–48):4458–4478MathSciNetzbMATHGoogle Scholar
  29. Muñoz E, Stolpe M (2011) Generalized benders’ decomposition for topology optimization problems. J Glob Optim 51(1):149–183.  https://doi.org/10.1007/s10898-010-9627-4. ISSN: 0925-5001MathSciNetzbMATHGoogle Scholar
  30. Muñoz Romero J (2004) Finite-element analysis of flexible mechanisms using the master–slave approach with emphasis on the modelling of joints. PhD thesis, IC LondonGoogle Scholar
  31. Naumenko K, Altenbach H, Kutschke A (2010) A combined model for hardening, softening, and damage processes in advanced heat resistant steels at elevated temperature. Int J Damage Mech 20(4):578–597Google Scholar
  32. Polzin T, Daneshmand SV (2001) A comparison of Steiner tree relaxations. Discrete Appl Math 112(1–3):241–261.  https://doi.org/10.1016/S0166-218X(00)00318-8. ISSN: 0166-218XMathSciNetzbMATHGoogle Scholar
  33. Rasmussen MH, Stolpe M (2008) Global optimization of discrete truss topology design problems using a parallel cut-and-branch method. In: Comput Struct 86(13), Structural Optimization, pp. 1527–1538.  https://doi.org/10.1016/j.compstruc.2007.05.019. ISSN: 0045-7949
  34. Richards DS, Hwang FK, Winter P (eds) (1992) The Steiner tree problem, annals of discrete mathematics, vol 53. Elsevier, Amsterdam.  https://doi.org/10.1016/S0167-5060(08)70188-2 Google Scholar
  35. Sandurkar S, Chen W (1999) GAPRUSgenetic algorithms based pipe routing using tessellated objects. Comput Ind 38(3):209–223.  https://doi.org/10.1016/S0166-3615(98)00130-4. ISSN: 0166-3615Google Scholar
  36. Schelbert J (2015) Discrete approaches for optimal routing of high pressure pipes. PhD thesis, FAU Erlangen-Nuremberg, pp I – XVIII; 1 –179Google Scholar
  37. Stolpe M (2007) On the reformulation of topology optimization problems as linear or convex quadratic mixed 0–1 programs. Optim Eng 8(2):163–192.  https://doi.org/10.1007/s11081-007-9005-3. ISSN: 1573-2924MathSciNetzbMATHGoogle Scholar
  38. Stolpe M (2015) Truss topology optimization with discrete design variables by outer approximation. J Global Optim 61(1):139–163.  https://doi.org/10.1007/s10898-014-0142-x. ISSN: 1573-2916MathSciNetzbMATHGoogle Scholar
  39. Stolpe M, Svanberg K (2003) Modelling topology optimization problems as linear mixed 01 programs. Int J Numer Methods Eng 57(5):723–739.  https://doi.org/10.1002/nme.700. https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme (eprint)
  40. Stromberg LL, Beghini A, Baker WF, Paulino GH (2011) Application of layout and topology optimization using pattern gradation for the conceptual design of buildings. Struct Multidiscip Optim 43(2):165–180Google Scholar
  41. Wossog G (2013) Handbuch Rohrleitungsbau: Berechnung, 3rd edn. Vulkan-Verlag, Essen Handbuch Rohrleitungsbau, ISBN: 9783802727689Google Scholar
  42. Yamada Y, Teraoka Y (1998) An optimal design of piping route in a cad system for power plant. Comput Math Appl 35(6):137–149.  https://doi.org/10.1016/S0898-1221(98)00025-X. ISSN: 0898-1221zbMATHGoogle Scholar
  43. Yonekura K, Kanno Y (2010) Global optimization of robust truss topology via mixed integer semidefinite programming. Optim Eng 11(3):355–379.  https://doi.org/10.1007/s11081-010-9107-1. ISSN: 1573-2924MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsFriedrich-Alexander-Universität Erlangen-Nürnberg (FAU)ErlangenGermany
  2. 2.aenergen GmbHMannheimGermany

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