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Simultaneous optimization of topology and geometry of flow networks

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Abstract

We consider a problem of minimizing a pressure drop due to a flow of a fluid or gas through an interconnected system of pipes. We show that simultaneous optimization of pipe diameters and nodal positions (topology and geometry optimization) results for fluid networks in a better optimization strategy than traditionally used ground-structure approach (topology optimization only), as opposed to the linear truss case. We also show how the results for linear flow networks can be easily carried out to nonlinear transient and turbulent cases. Stating the optimality conditions for the latter types of flow, we give an alternative derivation of generalized Murray’s law, which is well-known in physiology. We illustrate our theoretical findings with numerical examples.

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References

  • Achtziger W (1998) Multiple-load truss topology and sizing optimization: Some properties of minimax compliance. J Optim Theory Appl 98(2):255–280

    Article  MATH  MathSciNet  Google Scholar 

  • Bendsøe MP, Sigmund O (2003) Topology optimization: theory, methods, and applications. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Bendsøe MP, Ben-Tal A, Zowe J (1994) Optimization methods for truss geometry and topology design. Struct Optim 7:141–159

    Article  Google Scholar 

  • Ford LR Jr, Fulkerson DR (1962) Flows in networks. Princeton University Press, Princeton, NJ

    MATH  Google Scholar 

  • Gill PE, Murray W, Saunders MA (2002) SNOPT: an SQP algorithm for large-scale constrained optimization. SIAM J Optim 12(4):979–1006

    Article  MathSciNet  MATH  Google Scholar 

  • Hyman SI, Stoner MA, Karnitz MA (1975) Gas flow formulas—strengths, weaknesses and practical applications. American Gas Association, Arlington, pp 125–132

    Google Scholar 

  • Klarbring A, Petersson J, Torstenfelt B, Karlsson M (2003) Topology optimization of flow networks. Comput Methods Appl Mech Eng 192(35–36):3909–3932

    Article  MathSciNet  MATH  Google Scholar 

  • Murray CD (1926) The physiological principle of minimum work. I. The vascular system and the cost of blood volume. Proc Natl Acad Sci U S A 12:207–214

    Article  Google Scholar 

  • Rockafellar RT (1970) Convex analysis. Princeton University Press, Princeton, NJ

    MATH  Google Scholar 

  • Schreiner W, Buxbaum PF (1993) Computer-optimization of vascular trees. IEEE Trans Biomed Eng 40(5):482–491

    Article  Google Scholar 

  • Sempler K (2004) Algebra terrorists have weapons of math instruction! Ny Teknik, September 2004. http://www.nyteknik.se/pub/ipsart.asp?art_id=35912

  • Zamir M (2000) The physics of pulsatile flow. Springer, Berlin Heidelberg New York

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Aerospace Engineering Sciences, Center for Aerospace Structures, University of Colorado, Boulder, CO, 80309-0429, USA

    Anton Evgrafov

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  1. Anton Evgrafov
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Correspondence to Anton Evgrafov.

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Evgrafov, A. Simultaneous optimization of topology and geometry of flow networks. Struct Multidisc Optim 32, 99–109 (2006). https://doi.org/10.1007/s00158-005-0590-5

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  • DOI: https://doi.org/10.1007/s00158-005-0590-5

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