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Topology optimization of flow networks
Linköping University, The Institute of Technology. Linköping University, Department of Management and Engineering, Mechanics .ORCID iD: 0000-0001-8460-0131
Linköping University, The Institute of Technology. Linköping University, Department of Management and Engineering, Mechanics .
Linköping University, The Institute of Technology. Linköping University, Department of Management and Engineering, Solid Mechanics .
Linköping University, The Institute of Technology. Linköping University, Department of Biomedical Engineering, Biomedical Modelling and Simulation .ORCID iD: 0000-0001-5526-2399
2003 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 192, no 35-36, 3909-3932 p.Article in journal (Refereed) Published
Abstract [en]

The field of topology optimization is well developed for load carrying trusses, but so far not for other similar network problems. The present paper is a first study in the direction of topology optimization of flow networks. A linear network flow model based on Hagen-Poiseuille's equation is used. Cross-section areas of pipes are design variables and the objective of the optimization is to minimize a measure, which in special cases represents dissipation or pressure drop, subject to a constraint on the available (generalized) volume. A ground structure approach where cross-section areas may approach zero is used, whereby the optimal topology (and size) of the network is found.A substantial set of examples is presented: Small examples are used to illustrate difficulties related to non-convexity of the optimization problem, larger arterial tree-type networks, with bio-mechanics interpretations, illustrate basic properties of optimal networks, the effect of volume forces is exemplified.We derive optimality conditions which turns out to contain Murray's law, thereby, presenting a new derivation of this well known physiological law. Both our numerical algorithm and the derivation of optimality conditions are based on an e-perturbation where cross-section areas may become small but stay finite. An indication of the correctness of this approach is given by a theorem, the proof of which is presented in an appendix. © 2003 Elsevier B.V. All rights reserved.

Place, publisher, year, edition, pages
2003. Vol. 192, no 35-36, 3909-3932 p.
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-46516DOI: 10.1016/S0045-7825(03)00393-1OAI: oai:DiVA.org:liu-46516DiVA: diva2:267412
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2017-12-13

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Klarbring, AndersPetersson, JoakimTorstenfelt, BoKarlsson, Matts

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