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On minimum length scale control in density based topology optimization
Umeå University, Faculty of Science and Technology, Department of Computing Science.
Umeå University, Faculty of Science and Technology, Department of Computing Science.
2018 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 58, no 3, p. 1015-1032Article in journal (Refereed) Published
Abstract [en]

The archetypical topology optimization problem concerns designing the layout of material within a given region of space so that some performance measure is extremized. To improve manufacturability and reduce manufacturing costs, restrictions on the possible layouts may be imposed. Among such restrictions, constraining the minimum length scales of different regions of the design has a significant place. Within the density filter based topology optimization framework the most commonly used definition is that a region has a minimum length scale not less than D if any point within that region lies within a sphere with diameter D > 0 that is completely contained in the region. In this paper, we propose a variant of this minimum length scale definition for subsets of a convex (possibly bounded) domain We show that sets with positive minimum length scale are characterized as being morphologically open. As a corollary, we find that sets where both the interior and the exterior have positive minimum length scales are characterized as being simultaneously morphologically open and (essentially) morphologically closed. For binary designs in the discretized setting, the latter translates to that the opening of the design should equal the closing of the design. To demonstrate the capability of the developed theory, we devise a method that heuristically promotes designs that are binary and have positive minimum length scales (possibly measured in different norms) on both phases for minimum compliance problems. The obtained designs are almost binary and possess minimum length scales on both phases.

Place, publisher, year, edition, pages
Springer, 2018. Vol. 58, no 3, p. 1015-1032
Keywords [en]
topology optimization, nonlinear filters, size control, mathematical morphology
National Category
Computer Sciences Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-151378DOI: 10.1007/s00158-018-1944-0ISI: 000441847800010OAI: oai:DiVA.org:umu-151378DiVA, id: diva2:1245951
Funder
Swedish Foundation for Strategic Research , AM13-0029Swedish Research Council, 621-3706Available from: 2018-09-06 Created: 2018-09-06 Last updated: 2018-09-06Bibliographically approved

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Hägg, LinusWadbro, Eddie

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