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On minimum length scale control in density based topology optimization
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
2018 (Engelska)Ingår i: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 58, nr 3, s. 1015-1032Artikel i tidskrift (Refereegranskat) 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.

Ort, förlag, år, upplaga, sidor
Springer, 2018. Vol. 58, nr 3, s. 1015-1032
Nyckelord [en]
topology optimization, nonlinear filters, size control, mathematical morphology
Nationell ämneskategori
Datavetenskap (datalogi) Beräkningsmatematik
Identifikatorer
URN: urn:nbn:se:umu:diva-151378DOI: 10.1007/s00158-018-1944-0ISI: 000441847800010OAI: oai:DiVA.org:umu-151378DiVA, id: diva2:1245951
Forskningsfinansiär
Stiftelsen för strategisk forskning (SSF), AM13-0029Vetenskapsrådet, 621-3706Tillgänglig från: 2018-09-06 Skapad: 2018-09-06 Senast uppdaterad: 2018-09-06Bibliografiskt granskad

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