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A simple approach to deal with zero densities in topology optimisation
Topology optimisation techniques typically use a very small positive density $$varepsilon $$to model voids. Despite its simplicity and generally acceptable results, this approach can impose a number of difficulties. The weak material should be weak enough to validate the approximation of void areas, but on the other hand, using a very weak material can result in ill-conditioning of the stiffness matrix. Further and more serious complications can arise, for example in non-linear problems where weak elements cause numerical instabilities in the solution procedure. By studying the mechanical responses of structures when $$varepsilon rightarrow 0$$, this paper presents a simple approach to use arbitrarily weak material properties in void areas. This approach would effectively allow us to actually remove the void areas from the mesh in a range of problems and avoid the above-mentioned complexities.
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Structural and Multidisciplinary Optimization. Conference (12th : 2017 : Braunschweig, Germany)Pagination
1019 - 1026Publisher
SpringerLocation
Braunschweig, GermanyPlace of publication
Cham, GermanyPublisher DOI
Start date
2017-06-05End date
2017-06-09ISBN-13
9783319679884Language
engPublication classification
E Conference publication; E1 Full written paper - refereedCopyright notice
2018, Springer International Publishing AGEditor/Contributor(s)
Axel Schumacher, Thomas Vietor, Sierk Fiebig, Kai-Uwe Bletzinger, Kurt MauteTitle of proceedings
WCSMO 2017 : Advances in Structural and Multidisciplinary Optimization : Proceedings of the World Congress of Structural and Multidisiplinary Optimization (WCSM012)Usage metrics
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