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Structural and Multidisciplinary Optimization
Erschienen in: Structural and Multidisciplinary Optimization 6/2011

01.06.2011 | Research Paper

On projection methods, convergence and robust formulations in topology optimization

verfasst von: Fengwen Wang, Boyan Stefanov Lazarov, Ole Sigmund

Erschienen in: Structural and Multidisciplinary Optimization | Ausgabe 6/2011

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Abstract

Mesh convergence and manufacturability of topology optimized designs have previously mainly been assured using density or sensitivity based filtering techniques. The drawback of these techniques has been gray transition regions between solid and void parts, but this problem has recently been alleviated using various projection methods. In this paper we show that simple projection methods do not ensure local mesh-convergence and propose a modified robust topology optimization formulation based on erosion, intermediate and dilation projections that ensures both global and local mesh-convergence.
Vorheriger Artikel Connections between topological sensitivity analysis and material interpolation schemes in topology optimization
Nächster Artikel An improved decomposition method in probabilistic analysis using Chebyshev approximations

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Fußnoten
1
The difference between the present robust formulation and the one introduced in Sigmund (2009) is the representation of the intermediate design and the volume bound which is applied on the dilated structure instead of the intermediate. In Sigmund (2009) the intermediate design is simply the design variable field ρ. However, in the present approach the intermediate design has gone through the same density filtering as the dilated and eroded designs and it is obtained as the projection for η = 0.5. The modifications eliminate numerical artifacts associated with the old approach and result in much more stable convergence of the optimization problem.
 
2
It is interesting to note that there are many similarities between the threshold projection schemes and the level-set approach to topology optimization (Allaire et al. 2004; Wang et al. 2003; Kawamoto et al. 2010). In the presented scheme the filtered density field \(\widetilde{\rho}\) correspond to the level-set function φ and the projections correspond to zero and ±Δη level curves. Hence it is obvious that the proposed robust optimization scheme can be implemented using a level-set approach as well.
 
Literatur
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Metadaten
Titel
On projection methods, convergence and robust formulations in topology optimization
verfasst von
Fengwen Wang
Boyan Stefanov Lazarov
Ole Sigmund
Publikationsdatum
01.06.2011
Verlag
Springer-Verlag
Erschienen in
Structural and Multidisciplinary Optimization / Ausgabe 6/2011
Print ISSN: 1615-147X
Elektronische ISSN: 1615-1488
DOI
https://doi.org/10.1007/s00158-010-0602-y

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