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A consistent relaxation of optimal design problems for coupling shape and topological derivatives

Author
Amstutz, S.; Dapogny, C.; Ferrer, A.
Type of activity
Journal article
Journal
Numerische mathematik
Date of publication
2018-09
Volume
140
Number
1
First page
35
Last page
94
DOI
https://doi.org/10.1007/s00211-018-0964-4 Open in new window
Repository
http://hdl.handle.net/2117/118037 Open in new window
URL
https://link.springer.com/article/10.1007%2Fs00211-018-0964-4 Open in new window
Abstract
In this article, we introduce and analyze a general procedure for approximating a ‘black and white’ shape and topology optimization problem with a density optimization problem, allowing for the presence of ‘grayscale’ regions. Our construction relies on a regularizing operator for smearing the characteristic functions involved in the exact optimization problem, and on an interpolation scheme, which endows the intermediate density regions with fictitious material properties. Under mild hy...
Citation
Amstutz, S., Dapogny, C., Ferrer, A. A consistent relaxation of optimal design problems for coupling shape and topological derivatives. "Numerische mathematik", setembre 2018, vol. 140, núm. 1, p. 35-94
Keywords
Level set method, Material interpolation, Optimal design, Relaxation, Shape derivative, topological derivative
Group of research
(MC)2 - UPC Computational continuum mechanics
RMEE - Strength of Materials and Structural Engineering Research Group

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