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

Cita com:
hdl:2117/118037
Document typeArticle
Defense date2018-09
Rights accessOpen Access
ProjectCOMP-DES-MAT - Advanced tools for computational design of engineering materials (EC-FP7-320815)
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 hypotheses
on the smoothing operator and on the interpolation scheme, we prove that the features of the approximate density optimization problem (material properties, objective function, etc.) converge to their exact counterparts as the smoothing parameter vanishes. In particular, the gradient of the approximate objective functional with respect to the density function converges to either the shape or the topological derivative of the exact
objective. These results shed new light on the connections between these two different notions of sensitivities for functions of the domain, and they give rise to different numerical algorithms which are illustrated by several experiments
CitationAmstutz, 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
ISSN0029-599X
Publisher versionhttps://link.springer.com/article/10.1007%2Fs00211-018-0964-4
Collections
Files | Description | Size | Format | View |
---|---|---|---|---|
consistent relaxation of optimal design.pdf | 2,007Mb | View/Open |
All rights reserved. This work is protected by the corresponding intellectual and industrial
property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public
communication or transformation of this work are prohibited without permission of the copyright holder