Article (Scientific journals)
Analytical sensitivity analysis using the extended finite element method in shape optimization of bimaterial structures
Noël, Lise; Van Miegroet, Laurent; Duysinx, Pierre
2016In International Journal for Numerical Methods in Engineering
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Keywords :
shape optimization; analytical sensitivity analysis; XFEM level set
Abstract :
[en] The present work investigates the shape optimization of bimaterial structures. The problem is formulated using a level set description of the geometry and the extended finite element method (XFEM) to enable an easy treatment of complex geometries. A key issue comes from the sensitivity analysis of the structural responses with respect to the design parameters ruling the boundaries. Even if the approach does not imply any mesh modification, the study shows that shape modifications lead to difficulties when the perturbation of the level sets modifies the set of extended finite elements. To circumvent the problem, an analytical sensitivity analysis of the structural system is developed. Differences between the sensitivity analysis using FEM or XFEM are put in evidence. To conduct the sensitivity analysis, an efficient approach to evaluate the so-called velocity field is developed within the XFEM domain. The proposed approach determines a continuous velocity field in a boundary layer around the zero level set using a local finite element approximation. The analytical sensitivity analysis is validated against the finite differences and a semi- analytical approach. Finally our shape optimization tool for bimaterial structures is illustrated by revisiting the classical problem of the shape of soft and stiff inclusions in plates.
Disciplines :
Mechanical engineering
Author, co-author :
Noël, Lise ;  Université de Liège > Département d'aérospatiale et mécanique > Ingénierie des véhicules terrestres
Van Miegroet, Laurent
Duysinx, Pierre  ;  Université de Liège > Département d'aérospatiale et mécanique > Ingénierie des véhicules terrestres
Language :
English
Title :
Analytical sensitivity analysis using the extended finite element method in shape optimization of bimaterial structures
Publication date :
2016
Journal title :
International Journal for Numerical Methods in Engineering
ISSN :
0029-5981
eISSN :
1097-0207
Publisher :
Wiley, Chichester, United Kingdom
Peer reviewed :
Peer Reviewed verified by ORBi
Funders :
F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]
Available on ORBi :
since 02 May 2016

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