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Analytical sensitivity analysis using the extended finite element method in shape optimization of bimaterial structures
Author(s) -
Noël Lise,
Miegroet Laurent Van,
Duysinx Pierre
Publication year - 2015
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5181
Subject(s) - finite element method , sensitivity (control systems) , extended finite element method , shape optimization , boundary (topology) , mathematics , perturbation (astronomy) , set (abstract data type) , mathematical optimization , boundary value problem , computer science , mathematical analysis , structural engineering , engineering , physics , electronic engineering , quantum mechanics , programming language
Summary 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. Copyright © 2015 John Wiley & Sons, Ltd.