Fast and accurate algorithm for cavities reconstruction in an elasticity problem

The aim of this work is to reconstruct the location and geometry of a cavity C embedded in a linear isotropic material Ω via an exterior boundary measurement of the displacement field. The considered problem is governed by the linear elasticity system. This inverse problem of geometry reconstruction...

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Bibliographic Details
Published inMathematical methods in the applied sciences Vol. 42; no. 18; pp. 6083 - 6100
Main Authors Hrizi, Mourad, Hassine, Maatoug, Abdelwahed, Mohamed, Chorfi, Nejmeddine
Format Journal Article
LanguageEnglish
Published Freiburg Wiley Subscription Services, Inc 01.12.2019
Subjects
Algorithms
Elasticity
Geometric algorithms
Holes
Inverse problems
Isotropic material
Kohn‐Vogelius functional
linear elasticity
Reconstruction
shape optimization
topological gradient
topological sensitivity analysis
Topology optimization
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Summary:The aim of this work is to reconstruct the location and geometry of a cavity C embedded in a linear isotropic material Ω via an exterior boundary measurement of the displacement field. The considered problem is governed by the linear elasticity system. This inverse problem of geometry reconstruction (ie, location and shape) is formulated as a topology optimization one and solved by minimizing a Kohn‐Vogelius type functional with the help of the topological sensitivity method. Some numerical results are presented using a noniterative geometric algorithm.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.5706