THE ESHELBY THEOREM AND APPLICATION TO THE OPTIMIZATION OF AN ELASTIC PATCH

We present the analysis for finding optimal locations and rotations of anisotropic material inclusions in a matrix material by using the polarization matrix. We compare different types of cost funcþionale, in particular local ones, and show their respective differences. We use the Eshelby theorem an...

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Bibliographic Details
Published inSIAM journal on applied mathematics Vol. 72; no. 2; pp. 512 - 534
Main Authors LEUGERING, G., NAZAROV, S., SCHURY, F., STINGL, M.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2012
Subjects
Applied mathematics
Boundary conditions
Boundary value problems
Compliance
Coordinate systems
Cost functions
Elastic anisotropy
Elastic bodies
Mathematical inequalities
Mathematical theorems
Mathematics
Optimization
Tensors
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Summary:We present the analysis for finding optimal locations and rotations of anisotropic material inclusions in a matrix material by using the polarization matrix. We compare different types of cost funcþionale, in particular local ones, and show their respective differences. We use the Eshelby theorem and the representation of stresses based on the link matrix. As an analytical model reduction technique, this allows for efficient numerical computation which is demonstrated for two selected examples.
ISSN:0036-1399
1095-712X
DOI:10.1137/110823110