Explicit Analytic Solution for the Plane Elastostatic Problem with a Rigid Inclusion of Arbitrary Shape Subject to Arbitrary Far-Field Loadings

We provide an analytical solution for the elastic fields in a two-dimensional unbounded isotropic body with a rigid inclusion. Our analysis is based on the boundary integral formulation of the elastostatic problem and geometric function theory. Specifically, we use the coordinate system provided by...

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Bibliographic Details
Published inJournal of elasticity Vol. 144; no. 1; pp. 81 - 105
Main Authors Mattei, Ornella, Lim, Mikyoung
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.04.2021
Springer Nature B.V
Subjects
Automotive Engineering
Basis functions
Classical Mechanics
Conformal mapping
Coordinates
Elastostatics
Exact solutions
Mathematical analysis
Physics
Physics and Astronomy
Polynomials
Two dimensional bodies
Transmission problem
Faber polynomials
30C55
Linear elasticity
74B05
Lamé system
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Summary:We provide an analytical solution for the elastic fields in a two-dimensional unbounded isotropic body with a rigid inclusion. Our analysis is based on the boundary integral formulation of the elastostatic problem and geometric function theory. Specifically, we use the coordinate system provided by the exterior conformal mapping of the inclusion to define a density basis functions on the boundary of the inclusion, and we use the Faber polynomials associated with the inclusion for a basis inside the inclusion. The latter, which constitutes the main novelty of our approach, allows us to obtain an explicit series solution for the plane elastostatic problem for an inclusion of arbitrary shape in terms of the given arbitrary far-field loading.
Bibliography:ObjectType-Article-1
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ISSN:0374-3535
1573-2681
DOI:10.1007/s10659-021-09828-6