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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| Published in | Journal of elasticity Vol. 144; no. 1; pp. 81 - 105 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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01.04.2021
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Mattei, Ornella Lim, Mikyoung |
| Author_xml | – sequence: 1 givenname: Ornella orcidid: 0000-0002-9342-6291 surname: Mattei fullname: Mattei, Ornella organization: Department of Mathematics, San Francisco State University – sequence: 2 givenname: Mikyoung surname: Lim fullname: Lim, Mikyoung email: mklim@kaist.ac.kr organization: Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology |
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| CitedBy_id | crossref_primary_10_1103_PhysRevE_109_014901 crossref_primary_10_1016_j_mechrescom_2022_103976 crossref_primary_10_3390_sym16030360 crossref_primary_10_1137_24M1646479 |
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| References_xml | – reference: KangH.YuS.Quantitative characterization of stress concentration in the presence of closely spaced hard inclusions in two-dimensional linear elasticityArch. Ration. Mech. Anal.20192321121196391697310.1007/s00205-018-1318-11415.74028 – reference: DurenP.Univalent Functions1983New YorkSpringer0514.30001https://www.springer.com/kr/book/9780387907956 – reference: FaberG.Über polynomische EntwicklungenMath. Ann.1903573389408151121610.1007/BF01444293 – reference: KangH.Conjectures of Pólya–Szegő and Eshelby, and the Newtonian potential problem: a reviewInt. J. Mech. Mater. Des.200941440541010.1016/j.mechmat.2009.01.019Special Issue in Honor of Graeme W. Milton, 2007 Winner of the William Prager Medal of the Society of Engineering Science – reference: KangH.MiltonG.W.Solutions to the Pólya–Szegő conjecture and the Weak Eshelby ConjectureArch. Ration. Mech. 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| SubjectTerms | Automotive Engineering Basis functions Classical Mechanics Conformal mapping Coordinates Elastostatics Exact solutions Mathematical analysis Physics Physics and Astronomy Polynomials Two dimensional bodies |
| Title | Explicit Analytic Solution for the Plane Elastostatic Problem with a Rigid Inclusion of Arbitrary Shape Subject to Arbitrary Far-Field Loadings |
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