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

Journal of Elasticity - Tập 144 - Trang 81-105 - 2021
Ornella Mattei1, Mikyoung Lim2
1Department of Mathematics, San Francisco State University, San Francisco, USA
2Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon, Republic of Korea

Tóm tắt

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.

Tài liệu tham khảo

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