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arXiv · 2403.15713

A matrix formulation of the plane elastostatic inclusion problem via geometric function theory

Daehee Cho·Doosung Choi·Mikyoung Lim
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Abstract

We investigate the two-dimensional elastostatic inclusion problem in an unbounded medium. Building on the recent developments for rigid inclusions \cite{Mattei:2021:EAS} and conductivity inclusions \cite{Jung:2021:SEL}, we extend these methodologies to the more general case of elastic inclusions with arbitrary Lam\'{e} constants. Our approach integrates layer potential techniques, geometric function theory, and the complex-variable formulation in plane elasticity. As a main result, we derive a matrix formulation of the elastostatic inclusion problem using basis functions defined via the exterior conformal mapping of the inclusion. This leads to a series solution framework that incorporates the geometry of the inclusion.

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Daehee Cho, Doosung Choi, Mikyoung Lim. 2024-03-23. A matrix formulation of the plane elastostatic inclusion problem via geometric function theory. https://arxiv.org/abs/2403.15713

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