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

2024/03/23 by Daehee Cho, Cho, Daehee, Doosung Choi +3
Engineering · #Analysis of PDEs (math.AP) #Elasticity and Wave Propagation #FOS: Mathematics #Geotechnical and Geomechanical Engineering #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2403.15713

openalex publication_date 2024/03/23 · openalex created_date 2024/03/27 · openalex updated_date 2026/07/28

Abstract

We investigate the two-dimensional elastostatic inclusion problem in an unbounded medium. Building on the recent developments for rigid inclusions \citeMattei:2021:EAS and conductivity inclusions \citeJung:2021:SEL, we extend these methodologies to the more general case of elastic inclusions with arbitrary Lamé 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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