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Stress concentration for two nearly touching circular holes

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arxiv 1705.10400 v1 pith:6JXQ7FPS submitted 2017-05-29 math.AP

classification math.AP
keywords holesstressasymptoticcircularconcentrationtouchingbehaviorcharacterize
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We consider the plane elasticity problem for two circular holes. When two holes are close to touching, the stress concentration happens in the narrow gap region. In this paper, we characterize the stress singularity between the two holes by an explicit function. A new method of a singular asymptotic expansion for the Fourier series with slowing decaying coefficients is developed to investigate the asymptotic behavior of the stress.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Optimal higher derivative estimates for solutions of the Lam\'e system with closely spaced hard inclusions

    math.AP 2024-11 conditional novelty 7.0 of 10

    For the Lamé system with two hard inclusions a distance ε apart, all m-th derivatives blow up at the optimal rate (ε+...)^(-m/2), with log factors in 3D and matching lower bounds in symmetric cases.

  2. Non-singular hotspots between closely spaced high-index nanoparticles

    math.AP 2026-07 conditional novelty 6.0 of 10

    Gap gradients between resonant high-index particles grow like 1/κ under weak coupling via a mean-value contrast, then saturate when coupling ceases to be perturbative—without any true singularity.

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