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Stress concentration for two nearly touching circular holes

by M. Lim and S. Yu

(Report number 2017-32)

Abstract
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.

Keywords: Linear elasticity; Lam\'{e} system; Stress concentration; Singular asymptotic expansion; Bipolar coordinates

@Techreport{LY17_728,
  author = {M. Lim and S. Yu},
  title = {Stress concentration for two nearly touching circular holes},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2017-32},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2017/2017-32.pdf },
  year = {2017}
}

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