Singular Integral Equation Method in the Analysis of Interaction between Diamond-Shaped Inclusions.

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Other Title
  • 特異積分方程式による菱形介在物の干渉効果の解析
  • トクイ セキブン ホウテイシキ ニヨル リョウケイ カイザイブツ ノ カンショ
Published
1996
Resource Type
journal article
DOI
  • 10.1299/kikaia.62.1456
Publisher
The Japan Society of Mechanical Engineers

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This paper deals with numerical solutions of singular integral equations in interaction problems of diamond-shaped inclusions with angular corners under various loading conditions. The problems are formulated as a system of singular integral equations with Cauchy-type or logarithmic-type singularities, where the unknown functions are the densities of body forces distributed in infinite plates having the same elastic constants as those of the matrix and inclusions. In order to analyze the problems accurately, the unknown functions of the body force densities are expressed as a linear combination of two types of fundamental density functions and power series, where the fundamental density functions are chosen to represent the symmetric stress singularity of 1/r1-λ1 and the skew-symmetric stress singularity of 1/r1-λ2. Then, newly defined stress intensity factors of angular corners are systematically calculated for various shapes and spacings of two diamond-shaped inclusions in a plate subjected to uniaxial tension, biaxial tension and in-plane shear. The present method is found to yield rapidly converging numerical results for the interaction of diamond-shaped inclusions.

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