This paper deals with numerical solutions of singular integral equations in interaction problems of elliptical inclusions under general loading conditions. The stress and displacement fields due to a point force in infinite plates are used as fundamental solutions. Then, the problems are formulated as a system of singular integral equations with Cauchy-type or logarithmic-type singularities, where the unknowns are the body force densities distributed in infinite plates having the same elastic constants as those of the matrix and inclusions. To determine the unknown body force densities to satisfy the boundary conditions, four auxiliary unknown functions are derived from each body force density. It is found that determining these four auxiliary functions in the range is equivalent to determining an original unknown density in the range . Then, these auxiliary unknowns are approximated by using fundamental densities and polynomials. Initially, the convergence of the results such as unknown densities and interface stresses are confirmed with increasing collocation points. Also, the accuracy is verified by examining the boundary conditions and relations between interface stresses and displacements. Randomly or regularly distributed elliptical inclusions can be treated by combining both solutions for remote tension and shear shown in this study.
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June 1998
Technical Papers
Singular Integral Equation Method for Interaction Between Elliptical Inclusions
Nao-Aki Noda,
Nao-Aki Noda
Department of Mechanical Engineering, Kyushu Institute of Technology, Kitakyushu 804-8550, Japan
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Tadatoshi Matsuo
Tadatoshi Matsuo
Department of Mechanical Engineering, Fukushima National College of Technology, Iwaki 970-8034, Japan
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Nao-Aki Noda
Department of Mechanical Engineering, Kyushu Institute of Technology, Kitakyushu 804-8550, Japan
Tadatoshi Matsuo
Department of Mechanical Engineering, Fukushima National College of Technology, Iwaki 970-8034, Japan
J. Appl. Mech. Jun 1998, 65(2): 310-319 (10 pages)
Published Online: June 1, 1998
Article history
Received:
February 13, 1995
Revised:
March 2, 1998
Online:
October 25, 2007
Citation
Noda, N., and Matsuo, T. (June 1, 1998). "Singular Integral Equation Method for Interaction Between Elliptical Inclusions." ASME. J. Appl. Mech. June 1998; 65(2): 310–319. https://doi.org/10.1115/1.2789056
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