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Elastic fields of a finite plate containing a circular inclusion by the distributed dislocation method

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Abstract

This paper presents a numerical solution to calculate the two-dimensional elastic fields of a finite plate containing a circular inclusion. The boundaries of the plate are modeled by distributed dislocations. This method results in a system of singular integral equations with Cauchy kernels which can be solved by Gauss–Chebyshev quadrature method. The elastic fields of the plate can be solved with the integral along the whole boundary which is modeled by distributed dislocations. Several numerical examples are given to assess the performance of the presented method.

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References

  1. Erdogan, F., Gupta, G.D.: Layered composites with an interface flaw. Int. J. Solids Struct. 7(8), 1089–1107 (1971)

    Article  MATH  Google Scholar 

  2. Erdogan, F., Gupta, G.D., Ratwani, M.: Interaction between a circular inclusion and an arbitrarily oriented crack. J. Appl. Mech. 41(4), 1007–1013 (1974)

    Article  MATH  Google Scholar 

  3. Comninou, M., Schmeuser, D.: The interface crack in a combined tension-compression and shear field. J. Appl. Mech. 46, 345–348 (1979)

    Article  MATH  Google Scholar 

  4. Comninou, M., Dundurs, J.: Effect of friction on the interface crack loaded in shear. J. Elast. 10(2), 203–212 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  5. Comninou, M., Chang, F.-K.: Effects of partial closure and friction on a radial crack emanating from a circular hole. Int. J. Fract. 28, 29–36 (1985)

    Google Scholar 

  6. Hills, D.A., Comninou, M.: A normally loaded half plane with an edge crack. Int. J. Solids Struct. 21(4), 399–410 (1985)

    Article  Google Scholar 

  7. Nowell, D., Hills, D.A.: Open cracks at or near free of positive radial stresses along the crack line in the edges. J. Strain Anal. Eng. Des. 22(3), 177–185 (1987)

    Article  Google Scholar 

  8. Hills, D.A., Nowell, D.: Stress intensity calibrations for closed cracks. J. Strain Anal. Eng. Des. 24(1), 37–43 (1989)

    Article  Google Scholar 

  9. Hills, D.A., Kelly, P.A., Dai, D.N., Korsunsky, A.M.: Solution of Crack Problems: The Distributed Dislocation. Kluwer Academic Publishers, Dordrecht (1996)

    Book  MATH  Google Scholar 

  10. Weertman, J.: Dislocation Based Fracture Mechanics. World Scientific, Singapore (1996)

    Book  MATH  Google Scholar 

  11. Sheng, C.F.: Boundary element method by dislocation distribution. J. Appl. Mech. 54(1), 105–109 (1987)

    Article  MATH  Google Scholar 

  12. Dai, D.N.: Modeling cracks in finite bodies by distributed dislocation dipoles. Fatigue Fract. Eng. Mater. Struct. 25(1), 27–39 (2002)

    Article  Google Scholar 

  13. Han, J.J., Dhanasekar, M.: Modeling cracks in arbitrarily shaped finite bodies by distribution of dislocation. Int. J. Solids Struct. 41(2), 399–411 (2004)

    Article  MATH  Google Scholar 

  14. Zhang, J., Qu, Z., Huang, Q., et al.: Interaction between cracks and a circular inclusion in a finite plate with the distributed dislocation method. Arch. Appl. Mech. 83(6), 861–873 (2013)

    Article  MATH  Google Scholar 

  15. Erdogan, F., Gupta, G.D., Cook, T.S.: Numerical solution of singular integral equations. In: Sih, G.C. (ed.) Methods of Analysis and Solutions of Crack Problems, pp. 368–425. Noordhoff, Leyden (1973)

    Chapter  Google Scholar 

  16. Jin, X.: Analysis of Some Two Dimensional Problems Containing Cracks and Holes. Northwestern University, Chicago (2006)

    Google Scholar 

Download references

Acknowledgments

This work was financially supported by National Natural Science Foundation of China (No. 51174162) and the Doctoral Scientific Research Foundation of Wuyi University (No. 2015BS14).

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Authors and Affiliations

  1. School of Civil Engineering and Architecture, Wuyi University, 22 Dongcheng Village, Jiangmen, 529030, People’s Republic of China

    Jiong Zhang

  2. School of Aeronautics, Northwestern Polytechnical University, 127 Youyi West Road, Xi’an, 710072, People’s Republic of China

    Jiong Zhang, Zhan Qu & Qiqing Huang

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  1. Jiong Zhang
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  2. Zhan Qu
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  3. Qiqing Huang
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Correspondence to Jiong Zhang.

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Zhang, J., Qu, Z. & Huang, Q. Elastic fields of a finite plate containing a circular inclusion by the distributed dislocation method. Arch Appl Mech 86, 701–712 (2016). https://doi.org/10.1007/s00419-015-1056-x

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  • DOI: https://doi.org/10.1007/s00419-015-1056-x

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