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Numerical solution for multiple confocal elliptic dissimilar cylinders

  • Chen, Y.Z. (Division of Engineering Mechanics, Jiangsu University)
  • Received : 2016.02.16
  • Accepted : 2016.11.30
  • Published : 2017.02.25
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Abstract

This paper provides a numerical solution for multiple confocal elliptic dissimilar cylinders. In the problem, the inner elliptic notch is under the traction free condition. The medium is composed of many confocal elliptic dissimilar cylinders. The transfer matrix method is used to study the continuity condition for the stress and displacement along the interfaces. Two cases, or the infinite matrix case and the finite matrix case, are studied in this paper. In the former case, the remote tension is applied in y- direction. In the latter case, the normal loading is applied along the exterior elliptic contour. For two cases, several numerical results are provided.

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References

  1. Chen, J.T. and Wu, A.C. (2007), "Null-field approach for the multi-inclusion problem under antiplane shears", J. Appl. Mech., 74(3), 469-487. https://doi.org/10.1115/1.2338056
  2. Chen, T. (2004), "A confocally multicoated elliptical inclusion under antiplane shear: some new results", J. Elas., 74(1), 87-97. https://doi.org/10.1023/B:ELAS.0000026107.75593.65
  3. Chen, Y.Z. (2013), "Closed-form solution for Eshelby's elliptic inclusion in antiplane elasticity using complex variable", Z. Angew. Math. Phys., 64(6), 1797-1805. https://doi.org/10.1007/s00033-013-0305-5
  4. Chen, Y.Z. (2015a), "Transfer matrix method for the solution of multiple elliptic layers with different elastic properties. Part I: infinite matrix case", Acta Mech., 226(1), 191-209. https://doi.org/10.1007/s00707-014-1164-7
  5. Chen, Y.Z. (2015b), "A novel solution for thick-walled cylinders made of functionally graded materials", Smart Struct. Syst., 15(6), 1503-1520. https://doi.org/10.12989/sss.2015.15.6.1503
  6. Gong, S.X. (1995), "A unified treatment of the elastic elliptical inclusion under antiplane shear", Arch. Appl. Mech., 65(2), 55-64. https://doi.org/10.1007/BF00787899
  7. Markenscoff, X. and Dundurs, J. (2014), "Annular inhomogeneities with eigenstrain and interphase modeling", J. Mech. Phys. Solids, 64, 468-482. https://doi.org/10.1016/j.jmps.2013.12.003
  8. Muskhelishvili, N.I. (1963), Some Basic Problems of the Mathematical Theory of Elasticity. Noordhoff, Groningen.
  9. Wang, X. and Gao, X.L. (2011), "On the uniform stress state inside an inclusion of arbitrary shape in a three-phase composite", Z. Angew. Math. Phys., 62(6), 1101-1116. https://doi.org/10.1007/s00033-011-0134-3
  10. Wu, C.H. and Chen, C.H. (1990), "A crack in a confocal elliptic inhomogeneity embedded in an infinite medium", J. Appl. Mech., 57(1), 91-96. https://doi.org/10.1115/1.2888330
  11. Zhu, L., Hoh, H.J., Wang, X., Keer, L.M., Pang, J.H.L., Song, B. and Wang, Q.J. (2013), "A review of recent works on inclusions", Mech. Mater., 60, 144-158. https://doi.org/10.1016/j.mechmat.2013.01.005

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