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Journal of Mathematical Sciences

, Volume 167, Issue 2, pp 162–172 | Cite as

Application of the boundary element method for analysis of the antiplane shear of anisotropic bodies containing thin-walled structures

  • H. T. Sulym
  • Ia. M. Pasternak
Article

We have ascertained the limits of reasonable application of the classical boundary element method for the solution of the antiplane problem of the theory of elasticity in the study of bodies with thin-walled elements of structure and geometry. We have proposed an approach for the regularization of singular and quasisingular integrals, which appear inevitably in analyzing thin structures. We give also numerical examples demonstrating the reliability and efficiency of the proposed approach.

Keywords

Boundary Element Method Singular Integral Stress Concentration Factor Rigid Inclusion Elliptic Hole 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    P. K. Banerjee and R. Butterfield, Boundary Element Methods in Engineering Sciences, McGraw-Hill, London (1981).Google Scholar
  2. 2.
    S. G. Lekhnitskii, Theory of Elasticity of an Anisotropic Body [in Russian], Nauka, Moscow (1977).MATHGoogle Scholar
  3. 3.
    A. M. Lin’kov, Complex Method of Boundary Integral Equations of the Theory of Elasticity [in Russian], Nauka, St. Petersburg (1999).Google Scholar
  4. 4.
    G. C. Sih and H. Liebowitz, “Mathematical theory of brittle fracture,” in: H. Liebowitz (editor), Fracture [Russian translation], Vol. 2: Mathematical Fundamentals of the Theory of Fracture, Mir, Moscow (1975), pp. 83–203.Google Scholar
  5. 5.
    H. Sulym and Ia. Pasternak, “Regularized Somigliana identity for problems of the theory of elasticity with thin-walled structures,” in: Bulletin of Lviv University, Ser. “Applied Mathematics and Informatics” [in Ukrainian], Issue 13 (2007), pp. 142–150.Google Scholar
  6. 6.
    H. T. Sulym, Foundations of the Mathematical Theory of Thermoelastic Equilibrium of Deformable Solids with Thin Inclusions [in Ukrainian], NTSh Res.-Publ. Center, Lviv (2007).Google Scholar
  7. 7.
    H. T. Sulym and Ia. M. Pasternak, “A study of the accuracy of different modifications of the DBEM for plane problems of the theory of elasticity of bodies with inclusions,” in: Scientific Notes: Intercollegiate Collection [in Ukrainian], Vol. 21, Luts’k (2008), pp. 290–298.Google Scholar
  8. 8.
    A. A. Becker, The Boundary Element Method in Engineering: a Complete Course, McGraw-Hill, New York (1992).Google Scholar
  9. 9.
    T. A. Cruse and J. D. Richardson, “Non-singular Somigliana stress identities in elasticity,” Int. J. Numer. Methods Eng., 39, 3273–3304 (1996).MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    J. F. Luo, Y. J. Liu, and E. Berger, “Analysis of two-dimensional thin-structures (from micro- to nano-scales) using the boundary element method,” Comput. Mech., 22, 404–412 (1998).MATHCrossRefGoogle Scholar
  11. 11.
    S. Lu and M. Dong, “An advanced BEM for thermal and stress analyses of components with thermal barrier coating,” Electron. J. Bound. Elem., 1, No. 2, 302–315 (2003).MathSciNetGoogle Scholar
  12. 12.
    S. Mukherjee and Y. Mukherjee, Boundary Methods: Elements, Contours, and Nodes, Taylor & Francis, New York (2005).MATHGoogle Scholar
  13. 13.
    C. Q. Ru and P. Schiavone, “On the elliptic inclusion in antiplane shear,” Math. Mech. Solids, 1, No. 3, 327–333 (1996).MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  • H. T. Sulym
    • 1
    • 2
  • Ia. M. Pasternak
    • 3
  1. 1.Franko Lviv National UniversityLvivUkraine
  2. 2.Pidstryhach Institute for Applied Problems of Mechanics and MathematicsUkrainian National Academy of SciencesLvivUkraine
  3. 3.Luts’k National Technical UniversityLuts’kUkraine

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