Advertisement

Torsion problem for a bar composed of confocally elliptical dissimilar layers

  • Y. Z. ChenEmail author
Original
  • 19 Downloads

Abstract

This paper provides a general solution for a torsion problem of bar composed of confocally elliptical dissimilar layers. Complex variable method is used to study the problem. The continuity conditions for the warping function and the normal shear stress along the interfaces are suggested. By using the transfer matrices, we can exactly link all sets of undetermined coefficients in the complex potentials defined for layers. Finally, from the conditions imposed on the interior inclusion and the exterior boundary, the solution is obtainable. Numerical examples are carried out to show the influence of the different shear moduli defined on different layers to the stress distribution. The applied torque at the ends of bar is evaluated.

Keywords

Torsion problem Bar composed of confocally elliptical dissimilar layers Complex variable method Transfer matrix method 

Notes

References

  1. 1.
    Sokolnikoff, I.S.: Mathematical Theory of Elasticity. McGraw-Hill, New York (1954)Google Scholar
  2. 2.
    Timoshenko, S.P., Goodier, J.N.: Theory of Elasticity. McGraw-Hill, New York (1970)zbMATHGoogle Scholar
  3. 3.
    Muskhelishvili, N.I.: Some Basic Problems of Mathematical Theory of Elasticity. Noordhoff, Groningen (1963)zbMATHGoogle Scholar
  4. 4.
    Chen, Y.Z.: Solutions of the torsion problem for bars with L\(-\) T- \(+\)-cross section by a harmonic function continuation technique. Int. J. Eng. Sci. 19, 791–804 (1981)CrossRefGoogle Scholar
  5. 5.
    Argatov, I.: Asymptotic models for optimizing the contour of multiply-connected cross-section of an elastic bar in torsion. Int. J. Solids Struct. 47, 1996–2005 (2010)CrossRefGoogle Scholar
  6. 6.
    Kolodziej, J.A., Jankowska, M.A., Mierzwiczak, M.: Meshless methods for the inverse problem related to the determination of elastoplastic properties from the torsional experiment. Int. J. Solids Struct. 50, 4217–4225 (2013)CrossRefGoogle Scholar
  7. 7.
    Hassani, A.R., Faal, R.T.: Saint-Venant torsion of orthotropic bars with rectangular cross section weakened by cracks. Int. J. Solids Struct. 52, 165–179 (2015)CrossRefGoogle Scholar
  8. 8.
    Hassani, A.R., Monfared, M.M.: Analysis of cracked bars with rectangular cross-section and isotropic coating layer under torsion. Int. J. Mech. Sci. 128(129), 23–36 (2017)CrossRefGoogle Scholar
  9. 9.
    Lee, J.W., Hong, H.K., Chen, J.T.: Generalized complex variable boundary integral equation for stress fields and torsional rigidity in torsion problems. Eng. Anal. Bound. Elem. 54, 86–96 (2015)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Chen, Y.Z.: Transfer matrix method for the solution of multiple elliptic layers with different elastic properties. Part I: infinite matrix case. Acta Mech. 226, 191–209 (2015)CrossRefGoogle Scholar
  11. 11.
    Chen, Y.Z.: Numerical solution for a crack embedded in multiple elliptic layers with different elastic properties. Acta Mech. 226, 2807–2829 (2015)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Division of Engineering MechanicsJiangsu UniversityZhenjiangPeople’s Republic of China

Personalised recommendations