Journal of Elasticity

, Volume 84, Issue 2, pp 153–166 | Cite as

Hertzian Contact of Anisotropic Piezoelectric Bodies



The Fourier transform method is applied to the Hertzian contact problem for anisotropic piezoelectric bodies. Using the principle of linear superposition, the resulting transformed (algebraic) equations, whose right-hand sides contain both pressure and electric displacement terms, can be solved by superposing the solutions of two sets of algebraic equations, one containing pressure and another containing electric displacement. By presupposing the forms of the pressure and electric displacement distribution over the contact area, the problem is solved successfully; then the generalized displacements, stresses and strains are expressed by contour integrals. Details are presented in the case of special orthotropic piezoelectricity whose material constants satisfy six relations, which can be easily degenerated to the case of transverse isotropic piezoelectricity. It can be shown that the result gained in this paper is of a universal and compact form for a general material.

Key words

anisotropic piezoelectric bodies Fourier transform Hertzian contact problem 

Mathematics Subject Classifications (2006)

74B99 74M15 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ding, H.J., Chen, W.Q.: Three Dimensional Problems of Piezoelasticity. Nova Science, New York (2000)Google Scholar
  2. 2.
    Sosa, H.A., Castro, M.A.: On concentrated loads at the boundary of a piezoelectric half-plane. J. Mech. Phys. Solids 42, 1105–1122 (1994)MATHCrossRefADSMathSciNetGoogle Scholar
  3. 3.
    Wang, Z.K., Zheng, B.L.: The general solution of three-dimensional problems in piezoelectric media. Int. J. Solids Struct. 32, 105–115 (1995)MATHCrossRefGoogle Scholar
  4. 4.
    Ding, H.J., Chen, B., Liang, J.: General solutions for coupled equations for piezoelectric media. Int. J. Solids Struct. 33, 2283–2298 (1996)MATHCrossRefGoogle Scholar
  5. 5.
    Fan, H., Sze, K.Y., Yang, W.: Two-dimensional contact on a piezoelectric half-space. Int. J. Solids Struct. 33, 1305–1315 (1996)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Ding, H.J., Hou, P.F., Guo, F.L.: The elastic and electric fields for three-dimensional contact for transversely isotropic piezoelectric materials. Int. J. Solids Struct. 37, 3201–3229 (2000).MATHCrossRefGoogle Scholar
  7. 7.
    Willis, J.R.: Hertzian contact of anisotropic bodies. J. Mech. Phys. Solids 14, 163–176 (1966)MATHCrossRefADSMathSciNetGoogle Scholar
  8. 8.
    Barnett, D.M., Lothe, J.: Dislocation and line charges in anisotropic piezoelectric insulators. Phys Status Solidi 67b, 105–111 (1975)CrossRefGoogle Scholar
  9. 9.
    Pan, E.N., Tonon, F.: Three-dimensional Green's functions in anisotropic piezoelectric solids. Int. J. Solids Struct. 37, 943–958 (2000)MATHCrossRefGoogle Scholar
  10. 10.
    Kimfs, I.V., Suncheleev, R.Y.: A contact problem for an orthotropic half-space. Int. Appl. Mech. 6, 40–47 (1970)Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.State Key Laboratory for Turbulence and Complex SystemsPeking UniversityBeijingPR China
  2. 2.Department of Mechanics and Engineering SciencePeking UniversityBeijingPR China

Personalised recommendations