Skip to main content
SpringerLink
Log in

Anisotropic thermopiezoelectric solids with an elliptic inclusion or a hole under uniform heat flow

  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

The two-dimensional problem of a thermopiezoelectric material containing an elliptic inclusion or a hole subjected to a remote uniform heat flow is studied. Based on the extended Lekhnitskii formulation for thermopiezoelectricity, conformal mapping and Laurent series expansion, the explicit and closed-form solutions are obtained both inside and outside the inclusion (or hole). For a hole problem, the exact electric boundary conditions on the hole surface are used. The results show that the electroelastic fields inside the inclusion or the electric field inside the hole are linear functions of the coordinates. When the elliptic hole degenerates into a slit crack, the electroelastic fields and the intensity factors are obtained. The effect of the heat flow direction and the dielectric constant of air inside the crack on the thermal electroelastic fields are discussed. Comparison is made with two special cases of which the closed solutions exist and it is shown that our results are valid.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Du SY, Liang J, Han JC. The general coupled solution of anisotropic piezoelectric materials with an elliptic inclusion.Acta Mechanica Sinica, 1994, 10(3): 273–281

    Article  Google Scholar 

  2. Chung MY, Ting TCT. Piezoelectric solids with an elliptic inclusion or hole.Int J Solids Structures, 1996, 33(23): 3343–3361

    Article  MATH  MathSciNet  Google Scholar 

  3. Sosa HA, Khutoryansky N. New developments concerning piezoelectric materials with defects.Int J Solids Structures, 1996, 33(23): 3399–3414

    Article  MATH  MathSciNet  Google Scholar 

  4. Chen TY, Lai DS. An exact correspondence between plane piezoelectricity and generalized plane strain in elasticity.Proc R Soc Lond A, 1997, 453: 2689–2713

    MATH  MathSciNet  Google Scholar 

  5. Hou MS, Yang QJ. Plane problems in piezoelectric media with elliptic inclusion.Appl Math Mech (Chinese Edition), 1998, 19(2): 137–144

    Google Scholar 

  6. Honein T, Honein B, Honein E, Herrmann G. On piezoelectric circular inclusion. In: Hsieh RKT ed. New Electromagnetic materials. Proceedings of the IUTAM Symposium on the Mechanical Modellings of New Electromagnetic Materials, Stockholm, Sweden. Amsterdam: Elsevier, 1990. 259–266

    Google Scholar 

  7. Pak YE. Circular inclusion problem in antiplane piezoelectricity.Int J Solids Structures, 1992, 29(19): 2403–2419

    Article  MATH  Google Scholar 

  8. Meguid SA, Zhong Z. Electroelastic analysis of a piezoelectric elliptical inhomogeneity.Int J Solids Structures, 1997, 34(26): 3401–3414

    Article  MATH  Google Scholar 

  9. Benveniste Y. Piezoelectric inhomogeneity problems in anti-plane shear and in-plane electric fields—how to obtain the coupled fields from the uncopuled dielectric solution.Mech Mater, 1997, 25: 59–65

    Article  Google Scholar 

  10. Chen T, Chiang SC. Electric fields and effective moduli of a medium containing cavities or rigid inclusions of arbitrary shape under anti-plane mechanical and in-plane electric fields.Acta Mechanica, 1997, 121: 79–96

    Article  MATH  MathSciNet  Google Scholar 

  11. Qin QH. A new solution for thermopiezoelectric solid with an insulated elliptic hole.Acta Mechanica Sinica, 1998, 14(2): 157–170

    Article  Google Scholar 

  12. Lu P, Tan MJ, Liew KM. Piezothermoelastic analysis of a piezoelectric material with an elliptic cavity under uniform heat flow.Archive Appl Mech, 1998, 68: 719–733

    Article  MATH  Google Scholar 

  13. Dunn ML. Exact relations between the thermoelectroelastic moduli of heterogeneous materials.Proc R Soc Lond A, 1993, 441: 549–557

    Article  MATH  MathSciNet  Google Scholar 

  14. Chen T, Yen WJ. Piezoelectric analogy of generalized torsion in anisotropic elasticity.J Elasticity, 1998, 49: 239–256

    Article  MATH  Google Scholar 

  15. Hwu C, Yen WJ. On the anisotropic elastic inclusions in plane elastostatics.ASME J Appl Mech, 1993, 60(3): 626–632

    Article  MATH  MathSciNet  Google Scholar 

  16. Chao CK, Shen MH. Thermal stresses in a generally anisotropic body with an elliptic inclusion subjected to uniform heat flow.ASME J Appl Mech, 1998, 65(1): 51–58

    Article  Google Scholar 

  17. Suo Z, Kuo CM, Barneet DM, Willis JR. Fracture mechanics for piezoelectric ceramics.J Mech Phys Solids, 1992, 40(4): 739–765

    Article  MATH  MathSciNet  Google Scholar 

  18. Lekhnitskii SG. Theory of Elasticity of an Anisotropic Body. Moscow: Mir Publication, 1981

    MATH  Google Scholar 

  19. Tarn JQ, Wang YM. Thermal stresses in anisotropic bodies with a hole or a rigid inclusion.J Thermal Stresses, 1993, 16: 455–471

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LNM, The Institute of Mechanics, Chinese Academy of Sciences, 100080, Beijing, China

    Liu Jinxi

  2. Shijiazhuang Railway Institute, 050043, Shijiazhuang, China

    Liu Jinxi

  3. Dept. of Basic Courses, Shijiazhuang Railway Institute, 050043, Shijiazhuang, China

    Zhang Xiaosong & Liu Xianglin

  4. Shijiazhuang Institute of Mechanical Engineering, 050003, Shijiazhuang, China

    Zheng Jian

Authors
  1. Liu Jinxi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhang Xiaosong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Liu Xianglin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zheng Jian
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jinxi, L., Xiaosong, Z., Xianglin, L. et al. Anisotropic thermopiezoelectric solids with an elliptic inclusion or a hole under uniform heat flow. Acta Mech Sinica 16, 148–163 (2000). https://doi.org/10.1007/BF02486707

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02486707

Key Words

Search

Navigation