Skip to main content
Log in

Two-dimensional deformation of an anisotropic elastic body with a parabolic boundary

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

In the present paper, two-dimensional deformation problems of an anisotropic body with a parabolic boundary are systematically analysed by using Lekhnitskii’s formalism and the mapping functions method, then a special structure—the half-infinite crack problem is studied through the obtained results, the singular fields and the stress intensity factors near the crack tip are also obtained.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Chien Wei-zang and Yeh Kai-Yuan.Theory of Elasticity, Science Press (1980). (in Chinese)

  2. Xu Zhi-lun,Elasticity, Science Press (1985). (in Chinese).

  3. Eshelby, J. D., W. T. Read and W. Shockley. Anisotropic elasticity with applications to dislocation theory.Acta. Metal.,1 (1953), 251–259.

    Article  Google Scholar 

  4. Stroh, A. N., Dislocations and cracks in anisotropic elasticity.Phil. Mag.,3 (1985), 625–646.

    Article  MathSciNet  Google Scholar 

  5. Stroh, A. N., Steady-state problems in anisotropic elasticity.J. Math. Phys.,41 (1962). 77–103.

    MATH  MathSciNet  Google Scholar 

  6. Barnett, D. M. and J. Lothe. An image force theorem for dislocations in anisotropic bicrystals.J. Phys. F.,4 (1974), 1618–1635.

    Article  Google Scholar 

  7. Barnett, D. M., and J. Lothe, K. Nishioka and R. J. Asaro. Elastic surface waves in anisotropic crystals: a simplified method for calculating Rayleigh velocities using dislocation theory.J. Phys. F.,3 (1973), 1083–1096.

    Article  Google Scholar 

  8. Lothe, J. and D. M. Barnett, On the existence of surface-wave solutions for anisotropic elastic half-spaces with free surface.J. Appl. Phys.,47, (1976), 428–433.

    Article  Google Scholar 

  9. Asaro, R. J., and J. P. Hirth, D. M. Barnett and J. Lothe. The elastic energy of a straight dislocation in an infinite anisotropoic elastic medium.Phys. Stat. Sol. B. 60 (1973), 261–271.

    Google Scholar 

  10. Lekhnitskii, S. G.,Theory of Elasticity of Anisotropic Body, MIR, Moscow (1981).

    Google Scholar 

  11. Wang, S. S. and I. Choi, Boundary layer thermal stress in angle-ply composite laminates.Modern Developments in Composite Materials and Structures, ASME, Edited by J. R. Virstor (1979), 315–341.

  12. Sih, G. C. and H. Liebowitz, Mathematical theory of Brittle fracture, inAn Advanced Treatise on Fracture, Ed. H. Liebowitz, Academic Press (1968), 67–190.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yuan-tai, H., Xing-hua, Z. Two-dimensional deformation of an anisotropic elastic body with a parabolic boundary. Appl Math Mech 15, 913–922 (1994). https://doi.org/10.1007/BF02451034

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02451034

Key words

Navigation