Applied Mathematics and Mechanics

, Volume 22, Issue 12, pp 1429–1435 | Cite as

Self-similar solutions of fracture dynamics problems on axially symmetry

  • Lü Nian-chun
  • Cheng Jin
  • Cheng Yun-hong
  • Qu De-zhi


By the theory of complex functions, a penny-shaped crack on axially symmetric propagating problems for composite materials was studied. The general representations of the analytical solutions with arbitrary index of self-similarity were presented for fracture elastodynamics problems on axially symmetry by the ways of self-similarity under the laddershaped loads. The problems dealt with can be transformed into Riemann-Hilbert problems and their closed analytical solutions are obtained rather simple by this method. After those analytical solutions are utilized by using the method of rotational superposition theorem in conjunction with that of Smirnov-Sobolev, the solutions of arbitrary complicated problems can be obtained.

Key words

penny-shaped crack axially symmetric composite materials analytical solutions 

CLC number



Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Charepanov G P.Mechanics of Brittle Fracture[M]. New York: McGraw-Hill International Book Company, 1979.Google Scholar
  2. [2]
    Kostrov B V. The axisymmetric problem of propagation of a tension crack[J].J Appl Math Mech, 1964,28(4):793–803.MATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    Kostrov B V. Self-similar problems of propagation of shear cracks[J].J Appl Math Mech, 1964,28 (5):1077–1087.MATHMathSciNetCrossRefGoogle Scholar
  4. [4]
    Muskhelishvili N I.Singular Integral Equations[M]. Moscow: Nauka, 1968.Google Scholar
  5. [5]
    Charepanov G P, Afanasoy E F. Some dynamic problems of the theory of elasticity—A review[J].Int J Engng Sci, 1970,12(5):665–690.Google Scholar
  6. [6]
    Erigen A C, Suhubi E S.Elastodynamics, Vol.2,Linear Theory[M]. New York, San Francisco, London: Academic Press, 1975.Google Scholar
  7. [7]
    Hoskins R F.Generalized Functions[M]. New York: Ellis Horwood, 1979.Google Scholar
  8. [8]
    Sih G C.Mechanics of Fracture 4. Elastodynamics Crack Problems[M]. Leyden: Noordhoff International Publishing, 1977, 213–247.Google Scholar
  9. [9]
    Kanwal R P, Sharma D L. Singularity methods for elastostatics[J].J Elasticity, 1976,6(4): 405–418.MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Shanghai University Press 2001

Authors and Affiliations

  • Lü Nian-chun
    • 1
  • Cheng Jin
    • 1
  • Cheng Yun-hong
    • 2
  • Qu De-zhi
    • 3
  1. 1.Department of Astronautics and MechanicsHarbin Institute of TechnologyHarbinP R China
  2. 2.Department of Civil EngineeringNortheastem UniversityShenyangP R China
  3. 3.Compressive Vessel Manufacturer of Constructive Installation Group Company of DaqingDaqingP R China

Personalised recommendations