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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
Article

Abstract

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

O346.1 

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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

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