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Self-Similar Solutions of Fracture Dynamics Problems on Axially Symmetry

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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 ladder-shaped 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.

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Authors and Affiliations

  1. Department of Astronautics and Mechanics, Harbin Institute of Technology, Harbin, 150001, P R China

    Nian-chun Lü & Jin Cheng

  2. Department of Civil Engineering, Northeastern University, Shenyang, 110006, P R China

    Yun-hong Cheng

  3. Compressive Vessel Manufacturer of Constructive Installation Group Company of Daqing, Daqing, 163711, P R China

    De-zhi Qu

Authors
  1. Nian-chun Lü
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  2. Jin Cheng
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  3. Yun-hong Cheng
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  4. De-zhi Qu
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Lü, Nc., Cheng, J., Cheng, Yh. et al. Self-Similar Solutions of Fracture Dynamics Problems on Axially Symmetry. Applied Mathematics and Mechanics 22, 1429–1435 (2001). https://doi.org/10.1023/A:1022890928044

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