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Analytical solutions of dynamic mode I crack under the conditions of displacement boundary

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Abstract

By the approaches of the theory of complex variable functions, the problems of dynamic mode I crack under the condition of displacement boundary are investigated. For this kind of dynamic crack extension problems with arbitrary index of self-similarity, the universal representations of analytical solutions are facilely deduced by the methods of self-similar functions. Analytical solutions of the stresses, displacements and stress intensity factors are readily acquired using the methods of self-similar functions. The problems studied can be very easily translated into Riemann–Hilbert problems and their closed solutions are gained rather straightforward in terms of this technique. According to corresponding material properties, the mutative rule of stress intensity factor was illustrated very well. Using those solutions and superposition theorem, the solutions of arbitrarily complex problems can be attained.

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Authors and Affiliations

  1. School of Material Science and Engineering, Shenyang Ligong University, Shenyang, 110159, China

    Nian-Chun Lü

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

    Yun-Hong Cheng

  3. School of Civil Engineering, Harbin Engineering University, Harbin, 150001, China

    Xin-Gang Li & Jin Cheng

  4. Department of Astronautics and Mechanics, Harbin Institute of Technology, Harbin, 150001, China

    Nian-Chun Lü

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  1. Nian-Chun Lü
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  2. Yun-Hong Cheng
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  3. Xin-Gang Li
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  4. Jin Cheng
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Correspondence to Nian-Chun Lü.

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Lü, NC., Cheng, YH., Li, XG. et al. Analytical solutions of dynamic mode I crack under the conditions of displacement boundary. Nonlinear Dyn 67, 2197–2205 (2012). https://doi.org/10.1007/s11071-011-0139-7

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