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<p>We solve the problem of finding the two-dimensional stress state of an elastic isotropic body containing a system of arbitrarily located cracks interacting with waves. The solution is based on the reduction of the original problem to a system of singular integrodifferential equations for the jumps of displacements on the crack surfaces. For the solution of this system, we propose to use an iterative method. This method enables us to avoid the difficulties connected with the necessity of solving the systems of integrodifferential equations of large dimensions. The analyzed examples demonstrate the convergence and stability of the proposed method also in the case of systems of densely located cracks of complex configurations.</p>

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Iterative Method for Finding the Stress State Under the Action of Waves Upon a System of Cracks

  • 期刊论文

  • 发表日期：

    2025年7月28日

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  • V. G. Popov,
  • O. I. Kyrylova

摘要

We solve the problem of finding the two-dimensional stress state of an elastic isotropic body containing a system of arbitrarily located cracks interacting with waves. The solution is based on the reduction of the original problem to a system of singular integrodifferential equations for the jumps of displacements on the crack surfaces. For the solution of this system, we propose to use an iterative method. This method enables us to avoid the difficulties connected with the necessity of solving the systems of integrodifferential equations of large dimensions. The analyzed examples demonstrate the convergence and stability of the proposed method also in the case of systems of densely located cracks of complex configurations.