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A comparative study of three BEM for transient dynamic crack analysis of 2-D anisotropic solids

Abstract

Three different boundary element methods (BEM) for transient dynamic crack analysis in two-dimensional (2-D), homogeneous, anisotropic and linear elastic solids are presented. Hypersingular traction boundary integral equations (BIEs) in frequency- domain, Laplace-domain and time-domain with the corresponding elastodynamic fundamental solutions are applied for this purpose. In the frequency-domain and the Laplace-domain BEM, numerical solutions are first obtained in the transformed domain for discrete frequency or Laplace-transform parameters. Time-dependent results are subsequently obtained by means of the inverse Fourier-transform and the inverse Laplace-transform algorithm of Stehfest. In the time-domain BEM, the quadrature formula of Lubich is adopted to approximate the arising convolution integrals in the time-domain BIEs. Hypersingular integrals involved in the traction BIEs are computed through a regularization process that converts the hypersingular integrals to regular integrals, which can be computed numerically, and singular integrals which can be integrated analytically. Numerical results for the dynamic stress intensity factors are presented and discussed for a finite crack in an infinite domain subjected to an impact crack-face loading.

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Correspondence to Chuanzeng Zhang.

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García-Sánchez, F., Zhang, C. A comparative study of three BEM for transient dynamic crack analysis of 2-D anisotropic solids. Comput Mech 40, 753–769 (2007). https://doi.org/10.1007/s00466-006-0137-7

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Keywords

  • Hypersingular traction BEM
  • Frequency-domain BEM
  • Laplace-domain BEM
  • Time-domain BEM
  • 2-D anisotropic solids