A 2D time-domain BEM for transient wave scattering analysis by a crack in anisotropic solids

Tan, A.H.; Hirose, Sohichi; Zhang, Ch.; Wang, C.-Y.

doi:10.1016/j.enganabound.2005.01.012

Cited by 22 publications

(6 citation statements)

References 42 publications

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“…6, which imply that the present time-domain BEM is quite insensitive to the selected time-steps. This is an important advantage over the classical time-domain BEM [24,25,31], which suffers from the stability problem.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…In contrast to the conventional time-domain BEM [24,25,31], the present method uses the Laplace-domain instead of the time-domain elastodynamic fundamental solutions. This is advantageous for cases where timedomain dynamic fundamental solutions are not available but their Laplace-transforms can be obtained.…”

Section: Time-domain Bemmentioning

confidence: 99%

“…Over the past years, three different BEM formulations, namely, the frequency-domain [5,9], the Laplacedomain [3] and the time-domain [2,24,25,29,33] BEM, are often applied to transient elastodynamic crack analysis. To analyze their accuracy and efficiency, a comparative study is performed in this paper.…”

Section: Introductionmentioning

confidence: 99%

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

García-Sánchez

Zhang

2006

Comput Mech

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International audienceThree 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 regulariza-tion 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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Section: Numerical Resultsmentioning

confidence: 99%

Section: Time-domain Bemmentioning

confidence: 99%

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

García-Sánchez

Zhang

2006

Comput Mech

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“…A time-domain displacement BEM for transient wave scattering analysis by cavities or holes has been presented by Wang et al [35], who used the time-domain elastodynamic fundamental solutions for anisotropic elastic solids derived by Wang and Achenbach [33] the isotropic case, time-domain fundamental solutions for homogenous, anisotropic and linear elastic solids have no closed-form expressions and can be represented only as line-integrals over a unit-circle in two-dimensional (2D) case. Hirose et al [23] and Tan et al [30,31] have developed a collocation-Galerkin BEM for transient dynamic crack analysis in infinite, homogeneous, anisotropic and linear elastic solids. In their time-domain BEM, regularized traction boundary integral equations (BIEs) have been applied, and a combination of the collocation method and the Galerkinmethod has been used.…”

Section: Introductionmentioning

confidence: 99%

On two hypersingular time-domain BEM for dynamic crack analysis in 2D anisotropic elastic solids

Wünsche

Zhang

García-Sánchez

et al. 2009

Computer Methods in Applied Mechanics and Engineering

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“…On the external boundary of the cracked solid and on the crack-faces away from the crack-tips, standard linear elements are adopted, while special crack-tip elements are implemented at the crack-tips to describe the local square-root behavior of the crack-opening-displacements (CODs) properly. Unlike the TDBEM presented in [16][17][18], which uses regularized time-domain traction BIEs, special analytical techniques are developed in the present TDBEM to directly compute the strongly singular and hypersingular boundary integrals without regularization. Spatial integrations of the double integrals arising in the Galerkin method are performed analytically.…”

mentioning

confidence: 99%

A hypersingular time‐domain BEM for 2D dynamic crack analysis in anisotropic solids

Wünsche

Zhang

Kuna

et al. 2008

Numerical Meth Engineering

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SUMMARYA hypersingular time-domain boundary element method (BEM) for transient elastodynamic crack analysis in two-dimensional (2D), homogeneous, anisotropic, and linear elastic solids is presented in this paper. Stationary cracks in both infinite and finite anisotropic solids under impact loading are investigated. On the external boundary of the cracked solid the classical displacement boundary integral equations (BIEs) are used, while the hypersingular traction BIEs are applied to the crack-faces. The temporal discretization is performed by a collocation method, while a Galerkin method is implemented for the spatial discretization. Both temporal and spatial integrations are carried out analytically. Special analytical techniques are developed to directly compute strongly singular and hypersingular integrals. Only the line integrals over an unit circle arising in the elastodynamic fundamental solutions need to be computed numerically by standard Gaussian quadrature. An explicit time-stepping scheme is obtained to compute the unknown boundary data including the crack-opening-displacements (CODs). Special crack-tip elements are adopted to ensure a direct and an accurate computation of the elastodynamic stress intensity factors from the CODs. Several numerical examples are given to show the accuracy and the efficiency of the present hypersingular time-domain BEM.

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A 2D time-domain BEM for transient wave scattering analysis by a crack in anisotropic solids

Cited by 22 publications

References 42 publications

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

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

On two hypersingular time-domain BEM for dynamic crack analysis in 2D anisotropic elastic solids

A hypersingular time‐domain BEM for 2D dynamic crack analysis in anisotropic solids

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