A time-domain collocation-Galerkin BEM for transient dynamic crack analysis in anisotropic solids

Tan, A.H.; Hirose, Sohichi; Zhang, Ch.

doi:10.1016/j.enganabound.2005.05.009

Cited by 15 publications

(12 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The singular static part of the elastodynamic fundamental solutions (17) corresponds to the elastostatic fundamental solutions for homogeneous, anisotropic, and linear elastic solids, which can be given by an explicit expression via the Stroh formalism [35,36] as…”

Section: Singular Static Partmentioning

confidence: 99%

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

Wünsche

Zhang

Kuna

et al. 2008

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Singular Static Partmentioning

confidence: 99%

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

Wünsche

Zhang

Kuna

et al. 2008

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…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%

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

García-Sánchez

Zhang

2006

Comput Mech

View full text Add to dashboard Cite

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

show abstract

“…The crack problem in an anisotropic elastic solid under impact loading was considered in [14,15]. In the paper [14], the time domain BEM for a transient elastodynamic crack analysis in homogeneous and linear elastic solids of general anisotropy was presented.…”

Section: Introductionmentioning

confidence: 99%

“…In the paper [14], the time domain BEM for a transient elastodynamic crack analysis in homogeneous and linear elastic solids of general anisotropy was presented. In the numerical analysis, special attention was given to the transient elastodynamic stress intensity factors.…”

Section: Introductionmentioning

confidence: 99%

A boundary integral equation method in the frequency domain for cracks under transient loading

et al. 2016

Self Cite

View full text Add to dashboard Cite

This paper concerns the fracture mechanics problem for elastic cracked materials under transient dynamic loading. The problem is solved by use of the boundary integral equations in the frequency domain, and the components of the solution are presented by the Fourier exponential series. The dynamic stress intensity factors are computed for different stress pulses and compared with those obtained for the case of the Heaviside loading.

show abstract

A time-domain collocation-Galerkin BEM for transient dynamic crack analysis in anisotropic solids

Cited by 15 publications

References 26 publications

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

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

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

A boundary integral equation method in the frequency domain for cracks under transient loading

Contact Info

Product

Resources

About