Dual reciprocity boundary element method in Laplace domain applied to anisotropic dynamic crack problems

Albuquerque, E.L.; Sollero, Paulo; Fedeliński, P.

doi:10.1016/s0045-7949(03)00184-6

Cited by 39 publications

(20 citation statements)

References 20 publications

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“…Albuquerque et al (2003Albuquerque et al ( , 2004 and Gaul et al (2003) used the dual reciprocity BEM. This method applies the corresponding elastostatic fundamental solutions and thus avoids the use of the mathematically complicated elastodynamic fundamental solutions for anisotropic solids.…”

Section: Introductionmentioning

confidence: 99%

Transient dynamic analysis of interface cracks in layered anisotropic solids under impact loading

et al. 2008

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Transient elastodynamic crack analysis in two-dimensional (2D), layered, anisotropic and linear elastic solids is presented in this paper. A time-domain boundary element method (BEM) in conjunction with a multi-domain technique is developed for this purpose. Time-domain elastodynamic fundamental solutions for homogenous, anisotropic and linear elastic solids are applied in the present time-domain BEM. The spatial discretization of the boundary integral equations is performed by a Galerkin-method, while a collocation method is adopted for the temporal discretization of the arising convolution integrals. An explicit time-stepping scheme is developed to compute the unknown boundary data and the crack-opening-displacements (CODs). To show the effects of the crack configuration, the material anisotropy, the layer combination and the dynamic loading on the dynamic stress intensity factors and the scattered elastic wave fields, several numerical examples are presented and discussed.

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Section: Introductionmentioning

confidence: 99%

Transient dynamic analysis of interface cracks in layered anisotropic solids under impact loading

et al. 2008

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“…Only some small deviations near the peaks of the K * I and K * II are observed. In the second example, we consider a finite crack of length 2a in an infinite, anisotropic, and linear elastic solid subjected to an impact shear loading 12 (t) = 0 ·H(t) as shown in Figure 4. Here again, the crack is divided into 20 elements and a time-step of c L t/a = 0.1 corresponding to = 1 is chosen.…”

Section: A Finite Crack In An Infinite Platementioning

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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“…Wang and Nakamura [1] have discussed four techniques, including the above three, for simulating material failure. Numerical techniques for modeling crack propagation include the finite difference method [2,3], the FEM [4,5], the boundary element method [6,7], and meshless methods [8][9][10][11]; only a few references are cited in each category to keep the list short, there is no way one can include here all papers dealing with fracture. Belytschko and Black [4] enriched the FE basis functions by adding to them four basis functions representative of the singular solution in linear elastic problems.…”

Section: Introductionmentioning

confidence: 99%

Search algorithm, and simulation of elastodynamic crack propagation by modified smoothed particle hydrodynamics (MSPH) method

Batra

Zhang

2006

Comput Mech

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We first present a nonuniform box search algorithm with length of each side of the square box dependent on the local smoothing length, and show that it can save up to 70% CPU time as compared to the uniform box search algorithm. This is especially relevant for transient problems in which, if we enlarge the sides of boxes, we can apply the search algorithm fewer times during the solution process, and improve the computational efficiency of a numerical scheme. We illustrate the application of the search algorithm and the modified smoothed particle hydrodynamics (MSPH) method by studying the propagation of cracks in elastostatic and elastodynamic problems. The dynamic stress intensity factor computed with the MSPH method either from the stress field near the crack tip or from the J-integral agrees very well with that computed by using the finite element method. Three problems are analyzed. One of these involves a plate with a centrally located crack, and the other with three cracks on plates's horizontal centroidal axis. In each case the plate edges parallel to the crack are loaded in a direction perpendicular to the crack surface. It is found that, at low strain rates, the presence of other cracks will delay the propagation of the central crack. However, at high strain rates, the speed of propagation of the central crack is unaffected by the presence of the other two cracks. In the third problem dealing with the simulation of crack propagation in a functionally graded plate, the crack speed is found to be close to the experimental one.

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Dual reciprocity boundary element method in Laplace domain applied to anisotropic dynamic crack problems

Cited by 39 publications

References 20 publications

Transient dynamic analysis of interface cracks in layered anisotropic solids under impact loading

Transient dynamic analysis of interface cracks in layered anisotropic solids under impact loading

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

Search algorithm, and simulation of elastodynamic crack propagation by modified smoothed particle hydrodynamics (MSPH) method

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