Boundary element formulations for the dynamic analysis of cracked structures

Fedeliński, P.; Aliabadi, M.H.; Rooke, D.P.

doi:10.1016/0955-7997(95)00089-5

Cited by 49 publications

(20 citation statements)

References 13 publications

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“…The material is linear elastic with E = 200 000 GPa, = 0·3 and = 5000 kg=m 3 . Plane strain solutions have been reported by Murti and Valliappan 70 using quarter-point FEM, Dominguez and Gallego 71 using time domain BEM, Fedelinski et al 72 We have studied the problem as 3-D (the depth of the plate being set to 10) with a grid of 21 × 37 × 9 cells: 3780 hexahedral ÿnite elements and an EFG model with 3213 background cells. The support size is 1·25 √ 3h, where h is the length of the longest edge of the background cell.…”

Section: Inclined Centre Crack In a ÿNite Platementioning

confidence: 96%

The Element Free Galerkin method for dynamic propagation of arbitrary 3-D cracks

Krysl

Belytschko

1999

Int. J. Numer. Meth. Engng.

236

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SUMMARYA technique for modelling of arbitrary three-dimensional dynamically propagating cracks in elastic bodies by the Element-Free Galerkin (EFG) method with explicit time integration is described. The meshless character of this approach expedites the description of the evolving discrete model; in contrast to the ÿnite element method no remeshing of the domain is required. The crack surface is deÿned by a set of triangular elements. Techniques for updating the surface description are reported. The paper concludes with several examples: a simulation of mixed-mode growth of a center crack, mode-I surface-breaking penny-shaped crack, penny-shaped crack growing under mixed-mode conditions in a cube, and a bar with centre through crack.

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Section: Inclined Centre Crack In a ÿNite Platementioning

confidence: 96%

The Element Free Galerkin method for dynamic propagation of arbitrary 3-D cracks

Krysl

Belytschko

1999

Int. J. Numer. Meth. Engng.

236

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“…The BEM solutions in elastodynamics are usually obtained by using one of the following approaches (Beskos, 1997): the time domain method (Dominguez, 1993;Dominguez and Gallego, 1992), Laplace or Fourier transforms method (Cruse, 1968;Sladek and Sladek, 1984;Fedelinski et al, 1996) and the dual reciprocity method (Partridge et al, 1992). A comparison of the time-domain, Laplace transform and the dual reciprocity method in terms of computing time and storage as well as accuracy has been presented by Fedelinski et al (1995a). In this paper all integral formulations are presented for the Laplace transforms.…”

Section: Introductionmentioning

confidence: 98%

Nonsingular traction BIEs for crack problems in elastodynamics

Sládek

2000

Computational Mechanics

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The nonsingular traction BIEs are derived for the Laplace transforms in elastodynamic crack problems. Two different forms of the ®nal nonsingular traction BIEs are received with respect to the leading singularity of the integral kernels involved. In the ®rst one, the traction BIE is derived from the integral representation of stresses which involves hypersingular kernels. In the second way, the partially regularized integral representation of stresses with strongly singular kernels is used as a starting point. The singular integrals are transformed to nonsingular ones by making use of the Stokes theorem.

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“…Many authors have developed solutions for the parallel loading problem of a plate. Several studies have investigated static and dynamic loading cases; Fedelinski et al [1] have calculated the dynamic stress intensity factors using the quarter-point elements and path independent Jˆ-integral, while Enderlein et al [2] have developed three methods to calculate the dynamic stress intensity factor for the mode I loading of a stationary crack. Hosseini-Tehrani et al [3] have presented a numerical technique for the calculation of stress intensity factors as a function of time for a coupled thermoelastic problem.…”

Section: Introductionmentioning

confidence: 99%

Analytical and Numerical Solution of the Stress Field and the Dynamic Stress Intensity Factors in a Cracked Plate under Sinusoidal Loading

Aloui

Hamrouni

Fakhfakh

et al. 2008

J Fail. Anal. and Preven.

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A cracked plate subjected to a sinusoidal loading perpendicular to its plane is considered, and the analytical solution of the dynamic vibration behavior of a plate, which allowed the determination of the stress field near the crack tip, is developed. A mixed mode of loading near the crack tip has been established and described with dynamic stress intensity factors K I (z,t) and K II (z,t) associated with modes I and II crack openings, respectively. To validate the analytical results, a finite element analysis (FEA) of a 1 9 1 m square plate with a thickness of 1 cm, having a middle crack of 10 cm in length, is made. The results have shown significant agreement between analytical and FEA findings.

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Boundary element formulations for the dynamic analysis of cracked structures

Cited by 49 publications

References 13 publications

The Element Free Galerkin method for dynamic propagation of arbitrary 3-D cracks

The Element Free Galerkin method for dynamic propagation of arbitrary 3-D cracks

Nonsingular traction BIEs for crack problems in elastodynamics

Analytical and Numerical Solution of the Stress Field and the Dynamic Stress Intensity Factors in a Cracked Plate under Sinusoidal Loading

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