Symmetric weak-form integral equation method for three-dimensional fracture analysis

Li, S.; Mear, Mark E.; Xiao, Long

doi:10.1016/s0045-7825(97)00199-0

Cited by 152 publications

(138 citation statements)

References 24 publications

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“…To allow comparison with corresponding numerical results Sukumar et al (2000) and Li et al (1998), first, it is considered a rectangular prism which contains a single edge crack. The top and bottom surface of this prism impose uniformly distributed normal forces as shown In Figure 4, the values of the SIF for the mode I for isotropic case i.e.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The top and bottom surface of this prism impose uniformly distributed normal forces as shown In Figure 4, the values of the SIF for the mode I for isotropic case i.e. are presented and comparisons with the results obtained by Sukumar et al (2000) and Li et al (1998) The graph of the dependencies between the ERR and s / t is given in Figure 5 . As can be seen in this graph that the increase of the absolute values of the ratio s / t causes the decrease of the values of the ERR.…”

Section: Numerical Resultsmentioning

confidence: 99%

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The Effect of the Shear Modulus on Planes which is Perpendicular to the Crack’s Edge-planes and Parallel to the Crack’s Front on the ERR in an Orthotropic Rectangular Prism with a Band Crack

Ocak¹

2017

AKU-J. Sci. Eng.

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In this study, a rectangular prism made of an orthotropic material is considered. It is assumed that this prism contains a band crack whose edge-planes are parallel to the upper and lower face planes. It is also assumed that uniformly distributed normal forces are imposed the top and bottom surface of the prism. The aim of this paper is to analyze the effect of the shear modulus on planes which is perpendicular to the crack's edge-planes and parallel to the crack's front on the Energy Release Rate (ERR) for different geometric parameters in a rectangular prism. The mathematical formulation of the corresponding boundary-value problem is carried out within the framework of the 3-dimensional linear theory of elasticity. In order to solve this problem, the 3D finite element method was employed. The numerical results are presented.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Numerical Resultsmentioning

confidence: 99%

The Effect of the Shear Modulus on Planes which is Perpendicular to the Crack’s Edge-planes and Parallel to the Crack’s Front on the ERR in an Orthotropic Rectangular Prism with a Band Crack

Ocak¹

2017

AKU-J. Sci. Eng.

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“…The distribution of the stress intensity factor along the circular crack front obtained by the X-FEM analysis is shown in Fig. 13, as compared with the reference (20) . The difference between the X-FEM results and the reference solution is within 1%, indicating that the results obtained in the present study are appropriate.…”

Section: Penny-shaped Crackmentioning

confidence: 99%

Three-Dimensional Crack Analysis using X-FEM Considering Symmetric Conditions

Nagashima

Miura

2008

JCST

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The extended finite element method (X-FEM), which can model the domain without explicitly meshing the crack surface, can be used to perform stress analyses for efficiently solving fracture mechanics problems. In the present study, the constraint condition enforcement for X-FEM analysis considering symmetry is presented. Since the interpolation functions utilized in X-FEM analysis include the enrichment basis functions, the freedoms of the node on the symmetric plane should be constrained properly in the X-FEM model with symmetric conditions. Moreover, evaluation of the energy release rate by the domain integral method should be performed considering the symmetry conditions. In the present paper, the constraint conditions for three-dimensional X-FEM analysis considering symmetric conditions are summarized, and numerical examples using symmetric X-FEM models are shown. The proposed procedure can be used to perform efficient X-FEM analyses of practical fracture problems.Key words: Extended FEM, Fracture Mechanics, Energy Release Rate, Symmetric Conditions IntroductionThe extended finite element method (X-FEM)(1)-(3) can approximate the discontinuous displacement field near cracks independently of the finite element mesh by using the interpolation functions, which can describe the displacement field near cracks in structures. Therefore, the crack modeling for stress analyses can be performed more easily by X-FEM, as compared to conventional FEM. As the information with respect to the crack geometry is required in order to determine the interpolation functions in X-FEM, the level set method (4) , which expresses the geometry implicitly as the zero contour of the level set function, can be used in order to simplify the computation process in X-FEM analysis (5) . The X-FEM analyses in conjunction with the level set method (6) have been applied to the three-dimensional elastic stress and crack propagation analyses for planar and non-planar crack with complex geometry (7) (8) . Moreover, X-FEM has come to be applied to geometrically nonlinear (9) (10) and materially nonlinear problems (10)-(13) . In elastic problems, the energy release rate, which is one of fracture mechanics parameters, can be evaluated by the post processing for the results of X-FEM analysis, as well as FEM. Since the crack geometry does not always perfectly coincide with the element boundary in X-FEM models, neither the virtual crack closure method (14) nor the virtual crack extension method (15) (16) can be applied directly. Therefore, the domain integral method (17) (18) is used to evaluate the Vol. 2, No. 1, 2008 211 energy release rate Journal of Computational Science and Technology(1)- (3), (6)- (8) .The symmetrical conditions can be considered in order to reduce the number of nodes and elements and perform effective analyses in X-FEM as well as FEM when the geometry and boundary conditions have the symmetry properties. However, because the interpolation functions utilized in X-FEM analyses include the enrichment basis functions a...

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“…Among these boundary elements, the development of plate bending problems (Stern 1979;Hartmann & Zotemantel 1986;Shi & Bezine 1988) started relatively later than that of twodimensional or three-dimensional elastostatics (Rizzo 1967;Brebbia et al 1984). *chwu@mail.ncku.edu.tw For example, even though vast advances have been made in boundary element methods for two-and three-dimensional fracture problems (Li et al 1998;Frangi et al 2002;Rungamornrat & Mear 2008a,b), relatively few studies have been done on boundary element formulation for cracks in plates subjected to transverse loading or bending moments. As to the stretching-bending coupling analysis of composite laminates, as far as the author is aware, no associated boundary integral equation has ever been derived in the literature.…”

Section: Introductionmentioning

confidence: 99%

Boundary integral equations for general laminated plates with coupled stretching–bending deformation

Hwu

2009

Proc. R. Soc. A.

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The boundary integral equations for the stretching-bending coupling analysis of general laminated plates are derived in this paper with the aid of the reciprocal theorem of Betti and Raleigh. No restriction is placed on the location of the point load or moment, and so it can be an internal or external point or a smooth or non-smooth boundary point. The fundamental solutions derived from Green's function for an infinite laminated plate subjected to concentrated forces/moments are presented in the complex matrix form. Through the use of some identities converting complex form to real form, the free term coefficients, which are important for the boundary integral equations, are obtained explicitly and expressed in the real form. Alternative formulae for calculating the free term coefficients are also derived using five rigid body movements. By using the explicit real expressions obtained recently for the Stroh-like formalism of coupled stretching-bending analysis, the free term coefficients are further reduced to the cases of isotropic plates and are then compared with known expressions published in the literature. Since stretching and bending decouple for isotropic plates, comparison is made separately for the in-plane problem and plate bending problem, and it is shown that the boundary integral equations derived in this paper agree with previous results for these two special cases.

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Symmetric weak-form integral equation method for three-dimensional fracture analysis

Cited by 152 publications

References 24 publications

The Effect of the Shear Modulus on Planes which is Perpendicular to the Crack’s Edge-planes and Parallel to the Crack’s Front on the ERR in an Orthotropic Rectangular Prism with a Band Crack

The Effect of the Shear Modulus on Planes which is Perpendicular to the Crack’s Edge-planes and Parallel to the Crack’s Front on the ERR in an Orthotropic Rectangular Prism with a Band Crack

Three-Dimensional Crack Analysis using X-FEM Considering Symmetric Conditions

Boundary integral equations for general laminated plates with coupled stretching–bending deformation

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