Boundary element solution for elastic orthotropic half-plane problems

Dumir, P.C.; Mehta, A.K.

doi:10.1016/0045-7949(87)90043-5

Cited by 19 publications

(6 citation statements)

References 2 publications

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“…By substituting Equations (1) into Equation (5), it can be shown that for a transversely isotropic plate and for a given inclination angle , the roots depend on E/E , E/G and . As shown by Lekhnitskii [38], the first derivatives of F with respect to x and y can be expressed as…”

Section: Anisotropy Elasticitymentioning

confidence: 99%

Modeling crack propagation path of anisotropic rocks using boundary element method

Ke¹,

Chen

et al. 2008

Num Anal Meth Geomechanics

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SUMMARYIn a cracked material, the stress intensity factors (SIFs) at the crack tips, which govern the crack propagation and are associated with the strength of the material, are strongly affected by the crack inclination angle and the orientation with respect to the principal direction of anisotropy. In this paper, a formulation of the boundary element method (BEM), based on the relative displacements of the crack tip, is used to determine the mixed-mode SIFs of isotropic and anisotropic rocks. Numerical examples of the application of the formulation for different crack inclination angles, crack lengths, and degree of material anisotropy are presented. Furthermore, the BEM formulation combined with the maximum circumferential stress criterion is adopted to predict the crack initiation angles and simulate the crack propagation paths. The propagation path in cracked straight through Brazilian disc specimen is numerically predicted and the results of numerical and experimental data compared with the actual laboratory observations. Good agreement is found between the two approaches. The proposed BEM formulation is therefore suitable to simulate the process of crack propagation.

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Section: Anisotropy Elasticitymentioning

confidence: 99%

Modeling crack propagation path of anisotropic rocks using boundary element method

Ke¹,

Chen

et al. 2008

Num Anal Meth Geomechanics

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“…The basic solutions calculated from these stress functions are taken from the work of Dumir and Mehta [16]. Accordingly, the displacement function u I (Q) and stress function r ij ðQÞ at the field point Q is generally calculated as follows:…”

Section: Fundamental Solution For Anisotropic Elastic Mediummentioning

confidence: 99%

“…The fundamental solutions for semi-infinite planes can be represented by adding a complementary part ( ) c to the two-dimensional Kelvin fundamental solution (denoted by ( ) k ) [16]. The Kelvin solution is the solution for an infinite plane (In Fig.…”

Section: Fundamental Solution For Anisotropic Elastic Mediummentioning

confidence: 99%

Influence functions of the displacement discontinuity method for anisotropic bodies

Kimençe

Ergüven

2005

Comput Mech

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In this study, the boundary element equations are obtained from the influence functions of a displacement discontinuity in an anisotropic elastic medium. For this purpose, Kelvin fundamental solutions for anisotropic media on infinite and semi-infinite planes are used to form dipoles from singular loads. Various combinations of these dipoles are used to obtain the influence functions of the displacement discontinuity. Boundary element equations are then derived analytically by the integration of these influence functions on a constant element which results in a linear system for unknown displacement discontinuities. The boundary integrals are calculated in closed form over constant elements. The obtained formulation is applied to a number of classical engineering problems.

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“…. , t (s) (z, ξ) are defined by (1)-(4) and the functions (16). The stress intensity factors are still given by (19).…”

Section: Numerical Green's Functionmentioning

confidence: 99%

“…Given these fundamental solutions, we establish a technique to determine their Green's functions numerically when multiple cracks are present in two-dimensional isotropic solids. Such Green's functions are called the numerical Green's functions by Telles et al [1,2,3] The majority of the Green's functions are analytical and are concerned about the simplest defect/inhomogeneity geometries possible such as the single center crack(Snider and Cruse [4], Cruse [5], Clements and Haselgrove [6]) or interface crack(Berger and Tewary [7], Yuuki and Cho [8]), the single elliptical hole (Morjaria and Mukherjee [9], Ang and Clements [10], Kamel and Liaw [11], Hwu and Yen [12], Denda and Kosaka [13]), and the half-plane/bimaterial domain (Telles and Brebbia [14], Meek and Dai [15], Dumir and Mehta [16], Pan et al [17], Berger [18], Denda [19]). The only simple geometric configurations have allowed the analytical derivation of these Green's functions.…”

Section: Introductionmentioning

confidence: 99%

Numerical Green's Functions for Line Force and Dislocation around Multiple Cracks

Denda

Quick

2007

EJBE

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The numerical Green's function technique for an infinite isotropic domain with multiple cracks is developed. The singularities considered are the line force and dislocation. The Green's function is decomposed into the singular and the image terms. To obtain the image term we represent the crack opening displacement (COD) by the dislocation dipole distribution, embed the √ r crack tip behavior, and integrate the resulting singular/hyper-singular integrals analytically. The resulting whole crack singular element (WCSE) consists of multiple independent crack opening modes and is strictly algebraic with the correct crack tip singular behavior but the magnitude for each mode is unknown. They are determined to give the negative of the crack surface traction induced by the singular term. Extensive error analysis is performed for the line force and dislocation in an infinite domain with a single crack to identify the region where, when these singularities are placed, the solution achieves high accuracy. Following the guideline set by the error analysis, numerical Green's functions for a few multiple crack configurations are obtained for the line force and dislocation. IntroductionThe fundamental solutions, such as for the line force and dislocation, are defined in an infinite homogeneous body and their main characteristic is the singularity. When defects (such as cracks and holes) and inhomogeneities (such as inclusions) are introduced the fundamental solutions do not satisfy their required boundary conditions for the defects any more and additional terms are needed if these boundary conditions are enforced. The fundamental solution augmented by the additional image term that satisfy the required boundary conditions is called the Green's function. The fundamental solutions considered in this paper are for the line force and dislocation. These fundamental solutions serve as the essential building block for the solutions of the linear elastic problems by the boundary element method (BEM). Given these fundamental solutions, we establish a technique to determine their Green's functions numerically when multiple cracks are present in two-dimensional isotropic solids. Such Green's functions are called the numerical Green's functions by Telles et al. [1,2,3] The majority of the Green's functions are analytical and are concerned about the simplest defect/inhomogeneity geometries possible such as the single center crack (Snider and Cruse [4], Cruse [5], Clements and Haselgrove [6]) or interface crack (Berger and Tewary [7], Yuuki and Cho [8]), the single elliptical hole (Morjaria and Mukherjee [9], Ang and Clements [10], Kamel and Liaw [11], Hwu and M. Denda and P. Quick / Electronic Journal of Boundary Elements, Vol. 2, No. 1, pp. 22-68 (2004) 22 Yen [12], Denda and Kosaka [13]), and the half-plane/bimaterial domain (Telles and Brebbia [14], Meek and Dai [15], Dumir and Mehta [16], Pan et al. [17], Berger [18], Denda [19]). The only simple geometric configurations have allowed the analytical derivation of these Gree...

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Boundary element solution for elastic orthotropic half-plane problems

Cited by 19 publications

References 2 publications

Modeling crack propagation path of anisotropic rocks using boundary element method

Modeling crack propagation path of anisotropic rocks using boundary element method

Influence functions of the displacement discontinuity method for anisotropic bodies

Numerical Green's Functions for Line Force and Dislocation around Multiple Cracks

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