Hypersingular integrals in boundary element fracture analysis (original) (raw)
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Green's function: a numerical generation for fracture mechanics problems via boundary elements
Computer Methods in Applied Mechanics and Engineering, 2000
The paper discusses the application of the hyper-singular boundary integral equation to obtain Green's function solution to general geometry fracture mechanics problems, such as curved multifracture crack simulation, static and harmonic (extended to transient dynamic through inverse numerical transforms), in 2D and 3D. The numerical Green's function (NGF) can be implemented into a boundary element computer program, as the fundamental solution, to produce an accurate and ecient boundary element procedure. The complete formulation is presented in a uni®ed manner, generalizing previous problem oriented procedures proposed by the authors. The results to some typical linear fracture mechanics problems are presented.
A numerical green's function approach for boundary elements applied to fracture mechanics
International Journal for Numerical Methods in Engineering, 1995
The most accurate boundary element formulation to deal with fracture mechanics problems is obtained with the implementation of the associated Green's function acting as the fundamental solution. Consequently, the range of applications of this formulation is dependent on the availability of the appropriate Green's function for actual crack geometry. Analytical Green's functions have been presented for a few single crack configurations in 2-D applications and require complex variable theory. This work extends the applicability of the formulation through the introduction of efficient numerical means of computing the Green's function components for single or multiple crack problems, of general geometry, including the implementation to 3-D problems as a future development. Also, the approach uses real variables only and well-established boundary integral equations.
A hypersingular Green's function generation for fracture mechanics problems
1994
A boundary element formulation to deal with fracture mechanics problems can be obtained with the implementation of the associated Green's function acting as the fundamental solution. The range of applications of this formulation is dependent on the availability of the appropriate Green's function for actual crack geometry. Analytical Green' s functions have been presented for a few single crack configurations in 2-D applications and require complex variable theory. The present work extends the applicability of the formulation through the introduction of efficient numerical means of computing the Green's function components for single or multiple crack problems, of general geometry. Also, the approach uses real variables only and well established boundary integral equations.
Hypersingular quarter-point boundary elements for crack problems
International Journal for Numerical Methods in Engineering, 1995
The present paper deals with the study and effective implementation for Stress Intensity Factor computation of a mixed boundary element approach based on the standard displacement integral equation and the hypersingular traction integral equation. Expressions for the evaluation of the hypersingular integrals along general curved quadratic line elements are presented. The integration is carried out by transformation of the hypersingular integrals into regular integrals, which are evaluated by standard quadratures, and simple singular integrals, which are integrated analytically. The generality of the method allows for the modelling of curved cracks and the use of straight line quarter-point elements. The Stress Intensity Factors can be computed very accurately from the Crack Opening Displacement at collocation points extremely close to the crack tip. Several examples with different crack geometries are analyzed. The computed results show that the proposed approach for Stress Intensity Factors evaluation is simple, produces very accurate solutions and has little dependence on the size of the elements near the crack tip.
Dual boundary element method for axisymmetric crack analysis
International Journal of Fracture, 2002
In this paper a dual boundary element formulation is developed and applied to the evaluation of stress intensity factors in, and propagation of, axisymmetric cracks. The displacement and stress boundary integral equations are reviewed and the asymptotic behaviour of their singular and hypersingular kernels is discussed. The modified crack closure integral method is employed to evaluate the stress intensity factors.
Boundary integral equation method to solve embedded planar crack problems under shear loading
Computational Mechanics, 2004
The solution of three-dimensional planar cracks under shear loading are investigated by the boundary integral equation method. A system of two hypersingular integral equations of a three-dimensional elastic solid with an embedded planar crack are given. The solution of the boundary integral equations is succeeded taking into consideration an appropriate Gauss quadrature rule for finite part integrals which is suitable for the numerical treatment of any plane crack without a polygonal contour shape and permit the fast convergence for the results. The stress intensity factors at the crack front are calculated in the case of a circular and an elliptic crack and are compared with the analytical solution.
Boundary element analysis of an integral equation for three-dmensional crack problems
International Journal for Numerical Methods in Engineering, 1988
In another paper, the authors proposed an integral equation for arbitrary shaped three-dimensional cracks. In the present paper, a discretization of this equation using a tensor formalism is formulated. This approach has the advantage of providing the displacement discontinuity vector in the local basis which varies as a function of the point of the crack surface. This also facilitates the computation of the stress intensity factors along the crack edge. Numerical examples reported for a circular crack and a semi-elliptical surface crack in a cylindrical bar show that one can obtain good resuhs, using few Gaussian poilnts and no singular elements.
Three-dimensional fracture simulation with a single-domain, direct boundary element formulation
International Journal for Numerical Methods in Engineering, 1992
An efficient hypersingular boundary integral equation method for three-dimensional fracture mechanics was presented in a previous paper. The details of the numerical implementation of this method are further discussed herein. In particular, an algorithm for achieving the required differentiability of the crack surface displacement function is discussed. To illustrate the utility of the method, computational results for several strongly interacting multiple-crack geometries are presented. The calculated stress intensity factors are in excellent agreement with those obtained by an approximate analytical method due to Kachanov and Laures.
European Journal of Computational Mechanics
In the traditional boundary element methods, the numerical modelling of cracks is usually carried out by means of a hypersingular fundamental solution, which involves a 1=r 2 kernel for two-dimensional problems. A more natural procedure should make use of fundamental solutions that represent the square root singularity of the gradient field around the crack tip (a Green's function). Such a representation has been already accomplished in a variationally based framework that also addresses a convenient means of evaluating results at internal points. This paper proposes a procedure for the numerical simulation of two-dimensional problems with a fundamental solution that can be in part or for the whole structure based on generalised Westergaard stress functions. Problems of general topology can be modelled, such as in the case of unbounded and multiply-connected domains. The formulation is naturally applicable to notches and generally curved cracks. It also provides an easy means of evaluating stress intensity factors, when particularly applied to fracture mechanics. The main features of the theory are briefly presented in the paper, together with several validating examples and some convergence assessments.
The dual boundary element method: Effective implementation for crack problems
International Journal for Numerical Methods in Engineering, 1992
The present paper is concerned with the effective numerical implementation of the two-dimensional dual boundary element method, for linear elastic crack problems. The dual equations of the method are the displacement and the traction boundary integral equations. When the displacement equation is applied on one of the crack surfaces and the traction equation on the other, general mixed-mode crack problems can be solved with a single-region formulation. Both crack surfaces are discretized with discontinuous quadratic boundary elements; this strategy not only automatically satisfies the necessary conditions for the existence of the finite-part integrals, which occur naturally, but also circumvents the problem of collocation at crack tips, crack kinks and crack-edge corners. Examples of geometries with edge, and embedded crack are analysed with the present method. Highly accurate results are obtained, when the stress intensity factor is evaluated with the J-integral technique. The accuracy and efficiency of the implementation described herein make this formulation ideal for the study of crack growth problems under mixed-mode conditions.