Efficient boundary element analysis of sharp notched plates

Portela, A.; Aliabadi, M.H.; Rooke, D.P.

doi:10.1002/nme.1620320302

Cited by 75 publications

(44 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The use of the Williams expansions in the BEM has been presented by Portela et al [28] to subtract the singularity by dividing the domain into singular and regular fields. The technique was able to solve for K I and K II directly.…”

Section: Introductionmentioning

confidence: 99%

A direct evaluation of stress intensity factors using the Extended Dual Boundary Element Method

Alatawi

Trevelyan

2015

Engineering Analysis with Boundary Elements

View full text Add to dashboard Cite

Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Abstract We introduce an alternative method in computational fracture mechanics to evaluate Stress Intensity Factors (SIFs) directly using the Extended Dual Boundary Element Method (XBEM) for 2D problems. Like other enrichment approaches, the new approach is able to yield accurate results on coarse discretisations, and the enrichment increases the problem size by only two degrees of freedom per crack tip. The BEM equations formed by collocation at nodes are augmented by two additional equations that enforce continuity of displacement at the crack tip. The enrichment approach provides the values of SIFs KI and KII directly in the solution vector and without any need for postprocessing such as the J-integral. Numerical examples are used to compare the accuracy of these directly computed SIFs to J-integral processing of both conventional and enriched boundary element approximations.

show abstract

Section: Introductionmentioning

confidence: 99%

A direct evaluation of stress intensity factors using the Extended Dual Boundary Element Method

Alatawi

Trevelyan

2015

Engineering Analysis with Boundary Elements

View full text Add to dashboard Cite

show abstract

“…Two generally applicable special techniques have been devised to overcome this difficulty; they are the subregions method of Blandford, Ingraffea and Liggett [1] and the dual boundary element method of Portela, Aliabadi and Rooke [2]. The main drawback of the subregions method is that the introduction of artificial boundaries (which connect the cracks to the boundary so that the domain is partitioned into subregions without cracks) is not unique and thus it cannot easily be implemented into an automatic procedure.…”

Section: Introductionmentioning

confidence: 99%

“…The partition of the problem with an artificial boundary, passing through the crack tip, is an obvious way to circumvent this difficulty, as shown by Aliabadi [6]. However, artificial boundaries are not strictly necessary in the analysis of cracked plates, see [2]. Hence, instead of partitioning the problem into subregions, a new strategy was developed by Portela, Aliabadi and Rooke [7] which introduces the stress equ~/tions of an internal point, as it approaches the notch tip, as new primary unknowns into the boundary element formulation.…”

Section: Introductionmentioning

confidence: 99%

“…However, artificial boundaries are not strictly necessary in the analysis of cracked plates, see [2]. Hence, instead of partitioning the problem into subregions, a new strategy was developed by Portela, Aliabadi and Rooke [7] which introduces the stress equ~/tions of an internal point, as it approaches the notch tip, as new primary unknowns into the boundary element formulation. The accuracy and the efficiency of the internal point procedure in the SST was demonstrated with a mixed-mode analysis of notched plates [7].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dual boundary element analysis of cracked plates: singularity subtraction technique

Portela

Rooke²

1992

Int J Fract

Self Cite

View full text Add to dashboard Cite

The present paper is concerned with the formulation of the singularity subtraction technique in the dual boundary element analysis of the mixed-mode deformation of general homogeneous cracked plates.The equations of the dual boundary element 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 is applied on the other, general mixed-mode crack problems can be solved in a single region boundary element formulation, with both crack surfaces discretized with discontinuous quadratic boundary elements.The singularity subtraction technique is a regularization procedure that uses a singular particular solution of the crack problem to introduce the stress intensity factors as additional problem unknowns. The single-region boundary element analysis of a general crack problem restricts the availability of singular particular solutions, valid in the global domain of the problem. A modelling strategy, that considers an automatic partition of the problem domain in near-tip and far-tip field regions, is proposed to overcome this difficulty. After the application of the singularity subtraction technique in the near-tip field regions, regularized locally with the singular term of the Williams' eigenexpansion, continuity is restored with equilibrium and compatibility conditions imposed along the interface boundaries. The accuracy and efficiency of the singularity subtraction technique make this formulation ideal for the study of crack growth problems under mixed-mode conditions.

show abstract

“…The extension of the formulation to two-dimensional crack problems in elasticity was introduced by Aliabadi et al [12,13], who obtained both mode I and mode II stress intensity factors. This formulation was later extended to V-notched plates [55] with stress singularities of order ~-I where O.s:S;k:;1.In general, the displacement and traction fields in a given crack problem can be represented as The coefficient KI which arises from the new boundary conditions is now an unknown in the numerical problem. Following the same discretization procedure as described in sections 4.4 and 4.6, the matrix form of (4.49) will now become (S.101) After substitution of the modified boundary conditions, the resulting system of equations can be written as to the regular fields, noting that the terms u~(Xp) and ~.…”

mentioning

confidence: 99%

Application of Boundary Element Methods to Fracture Mechanics

Aliabadi¹,

Rooke²

1991

Solid Mechanics and Its Applications

Self Cite

View full text Add to dashboard Cite

the point P'(x,-y) has field parameters ~j' £~j' uj and ~, ~ they [,,11,,11,,11] [ ~' ; l{ 2 } + + 1 [,,11,,11,,11 [,,11,,11,,11] Now, since the integration path is taken to be symmetrical with respect to the crack along the x-axis (y=O), the outward normal components (nx,n» at points p(x,y) and P'(x,-y) have the following relationships (5.86) By using this relationship, the traction fields in (5.84) at point P(x,y) can be related to those at P'(x,-y), that is (5.87)Other field parameters are also related as follows:r;,} = { ~'} {:~}=r~J} Therefore using the above relationships the J-integral can be decoupled into mode I and mode II components, hence ~ and Kn can be evaluated separately from (5.81).The J-integral being a energy approach has the advantage that elaborate representation of the crack tip singular fields is not necessary. This is due to the relatively small contribution that the crack-tip fields make to the total J (Le. strain energy) of the body. Further advantage of the J-integral approach is that it can be used as a post-processing procedure for the evaluation of stress intensity factors with the internal stress components oj' evaluated from (4.9) using the boundary values of the displacements and tractioJs. The strain components £ij are Numerical Fracture Mechanics 171 subsequently evaluated using strain-stress relationships in (2.10) for plane strain or (2.12) for plane stress. The partial derivatives of displacement 8U/8X may be evaluated accurately using the formula in (4.8) or alternatively a simple approximation formula [51] It is worth noting that the denominator in (5.91) may become zero, depending on the integration path; in such cases it is possible to use the following relationship2 xy 8yIn order to assess the accuracy of the J-integral approach described above, the problem of a central slant crack of length 2a in a rectangular sheet of width W, height 2W and angle of inclination a.=fI1' (see figure 5.9) subjected to tensile uniform stress was studied since alternative accurate results are available [52]. Table 5.3 shows the percentage error compared to [52] in the calculated values of stress intensity factors for a/W=0.1 and 0.2 using different size circular integration paths of radius r centered at the crack tip. The results were obtained using 58 quadratic elements to model the boundary and 18 internal points. The partial derivatives of displacements were calculated from equation (4.8) So far all the techniques discussed in this chapter, have been based on attempts to model the singular stress behaviour at the crack tip. In contrast, the subtraction of the singularity technique avoids the need for this difficult task; it removes the singular fields completely. This leaves a non-singular field to be modelled numerically-a much simpler task. This approach was first introduced into the two-dimensional boundary element formulation of potential problems by Symm[53] and Papamichel and Symm[54] who used constant elements to model a symmetrical slit. Later Xanthis et al [ll] used th...

show abstract

Efficient boundary element analysis of sharp notched plates

Cited by 75 publications

References 28 publications

A direct evaluation of stress intensity factors using the Extended Dual Boundary Element Method

A direct evaluation of stress intensity factors using the Extended Dual Boundary Element Method

Dual boundary element analysis of cracked plates: singularity subtraction technique

Application of Boundary Element Methods to Fracture Mechanics

Contact Info

Product

Resources

About