Enriched partition-of-unity finite element method for stress intensity factors at crack tips

Fan, S.C.; Liu, X.; Lee, Chi King

doi:10.1016/j.compstruc.2003.10.019

Cited by 25 publications

(18 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is reflected in the literature by the large amount of scientific papers studying edge cracked specimens under load. The most commonly used methods for the numerical investigation of these problems are boundary element methods (or boundary integral equation methods) [1][2][3][4][5][6][7][8][9][10][11][12][13], finite element methods [14][15][16][17][18][19][20] and mesh independent methods (or partition of unity methods) [21][22][23][24][25]. Equations and geometries similar to those encountered in edge crack problems also appear in other contexts than fracture mechanics.…”

Section: Introductionmentioning

confidence: 99%

“…All papers cited above present values of numerically computed stress intensity factors. Four papers present T -stresses [3,12,13,15], three papers present the stress field for an entire specimen [24,25,27], and one paper presents strain energies [22].…”

Section: Introductionmentioning

confidence: 99%

“…One group consists of papers that focus on developing new algorithms and equations for solving the stress problem in edge cracked geometries [4,5,27]. Another group consists of papers that focus on improving existing algorithms, using for instance new basis functions or elements [6,[19][20][21][22]. A third group of papers primarily deal with developing auxiliary algorithms for the computation of fracture parameters [9,12,[14][15][16].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Efficient algorithm for edge cracked geometries

Englund

2005

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYThe stress field in a finite, edge cracked specimen under load is computed using algorithms based on two slightly different integral equations of the second kind. These integral equations are obtained through left regularizations of a first kind integral equation. In numerical experiments it is demonstrated that the stress field can be accurately computed. Highly accurate stress intensity factors and T -stresses are presented for several setups and extensive comparisons with results from the literature are made. For simple geometries the algorithms presented here achieve relative errors of less than 10 −10 . It is also shown that the present algorithms can accurately handle both geometries with arbitrarily shaped edge cracks and geometries containing several hundred edge cracks. All computations were performed on an ordinary workstation.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Efficient algorithm for edge cracked geometries

Englund

2005

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…In XFEM, the strains/stresses on both sides of a stress-free crack are fully decoupled, thus superior kinematic properties can be better captured than EFEM [12]. However, at present the main applications of XFEM approach are limited in either in-plane behaviour of structural members (achieved by very fine mesh with high computing cost), or confined to thin shells with assumed full-depth discontinuities within an element [13][14][15] based on regularized displacement discontinuity.…”

Section: Introductionmentioning

confidence: 99%

“…However, this method still has some limitations, such as the stress/strain on both sides cannot be evaluated accurately when they are split by discontinuity [12]. For XFEM approach, the enhancement is based on the Partition of Unity (PU) concept, which defines the percentage contribution from the node to a particular position [13]. The approximation 5 and enrichment functions are node-based, so the extra DoF cannot be eliminated at element level.…”

Section: Introductionmentioning

confidence: 99%

An embedded FE model for modelling reinforced concrete slabs in fire

Huang

2008

Engineering Structures

View full text Add to dashboard Cite

It is evident from a series of tests on simply supported reinforced concrete slabs that the failure of the slabs at large deflections is due to the formation of individual large cracks. This failure mode was also observed in the Cardington full-scale fire tests. Previous research indicates that the global behaviour of concrete slabs subject to large deflections can be well predicted by the smeared cracking model; however, the model cannot quantitatively predict the openings of individual cracks within the slabs at large deflection. For the discrete approach it is usually assumed that the cracks are formed along element edges, therefore continuous re-meshing is required during the analysis.Consequently, the results are mesh-dependent and the computing cost is high. In recent years, mesh independent finite element procedures, such as embedded (EFEM) and extended (XFEM) approaches, were widely used for modelling of the crack initiation and growth in structural members. However, most of the meshless models developed are either based on in-plane loading conditions or confined to thin shells with assumed full-depth cracks, which form apparent displacement jumps within an element.For a reinforced concrete slab, out-of -plane load causes coupled stretching and bending of the slab, cracks are usually initiated at discrete positions and then propagated, until at last some individual full-depth cracks are formed. Pure stretching or assumed full-depth cracking is inadequate for modelling this kind of failure. Therefore, in this research, a non-linear layered procedure with embedded weak discontinuity is developed to quantitatively model the progressive tensile failure of reinforced concrete slabs subjected to large deflections. The current model inherits the advantage of smeared approach, and at the same time, introduces the opening width of crack explicitly by taking the advantage of the better description of the kinematic characteristics of EFEM approach. A series of validations have been conducted against test data at both ambient and elevated temperatures, and as well as to identify the occurrence and severity of crack failure in reinforced concrete slabs subjected to extreme loading conditions, such as fire.

show abstract

MLS‐based variable‐node elements compatible with quadratic interpolation. Part II: application for finite crack element

Cho

2005

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYTwo-dimensional finite 'crack' elements for simulation of propagating cracks are developed using the moving least-square (MLS) approximation. The mapping from the parental domain to the physical element domain is implicitly obtained from MLS approximation, with the shape functions and their derivatives calculated and saved only at the numerical integration points. The MLS-based variable-node elements are extended to construct the crack elements, which allow the discontinuity of crack faces and the crack-tip singularity. The accuracy of the crack elements is checked by calculating the stress intensity factor under mode I loading. The crack elements turn out to be very efficient and accurate for simulating crack propagations, only with the minimal amount of element adjustment and node addition as the crack tip moves. Numerical results and comparison to the results from other works demonstrate the effectiveness and accuracy of the present scheme for the crack elements.

show abstract

Enriched partition-of-unity finite element method for stress intensity factors at crack tips

Cited by 25 publications

References 16 publications

Efficient algorithm for edge cracked geometries

Efficient algorithm for edge cracked geometries

An embedded FE model for modelling reinforced concrete slabs in fire

MLS‐based variable‐node elements compatible with quadratic interpolation. Part II: application for finite crack element

Contact Info

Product

Resources

About