Mixed-mode Bueckner weight functions using boundary element analysis

Aliabadi, M.H.; Rooke, D.P.; Cartwright, D.J.

doi:10.1007/bf00019768

Cited by 63 publications

(25 citation statements)

References 9 publications

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“…The plate is subjected to tensile loading of σ 1 and σ 2 in the x 1 -and x 2 -directions, respectively. The exact stress intensity factor is a function of the angle of the crack β with the x 2 -axial and is given by Aliabadi [17] as…”

Section: Oblique Crack In An Infinite Platementioning

confidence: 99%

A novel virtual node method for polygonal elements

唐旭海

吴圣川

郑超

et al. 2009

Appl. Math. Mech.-Engl. Ed.

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A novel polygonal finite element method (PFEM) based on partition of unity is proposed, termed the virtual node method (VNM). To test the performance of the present method, numerical examples are given for solid mechanics problems. With a polynomial form, the VNM achieves better results than those of traditional PFEMs, including the Wachspress method and the mean value method in standard patch tests. Compared with the standard triangular FEM, the VNM can achieve better accuracy. With the ability to construct shape functions on polygonal elements, the VNM provides greater flexibility in mesh generation. Therefore, several fracture problems are studied to demonstrate the potential implementation. With the advantage of the VNM, the convenient refinement and remeshing strategy are applied.

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Section: Oblique Crack In An Infinite Platementioning

confidence: 99%

A novel virtual node method for polygonal elements

唐旭海

吴圣川

郑超

et al. 2009

Appl. Math. Mech.-Engl. Ed.

View full text Add to dashboard Cite

show abstract

“…9a). The exact values of stress intensity factors are given by Aliabadi et al [73]: where σ 1 and σ 2 are the tensile loads in the x 1 -and x 2 -directions, a is the half-length of the crack, and β is the inclination angle with respect to the vertical axis. The ratio of the length of the crack to the length of the plate (a/w) is set to 1/10 so that the problem domain can adequately represent an infinite domain.…”

Section: Stress Intensity Factor Calculationsmentioning

confidence: 99%

Generalized Gaussian quadrature rules for discontinuities and crack singularities in the extended finite element method

Mousavi

Sukumar

2010

Computer Methods in Applied Mechanics and Engineering

112

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New Gaussian integration schemes are presented for the efficient and accurate evaluation of weak form integrals in the extended finite element method.For discontinuous functions, we construct Gauss-like quadrature rules over arbitrarily-shaped elements in two dimensions without the need for partitioning the finite element. A point elimination algorithm is used in the construction of the quadratures, which ensures that the final quadratures have minimal number of Gauss points. For weakly singular integrands, we apply a polar transformation that eliminates the singularity so that the integration can be performed efficiently and accurately. Numerical examples in elastic fracture using the extended finite element method are presented to illustrate the performance of the new integration techniques.

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“…15a. The exact stress intensity factors are a function of the angle of the crack β with the x 2 -axis and are given by [43] …”

Section: Oblique Crack In An Infinite Platementioning

confidence: 99%

Extended finite element method on polygonal and quadtree meshes

Tabarraei

Sukumar

2008

Computer Methods in Applied Mechanics and Engineering

143

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In this paper, we present mesh-independent modeling of discontinuous fields on polygonal and quadtree finite element meshes. This approach falls within the class of extended and generalized finite element methods, where the partition of unity framework is used to introduce additional (enrichment) functions within the classical displacement-based finite element approximation. For crack modeling, a discontinuous function and the two-dimensional asymptotic crack-tip fields are used as enrichment functions. Linearly complete partition of unity approximations are adopted on polygonal (convex and nonconvex elements) and quadtree meshes. Excellent agreement with reference solution results is obtained for mixed-mode stress intensity factors on benchmark crack problems, and crack growth simulations without remeshing are conducted on polygonal and quadtree meshes to reveal the potential of the proposed techniques in computational failure mechanics.

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Mixed-mode Bueckner weight functions using boundary element analysis

Cited by 63 publications

References 9 publications

A novel virtual node method for polygonal elements

A novel virtual node method for polygonal elements

Generalized Gaussian quadrature rules for discontinuities and crack singularities in the extended finite element method

Extended finite element method on polygonal and quadtree meshes

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