Stress intensity factor error index for finite element analysis with singular elements

Meshii, Toshiyuki; Watanabe, Katsuhiko

doi:10.1016/s0013-7944(02)00035-8

Cited by 6 publications

(3 citation statements)

References 10 publications

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“…Meanwhile, the hybrid method has been used in developing special crack tip elements (Tong et al 1973) and extended by Xiao and Karihaloo(2004). Meshii and Watanabe (2003) proposed an error index to evaluate the use of singular FEM to solve the SIFs. Long et al (1985Long et al ( , 1988 proposed a partitioned mixed FEM to calculate the SIFs of certain finite and infinite plates.…”

Section: Introductionmentioning

confidence: 99%

Construction of wavelet boundary element method for solving SIFs of two-dimensional plates

Yuan

Xiang

2022

Preprint

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Using one-dimensional (1D) scaling functions of B-spline wavelet on the interval (BSWI) as the interpolation functions, a wavelet boundary element method (WBEM) is presented to solve stress intensity factors (SIFs) for two-dimensional (2D) plates with singular stress fields. Firstly, to discrete the geometrical boundary, 1D wavelet-based elements are employed through the non-singular transformation matrices to transfer coefficients of wavelets expansions in the wavelet space to the physical space. The crack plate with symmetry is simplified according to symmetric conditions, and the asymmetric crack plate is divided into several subdomains to be solved according to the conditions of displacements continuity and traction equilibrium. Secondly, for the singular integrals in the WBEM, the gaussian integral and logarithmic gaussian integral are used to solve its by coordinate transformation matrices. Meanwhile, BSWI elements with good approximation characteristics and multi-resolution contain local asymptotic behavior of the stress fields at the tip of a crack, and can thus appropriately describe the singular near-tip stress fields for cracked plates. Finally, SIFs of crack tip are obtained by fitting the crack opening displacement. The performance of the method is investigated through the comparison of the results with six numerical cases of the plane stress elastic and bi-material plates.

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Section: Introductionmentioning

confidence: 99%

Construction of wavelet boundary element method for solving SIFs of two-dimensional plates

Yuan

Xiang

2022

Preprint

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“…Yang developed a special crack tip displacement discontinuity element to solve SIFs [13]. Meshii and Watanabe developed a novel singular finite element to simulate cracked plates and analyze the solution errors [14]. Daimon and Okada calculated Stress intensity factors using enriched crack tip finite elements in several typical mechanical loads [15].…”

Section: Introductionmentioning

confidence: 99%

“…(4) ~(14), f x and f y are the components of body forces in the x and y directions, u and v are the components of the displacement vector, p x and p y are the components of surface tractions in the x and y dithe vectors of the point displacements at the points of application of the point forces.…”

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confidence: 99%

Computation of Stress Intensity Factors Using Wavelet-Based Element

2016

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A new approach for the analysis of stress intensity factors (SIFs) for cracked plane plate is proposed based on the wavelet finite element method using the scaling functions of B-spline wavelet on the interval (BSWI). The performance of the method is investigated through the comparison of the results with the available numerical examples in the literate. It is shown that the solution quality is much better than that of the traditional adaptive finite element method. Though the method is applied to plane structures in this paper, it can be extended to solving problems for other classes of structures.

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Efficient algorithm for edge cracked geometries

Englund

2005

Numerical Meth Engineering

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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.

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Stress intensity factor error index for finite element analysis with singular elements

Cited by 6 publications

References 10 publications

Construction of wavelet boundary element method for solving SIFs of two-dimensional plates

Construction of wavelet boundary element method for solving SIFs of two-dimensional plates

Computation of Stress Intensity Factors Using Wavelet-Based Element

Efficient algorithm for edge cracked geometries

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