Calculation of stress intensity factor along the 3D crack front by dual BIE with new crack front elements

Xie, Guizhong; Zhang, Dehai; Meng, Fannian; Du, Wenliao; Zhang, Jianming

doi:10.1007/s00707-017-1875-7

Cited by 16 publications

(10 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where, in the crack surface, the CODs are Δu k (Q) which is u k (Q + ) − u k (Q − ), in which u k (Q + ) and u k (Q − ) represent displacements on the two crack surfaces. Equations (8) and (9) are collocated on noncrack surfaces and crack surfaces, respectively.…”

Section: The Displacement and Traction Boundary Integral Equationsmentioning

confidence: 99%

“…To achieve high computational accuracy, the integrals with singularity in the DBEM must be accurately computed [9,12,15,[19][20][21][22][23][24][25][26][27]. In this section, the singular integral is gradually computed through three steps.…”

Section: Regularization Of Singular Integralsmentioning

confidence: 99%

“…After these three steps of operation, the Cauchy principle value integral and the Hadamard finite part integral can be accurately calculated. A more detailed discussion about these two types of integrals can be found in [9,15].…”

Section: Regularization Of Singular Integralsmentioning

confidence: 99%

“…To cope with the singular integrals, the element subdivision is necessary in the 3D BEM [9,[19][20][21][22][23][24][25]. Moreover, a suitable integral area is of great importance to improving the accuracy of singular integral calculation, especially for Cauchy or Hadamard finite part integrals.…”

Section: Triangular Element Subdivision Techniquementioning

confidence: 99%

“…In the 3D BEM, however, the available crack front elements are only of quadrilateral type, such as 8-node crack front elements proposed by Mi and Aliabadi [5], 9-node crack front elements in the pioneering work of Li et al [6], and also crack front elements in the work of Pan and Yuan [7]. e crack front elements of the triangular type have not been found by authors [8,9]. Due to the general geometric adaptability of the triangular mesh, a special triangular crack front element of which one edge lies in the crack front for the BEM is also necessary.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A Generation of Special Triangular Boundary Element Shape Functions for 3D Crack Problems

Xie

Zhou

2020

Mathematical Problems in Engineering

Self Cite

View full text Add to dashboard Cite

This paper focuses on tackling the two drawbacks of the dual boundary element method (DBEM) when solving crack problems with a discontinuous triangular element: low accuracy of the calculation of integrals with singularity and crack front element must be utilized to model the square-root property of displacement. In order to calculate the integrals with higher order singularity, the triangular elements are segmented into several subregions which consist of subtriangles and subpolygons. The singular integrals in those subtriangles are handled by the singularity subtraction technique in the integration space and can be regularized and accurately calculated. For the nearly singular integrals in those subpolygons, the element subdivision technique is employed to improve the calculation accuracy. In addition, considering the location of the crack front in the element, special crack front elements are constructed based on a 6-node discontinuous triangular element, in which the displacement extrapolation method is introduced to obtain the stress intensity factors (SIFs) without consideration of orthogonalization of the crack front mesh. Several numerical results are investigated to fully verify the validation of the presented approach.

show abstract

Section: The Displacement and Traction Boundary Integral Equationsmentioning

confidence: 99%

Section: Regularization Of Singular Integralsmentioning

confidence: 99%

Section: Regularization Of Singular Integralsmentioning

confidence: 99%

Section: Triangular Element Subdivision Techniquementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Generation of Special Triangular Boundary Element Shape Functions for 3D Crack Problems

Xie

Zhou

2020

Mathematical Problems in Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

Boundary integrated neural networks and code for acoustic radiation and scattering

Qu,

Gu,

Zhao

et al. 2024

Int Journal of Mech Sys Dyn

View full text Add to dashboard Cite

This paper presents a novel approach called the boundary integrated neural networks (BINNs) for analyzing acoustic radiation and scattering. The method introduces fundamental solutions of the time‐harmonic wave equation to encode the boundary integral equations (BIEs) within the neural networks, replacing the conventional use of the governing equation in physics‐informed neural networks (PINNs). This approach offers several advantages. First, the input data for the neural networks in the BINNs only require the coordinates of “boundary” collocation points, making it highly suitable for analyzing acoustic fields in unbounded domains. Second, the loss function of the BINNs is not a composite form and has a fast convergence. Third, the BINNs achieve comparable precision to the PINNs using fewer collocation points and hidden layers/neurons. Finally, the semianalytic characteristic of the BIEs contributes to the higher precision of the BINNs. Numerical examples are presented to demonstrate the performance of the proposed method, and a MATLAB code implementation is provided as supplementary material.

show abstract

Novel boundary crack front elements with Williams' eigenexpansion properties for 3D crack analysis

et al. 2022

View full text Add to dashboard Cite

Calculation of stress intensity factor along the 3D crack front by dual BIE with new crack front elements

Cited by 16 publications

References 38 publications

A Generation of Special Triangular Boundary Element Shape Functions for 3D Crack Problems

A Generation of Special Triangular Boundary Element Shape Functions for 3D Crack Problems

Boundary integrated neural networks and code for acoustic radiation and scattering

Novel boundary crack front elements with Williams' eigenexpansion properties for 3D crack analysis

Contact Info

Product

Resources

About