Analysis of multi-crack problems by the spline fictitious boundary element method based on Erdogan fundamental solutions

Zong-ze, XU; Su, Cheng; Guan, Zhongwei

doi:10.1007/s00707-018-2160-0

Cited by 8 publications

(4 citation statements)

References 22 publications

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“…As the Erdogan fundamental solutions [11] for crack problems are derived by the method of complex variable function and expressed in a more complicated manner, it is more advantageous to employ SFBEM, a nonsingular indirect BEM, for the analysis of the cracked domain, in which singular integrals of the complex fundamental solutions are completely avoided [12][13][14]. In this section, the Erdogan fundamental solutions are first presented, and the stiffness matrix of the cracked superelement is then formulated using SFBEM.…”

Section: Formulation Of Stiffness Matrix For Cracked Superelement By ...mentioning

confidence: 99%

“…( 9) and ( 11) into Eq. ( 12) yields e U  A X HU (13) where X is the unknown vector consisting of the spline node parameters ()…”

Section: Consider An Arbitrary Cracked Superelement Ementioning

confidence: 99%

“…For the first category, the Kelvin fundamental solutions [8] for non-crack problems are adopted in the formulation of BEM, in which the stress boundary conditions along crack surfaces need to be satisfied and special boundary elements, e.g., the isoparametric singular boundary elements [9,10], are required at crack tips to reflect the singular behaviour. For the second category, the Erdogan fundamental solutions [11] for crack problems are employed in the BEM formulation [12][13][14], in which the stress boundary conditions on the crack surfaces are automatically satisfied and the singular behaviour at crack tips can be naturally reflected.…”

Section: Introductionmentioning

confidence: 99%

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A SFBEM–FEM coupling method for solving crack problems based on Erdogan fundamental solutions

Cai

Zong-ze

2022

J Eng Math

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The boundary element method (BEM) has proven to be an efficient approach for crack analysis in fracture mechanics, while its versatility in application to crack problems of complex structures with irregular boundaries deserves further attention. In this study, to improve the applicability to complex crack analysis, a cracked superelement is first established with BEM to model the near-crack region, and the crack problem is then solved within the frame of finite element method (FEM). The stiffness matrix of the cracked superelement is formulated using the spline fictitious boundary element method (SFBEM) based on the Erdogan fundamental solutions for an infinite plane with a single crack. The proposed superelement is further incorporated into a finite element mesh to simulate the behaviour of the crack zone, and the governing equation of the crack problem is finally established and solved using the typical procedure of FEM. After obtaining the nodal displacements of the superelement, the stress intensity factors (SIFs) of crack tips can be obtained by a backward analysis with SFBEM. The accuracy and efficiency of the proposed SFBEM-FEM coupling method are demonstrated by two numerical examples involving a rectangular plate with a central crack and a square plate with 100 horizontal cracks. The present approach is further applied to the analysis of the SIFs of multiple cracks exposed in a steel anchorage box for a hanger of a suspension bridge, which indicates the merging of the cracked superelements to the commercial FEM software is computationally efficient for the analysis of complex structures with multiple cracks.

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Section: Formulation Of Stiffness Matrix For Cracked Superelement By ...mentioning

confidence: 99%

“…( 9) and ( 11) into Eq. ( 12) yields e U  A X HU (13) where X is the unknown vector consisting of the spline node parameters ()…”

Section: Consider An Arbitrary Cracked Superelement Ementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A SFBEM–FEM coupling method for solving crack problems based on Erdogan fundamental solutions

Cai

Zong-ze

2022

J Eng Math

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“…Yu et al 20 researched the plane problem of a thermoelectric medium with collinear cracks and gave an explicit solution for SIFs. Based on Erdogan's fundamental solutions, Xu et al 21 examined multi‐crack problems. Zhu 22 proposed an analytical solution for the SIF of arbitrarily distributed offset parallel cracks in brittle solids based on the Kachanov methodology and superposition principle.…”

Section: Introductionmentioning

confidence: 99%

Theoretical analysis of two cracks in sandstone under the simultaneous action of pressure and shear stress

Huang

Wang

Zhou

et al. 2023

Fatigue Fract Eng Mat Struct

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The cracked rock mass could slide along the weak side under the action of compressive loads and shear loads in landslides; thus, the stability evaluation of the crack in rock mass media is of particular importance. The formulas of stress intensity factors (SIFs) for each crack tip are theoretically derived by implementing complex function theory. The results of the analytical solutions are then compared with the predicted results of the finite element analysis via ABAQUS software, revealing a slight relative error. Photo elastic experiment and static compression tests are conducted to verify the correctness of theoretical results. The obtained results reveal that the internal pressure leads to the increasing SIFs of mode II at crack tips. Further, the larger the difference between the horizontal and vertical compressive stresses, the more likely the occurrence of shear failure in the cracked rock mass. For the two cracks, the most dangerous point is the inner crack tip of the longer crack. K E Y W O R D S collinear cracks, digital image correlation, static compression test, stress intensity factor Highlights • Theoretical formulas of SIFs for two cracks under pressure and shear stress were proposed. • The theoretical results were verified by finite element, and they have a good agreement. • The influences of different factors on the SIFs at crack tip were discussed. • High-speed camera and DIC method were used to analyze the fracture model and strain field.

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Accurate evaluation of stress intensity factors using dual interpolation boundary face method

2019

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Analysis of multi-crack problems by the spline fictitious boundary element method based on Erdogan fundamental solutions

Cited by 8 publications

References 22 publications

A SFBEM–FEM coupling method for solving crack problems based on Erdogan fundamental solutions

A SFBEM–FEM coupling method for solving crack problems based on Erdogan fundamental solutions

Theoretical analysis of two cracks in sandstone under the simultaneous action of pressure and shear stress

Accurate evaluation of stress intensity factors using dual interpolation boundary face method

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