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

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Abstract

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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Acknowledgements

The research is funded by the National Natural Science Foundation of China (51678252, 52178479) and the Guangdong Provincial Key Laboratory of Modern Civil Engineering Technology (2021B1212040003).

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Authors and Affiliations

  1. School of Civil Engineering and Transportation, South China University of Technology, Guangzhou, 510640, China

    Cheng Su, Kemin Cai & Zhi Xu

  2. State Key Laboratory of Subtropical Building Science, South China University of Technology, Guangzhou, 510640, China

    Cheng Su

  3. Guangdong Artificial Intelligence and Digital Economy Laboratory, Guangzhou, 510335, China

    Cheng Su

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  1. Cheng Su
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  2. Kemin Cai
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  3. Zhi Xu
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Correspondence to Cheng Su.

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Su, C., Cai, K. & Xu, Z. A SFBEM–FEM coupling method for solving crack problems based on Erdogan fundamental solutions. J Eng Math 138, 3 (2023). https://doi.org/10.1007/s10665-022-10247-2

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