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

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Abstract

Accurate computation of stress intensity factors for two-dimensional cracks by a dual interpolation boundary face method (DiBFM) is presented in this paper. Dual interpolation method combines traditional element polynomial interpolation and moving least-squares approximation. Dual interpolation elements are obtained by adding virtual nodes on the boundary of traditional discontinuous elements, and they unify traditional continuous and discontinuous elements. With the dual interpolation elements, both the continuous and discontinuous fields can be approximated, and the accuracy of interpolation increases by two orders compared with the corresponding discontinuous elements. In addition, a new singular element based on the dual interpolation method for modeling displacement fields around the crack tip is proposed in this paper. The stress intensity factors are extracted from the relative displacements between the crack surfaces. Using the DiBFM combined with the proposed singular element, accurate results of the stress intensity factors can be obtained. Numerical examples have demonstrated the accuracy and efficiency of the proposed method.

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References

  1. Rooke, D.P., Cartwright, D.J.: Compendium of Stress Intensity Factors. Her Majesty’s Stationery Office, London (1976)

    Google Scholar 

  2. Murakami, Y.: Stress Intensity Factors Handbook. Pergamon Press, Oxford (1987)

    Google Scholar 

  3. Brebbia, C.A., Telles, J.C.F., Wrobel, L.C.: Boundary Element Techniques: Theory and Applications in Engineering. Springer, Berlin (1984)

    Book  Google Scholar 

  4. Cisilino, A.: Linear and Nonlinear Crack Growth Using Boundary Elements. WIT Press, Southampton (2000)

    MATH  Google Scholar 

  5. Cheng, A.H.D., Cheng, D.T.: Heritage and early history of the boundary element method. Eng. Anal. Bound. Elem. 29, 268–302 (2005)

    Article  Google Scholar 

  6. Sladek, V., Sladek, J., Tanaka, M.: Nonsingular BEM formulations for thin-walled structures and elastostatic crack problems. Acta Mech. 99(1–4), 173–190 (1993)

    Article  MathSciNet  Google Scholar 

  7. Xie, G.Z., Zhang, D.H., Meng, F.N., et al.: Calculation of stress intensity factor along the 3D crack front by dual BIE with new crack front elements. Acta Mech. 228(9), 3135–3153 (2017)

    Article  MathSciNet  Google Scholar 

  8. Xu, Z., Su, C., Guan, Z.W.: Analysis of multi-crack problems by the spline fictitious boundary element method based on Erdogan fundamental solutions. Acta Mech. 229(8), 3257–3278 (2018)

    Article  MathSciNet  Google Scholar 

  9. Guo, Z., Liu, Y.J., Ma, H., et al.: A fast multipole boundary element method for modeling 2-D multiple crack problems with constant elements. Eng. Anal. Bound. Elem. 47, 1–9 (2014)

    Article  MathSciNet  Google Scholar 

  10. Liu, Y.J., Xu, N.: Modeling of interface cracks in fiber-reinforced composites with the presence of interphases using the boundary element method. Mech. Mater. 32(12), 769–783 (2000)

    Article  Google Scholar 

  11. Pan, E.: A general boundary element analysis of 2-D linear elastic fracture mechanics. Int. J. Fract. 88(1), 41–59 (1997)

    Article  MathSciNet  Google Scholar 

  12. Blandford, G.E., Ingraffea, A.R., Liggett, J.A.: Two-dimensional stress intensity factor computations using the boundary element method. Int. J. Numer. Meth. Eng. 17(3), 387–404 (1981)

    Article  Google Scholar 

  13. Wen, P.H., Fan, T.H.: The discontinuity displacement method applied to three-dimensional co-planar crack problem for any boundary value condition. Eng. Fract. Mech. 48(5), 691–702 (1994)

    Article  Google Scholar 

  14. Ma, H., Guo, Z., Dhanasekar, M., et al.: Efficient solution of multiple cracks in great number using eigen COD boundary integral equations with iteration procedure. Eng. Anal. Bound. Elem. 37(3), 487–500 (2013)

    Article  MathSciNet  Google Scholar 

  15. Xie, G.Z., Zhang, J.M., Huang, C., et al.: A direct traction boundary integral equation method for three-dimension crack problems in infinite and finite domains. Comput. Mech. 53(4), 575–586 (2014)

    Article  MathSciNet  Google Scholar 

  16. Hong, H.K., Chen, J.T.: Derivations of integral equations of elasticity. J. Eng. Mech. 114(6), 1028–1044 (1988)

    Article  Google Scholar 

  17. Chen, J.T., Hong, H.K.: Review of dual boundary element methods with emphasis on hypersingular integrals and divergent series. Appl. Mech. Rev. 52(1), 17–33 (1999)

    Article  Google Scholar 

  18. Wang, P.B., Yao, Z.H.: Fast multipole DBEM analysis of fatigue crack growth. Comput. Mech. 38(3), 223–233 (2006)

    Article  Google Scholar 

  19. Zhang, J.M., Qin, X.Y., Han, X., et al.: A boundary face method for potential problems in three dimensions. Int. J. Numer. Meth. Eng. 80(3), 320–337 (2009)

    Article  MathSciNet  Google Scholar 

  20. Zhang, J.M., Huang, C., Lu, C.J., et al.: Automatic thermal analysis of gravity dams with fast boundary face method. Eng. Anal. Bound. Elem. 41, 111–121 (2014)

    Article  Google Scholar 

  21. Zhou, F.L., Li, Y., Zhang, J.M., et al.: A time step amplification method in boundary face method for transient heat conduction. Int. J. Heat Mass Transf. 84, 671–679 (2015)

    Article  Google Scholar 

  22. Zhang, J.M., Lin, W.C., Dong, Y.Q., et al.: A double-layer interpolation method for implementation of BEM analysis of problems in potential theory. Appl. Math. Model. 51, 250–269 (2017)

    Article  MathSciNet  Google Scholar 

  23. Zhang, J.M., Lin, W.C., Dong, Y.Q.: A dual interpolation boundary face method for elasticity problems. Eur. J. Mech. A/Solids 73, 500–511 (2019)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This work was supported in part by National Natural Science Foundation of China under Grant Numbers 11602229, 11602082, 11772125 and 11902141, in part by Opening Project of Cooperative Innovation Center for Nuclear Fuel Cycle Technology and Equipment, University of South China under Grant Number 2019KFQ07, in part by Key Scientific and Technological Project of Henan Province under Grant Number 192102210227.

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Authors and Affiliations

  1. School of Mechanical Engineering, University of South China, Hengyang, 421001, China

    Yunqiao Dong

  2. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, China

    Jianming Zhang & Weicheng Lin

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  1. Yunqiao Dong
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  2. Jianming Zhang
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  3. Weicheng Lin
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Correspondence to Jianming Zhang.

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Dong, Y., Zhang, J. & Lin, W. Accurate evaluation of stress intensity factors using dual interpolation boundary face method. Acta Mech 231, 733–741 (2020). https://doi.org/10.1007/s00707-019-02573-x

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