Acta Mechanica Solida Sinica

, Volume 30, Issue 2, pp 123–136 | Cite as

A refined global-local approach for evaluation of singular stress field based on scaled boundary finite element method

  • Lin Pang
  • Gao Lin
  • Zhiqiang Hu


A refined global-local approach based on the scaled boundary finite element method (SBFEM) is proposed to improve the accuracy of predicted singular stress field. The proposed approach is carried out in conjunction with two steps. First, the entire structure is analyzed by employing an arbitrary numerical method. Then, the interested region, which contains stress singularity, is re-solved using the SBFEM by placing the scaling center right at the singular stress point with the boundary conditions evaluated from the first step imposed along the whole boundary including the side-faces. Benefiting from the semi-analytical nature of the SBFEM, the singular stress field can be predicted accurately without highly refined meshes. It provides the FEM or other numerical methods with a rather simple and convenient way to improve the accuracy of stress analysis. Numerical examples validate the effectiveness of the proposed approach in dealing with various kinds of problems. © 2017 Published by Elsevier Ltd on behalf of Chinese Society of Theoretical and Applied Mechanics.


SBFEM Stress singularity Boundary conditions Side-faces Dam-reservoir-foundation interaction Thermal stress 


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  1. 1.
    T. Belytschko, R. Cracie, G. Ventura, A review of extended/generalized finite element methods for material modeling, Model. Simul. Mater. Sci. Eng. 17 (4) (2009) 043001.CrossRefGoogle Scholar
  2. 2.
    J.P. Wolf, C.M. Song, The scaled boundary finite-element method—a primer: derivations, Comput. Struct. 78 (1) (2000) 191–210.CrossRefGoogle Scholar
  3. 3.
    C. Li, L. Tong, A mixed SBFEM for stress singularities in nearly incompressible multi-materials, Comput. Struct. 157 (2015) 19–30.CrossRefGoogle Scholar
  4. 4.
    C. Song, F. Tin-Loi, W. Gao, Transient dynamic analysis of interface cracks in anisotropic bimaterials by the scaled boundary finite-element method, Int. J. Solids Struct. 47 (7–8) (2010) 978–989.CrossRefzbMATHGoogle Scholar
  5. 5.
    X. Long, C. Jiang, X. Han, et al., The Scaled boundary finite element second order sensitivity design and fracture mechanics analysis, Chin. J. Solid Mech. 36 (01) (2015) 42–54 (in Chinese).Google Scholar
  6. 6.
    S.S. Chen, Q.H. Li, Y.H. Liu, et al., Mode III 2-D fracture analysis by the scaled boundary finite element method, Acta Mech. Solida Sin. 26 (6) (2013) 619–628.CrossRefGoogle Scholar
  7. 7.
    Z.J. Yang, A.J. Deeks, Fully-automatic modelling of cohesive crack growth using a finite element-scaled boundary finite element coupled method, Eng. Fract. Mech. 74 (16) (2007) 2547–2573.CrossRefzbMATHGoogle Scholar
  8. 8.
    E.T. Ooi, C.M. Song, F. Tin-Loi, et al., Polygon scaled boundary finite elements for crack propagation modelling, Int. J. Numer. Methods Eng. 91 (3) (2012) 319–342.MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Z. Yang, Application of scaled boundary finite element method in static and dynamic fracture problems, Acta Mech. Sin. 22 (3) (2006) 243–256.CrossRefzbMATHGoogle Scholar
  10. 10.
    M. Shi, Y. Xu, H. Zhong, et al., Modelling of crack propagation for composite materials based on polygon scaled boundary finite elements, Eng. Mech. 31 (7) (2014) 1–7.CrossRefGoogle Scholar
  11. 11.
    Y. Wang, L. Gao, Z.Q. Hu, Novel nonreflecting boundary condition for an infinite reservoir based on the scaled boundary finite-element method, J. Eng. Mech. 141 (2015).Google Scholar
  12. 12.
    G. Lin, Y. Wang, Z.Q. Hu, An efficient approach for frequency-domain and time-domain hydrodynamic analysis of dam-reservoir systems, Earthq. Eng. Struct. Dyn. 41 (13) (2012) 1725–1749.CrossRefGoogle Scholar
  13. 13.
    Chen D., Du C. Dynamic analysis of bounded domains by SBFE and the improved continued-fraction expansion. Chin. J. Theor. Appl. Mech. 2013(02): 297–301 (in Chinese).Google Scholar
  14. 14.
    S.M. Li, H. Liang, A.M. Li, A semi-analytical solution for characteristics of a dam-reservoir system with absorptive reservoir bottom, J. Hydrodyn. 20 (6) (2008) 727–734.CrossRefGoogle Scholar
  15. 15.
    J.P. Wolf, C.M. Song, Finite-element Modeling of Unbounded Media, John Wiley, Chichester, 1996.zbMATHGoogle Scholar
  16. 16.
    B. Radmanović, C. Katz, A high performance scaled boundary finite element method, IOP Conference Series: Materials Science and Engineering, 10, IOP Publishing, 1996, p. 012214.CrossRefGoogle Scholar
  17. 17.
    Junyi Y., Feng J., Zhang C. Time domain coupling procedure for FE and SBFE based on linear system theory. J. Tsinghua Univ. 2003(11): 1554–1557.Google Scholar
  18. 18.
    A.J. Deeks, Prescribed side-face displacements in the scaled boundary finite-element method, Comput. Struct. 82 (15–16) (2004) 1153–1165.CrossRefGoogle Scholar
  19. 19.
    A.J. Deeks, J.P. Wolf, A virtual work derivation of the scaled boundary finite-element method for elastostatics, Comput. Mech. 28 (6) (2002) 489–504.MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    E.T. Ooi, Z.J. Yang, A hybrid finite element-scaled boundary finite element method for crack propagation modelling, Comput. Methods Appl. Mech. Eng. 199 (17–20) (2010) 1178–1192.MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    M.C. Genes, S. Kocak, A combined finite element based soil–structure interaction model for large-scale systems and applications on parallel platforms, Eng. Struct. 24 (9) (2002) 1119–1131.CrossRefGoogle Scholar
  22. 22.
    E. Protopapadakis, M. Schauer, E. Pierri, et al., A genetically optimized neural classifier applied to numerical pile integrity tests considering concrete piles, Comput. Struct. 162 (2016) 68–79.CrossRefGoogle Scholar
  23. 23.
    K.M. Mao, C.T. Sun, A refined global-local finite element analysis method, Int. J. Numer. Methods Eng. 32 (1991) 29–43.CrossRefzbMATHGoogle Scholar
  24. 24.
    C.M. Song, A matrix function solution for the scaled boundary finite-element equation in statics, Comput. Methods Appl. Mech. Eng. 193 (23–26) (2004) 2325–2356.MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    C.M. Song, Analysis of singular stress fields at multi-material corners under thermal loading, Int. J. Numer. Methods Eng. 65 (2006) 620–652.CrossRefzbMATHGoogle Scholar
  26. 26.
    C. Li, E.T. Ooi, C.M. Song, et al., SBFEM for fracture analysis of piezoelectric composites under thermal load, Int. J. Solids. Struct. 52 (2015) 114–129.CrossRefGoogle Scholar
  27. 27.
    M.H. Bazyar, C.M. Song, Time-harmonic response of non-homogeneous elastic unbounded domains using the scaled boundary finite-element method, Earthq. Eng. Struct. Dyn. 35 (3) (2006) 357–383.CrossRefGoogle Scholar
  28. 28.
    A. Yaseri, M.H. Bazyar, N. Hataf, 3D coupled scaled boundary finite-element/finite-element analysis of ground vibrations induced by underground train movement, Comput. Geotech. 60 (2014) 1–8.CrossRefGoogle Scholar
  29. 29.
    N.M. Syed, B.K. Maheshwari, Improvement in the computational efficiency of the coupled FEM-SBFEM approach for 3D seismic SSI analysis in the time domain, Comput. Geotech. 67 (2015) 204–212.CrossRefGoogle Scholar
  30. 30.
    G. Lin, Y. Zhang, Y. Wang, Z.Q. Hu, Coupled isogeometric and scaled boundary isogeometric approach for earthquake response analysis of dam-reservoir-foundation system, in: Proceedings of the 15th world conference of earth-quake engineering, Lisbon, 2012.Google Scholar
  31. 31.
    A.J. Deeks, J.P. Wolf, Semi-analytical elastostatic analysis of unbounded two-dimensional domains, Int. J. Numer. Anal. Methods Geomech. 26 (11) (2002) 1031–1057.CrossRefzbMATHGoogle Scholar
  32. 32.
    C.M. Song, F. Tin-Loi, W. Gao, A definition and evaluation procedure of generalized stress intensity factors at cracks and multi-material wedges, Eng. Fract. Mech. 77 (12) (2010) 2316–2336.CrossRefGoogle Scholar
  33. 33.
    D.P. Rooke, D.J. Cartwright, Compendium of Stress Intensity Factors, Her Majesty’s Office, London, 1976, pp. 233–234.Google Scholar
  34. 34.
    Z.L. Xu, Elasticity (Volume One), 4th ed., Higher Education Press, Beijing, 2006, pp. 81–83.Google Scholar
  35. 35.
    L. Bouhala, A. Makradi, S. Belouettar, Thermal and thermo-mechanical influence on crack propagation using an extended mesh free method, Eng. Fract. Mech. 88 (2012) 35–48.CrossRefGoogle Scholar
  36. 36.
    D.K.L. Tsang, S.O. Oyadiji, A.Y.T. Leung, Two-dimensional fractal-like finite element method for thermoelastic crack analysis, Int. J. Solids Struct. 44 (24) (2007) 7862–7876.CrossRefzbMATHGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2017

Authors and Affiliations

  1. 1.State Key Laboratory of Coastal and Offshore EngineeringDalian University of TechnologyDalianChina
  2. 2.Institute of Earthquake Engineering, Faculty of Infrastructure EngineeringDalian University of TechnologyDalianChina

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