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Frontiers of Structural and Civil Engineering

, Volume 13, Issue 1, pp 201–214 | Cite as

Scaled boundary finite element method with exact defining curves for two-dimensional linear multi-field media

  • Jaroon Rungamornrat
  • Chung Nguyen VanEmail author
Research Article
  • 33 Downloads

Abstract

This paper presents an efficient and accurate numerical technique based upon the scaled boundary finite element method for the analysis of two-dimensional, linear, second-order, boundary value problems with a domain completely described by a circular defining curve. The scaled boundary finite element formulation is established in a general framework allowing single-field and multi-field problems, bounded and unbounded bodies, distributed body source, and general boundary conditions to be treated in a unified fashion. The conventional polar coordinates together with a properly selected scaling center are utilized to achieve the exact description of the circular defining curve, exact geometry of the domain, and exact spatial differential operators. Standard finite element shape functions are employed in the discretization of both trial and test functions in the circumferential direction and the resulting eigenproblem is solved by a selected efficient algorithm. The computational performance of the implemented procedure is then fully investigated for various scenarios to demonstrate the accuracy in comparison with standard linear elements.

Keywords

multi-field problems defining curve exact geometry general boundary conditions SBFEM 

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Notes

Acknowledgements

The authors gratefully acknowledge the support provided by CU Scholarship for ASEAN Countries 2013 and Thailand Research Fund (Grant No. RSA5980032).

References

  1. 1.
    Wolf J P. The Scaled Boundary Finite Element Method. Chichester: John Wiley & Sons, 2003Google Scholar
  2. 2.
    Wolf J P, Song C. Finite-Element Modelling of Unbounded Domain. Chichester: John Wiley & Sons, 1996zbMATHGoogle Scholar
  3. 3.
    Deeks J A, Wolf J P. A virtual work derivation of the scaled boundary finite-element method for elastostatics. Computational Mechanics, 2002, 28(6): 489–504MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Cruse T A. Boundary Element Analysis in Computational Fracture Mechanics. Dordrecht: Kluwer Academic Publishers, 1988CrossRefzbMATHGoogle Scholar
  5. 5.
    Brebbia C A, Dominguez J. Boundary Elements: An Introductory Course. 2nd ed. New York: McGraw-Hill, 1989zbMATHGoogle Scholar
  6. 6.
    Bonnet M, Maier G, Polizzotto C. Symmetric Galerkin boundary element methods. Applied Mechanics Reviews, 1998, 51(11): 669–703CrossRefGoogle Scholar
  7. 7.
    Liu J, Lin G A. A scaled boundary finite element method applied to electrostatic problems. Engineering Analysis with Boundary Elements, 2012, 36(12): 1721–1732MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Li C, Man H, Song C, Gao W. Fracture analysis of piezoelectric materials using the scaled boundary finite element method. Engineering Fracture Mechanics, 2013, 97: 52–71CrossRefGoogle Scholar
  9. 9.
    Vu T H, Deeks A J. Using fundamental solutions in the scaled boundary finite element method to solve problems with concentrated loads. Computational Mechanics, 2014, 53(4): 641–657MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Ooi E T, Song C, Tin-Loi F. A scaled boundary polygon formulation for elasto-plastic analyses. Computer Methods in Applied Mechanics and Engineering, 2005, 268: 905–937MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Doherty J P, Deeks A J. Adaptive coupling of the finite-element and scaled boundary finite-element methods for non-linear analysis of unbounded media. Computers and Geotechnics, 2015, 32(6): 436–444CrossRefGoogle Scholar
  12. 12.
    Li F, Ren P. A novel solution for heat conduction problems by extending scaled boundary finite element method. International Journal of Heat and Mass Transfer, 2016, 95: 678–688CrossRefGoogle Scholar
  13. 13.
    Li M, Zhang H, Guan H. Study of offshore monopole behavior due to ocean waves. Ocean Engineering, 2011, 38(17–18): 1946–1956CrossRefGoogle Scholar
  14. 14.
    Meng X N, Zou Z J. Radiation and diffraction of water waves by an infinite horizontal structure with a sidewall using SBFEM. Ocean Engineering, 2013, 60: 193–199CrossRefGoogle Scholar
  15. 15.
    Gravenkamp H, Birk C, Song C. The computation of dispersion relations for axisymmetric waveguides using the scaled boundary finite element method. Ultrasonics, 2014, 54(5): 1373–1385CrossRefGoogle Scholar
  16. 16.
    Li C, Ooi E T, Song C, Natarajan S. SBFEM for fracture analysis of piezoelectric composites under thermal load. International Journal of Solids and Structures, 2015, 52: 114–129CrossRefGoogle Scholar
  17. 17.
    Song C, Wolf J P. The scaled boundary finite-element method —alias consistent infinitesimal finite-element cell method—for elastodynamics. Computer Methods in Applied Mechanics and Engineering, 1997, 147(3–4): 329–355MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Wolf J P, Song C. The scaled boundary finite-element method: A fundamental solution-less boundary-element method. Computer Methods in Applied Mechanics and Engineering, 2001, 190(42): 5551–5568CrossRefzbMATHGoogle Scholar
  19. 19.
    Deeks A J. Prescribed side-face displacements in the scaled boundary finite-element method. Computers & Structures, 2004, 82(15–16): 1153–1165CrossRefGoogle Scholar
  20. 20.
    Song C, Wolf J P. Body loads in scaled boundary finite-element method. Computer Methods in Applied Mechanics and Engineering, 1999, 180(1–2): 117–135CrossRefzbMATHGoogle Scholar
  21. 21.
    He Y, Yang H, Deeks A J. An element-free Galerkin (EFG) scaled boundary method. Finite Elements in Analysis and Design, 2012, 62: 28–36MathSciNetCrossRefGoogle Scholar
  22. 22.
    Vu T H, Deeks A J. Use of higher-order shape functions in the scaled boundary finite element method. International Journal for Numerical Methods in Engineering, 2006, 65(10): 1714–1733MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    He Y, Yang H, Deeks A J. Use of Fourier shape functions in the scaled boundary method. Engineering Analysis with Boundary Elements, 2014, 41: 152–159MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Deeks A J, Wolf J P. An h-hierarchical adaptive procedure for the scaled boundary finite-element method. International Journal for Numerical Methods in Engineering, 2002, 54(4): 585–605CrossRefzbMATHGoogle Scholar
  25. 25.
    Vu T H, Deeks A J. A p-adaptive scaled boundary finite element method based on maximization of the error decrease rate. Computational Mechanics, 2007, 41(3): 441–455MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Deeks A J, Augarde C E. A meshless local Petrov-Galerkin scaled boundary method. Computational Mechanics, 2005, 36(3): 159–170MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Chung N V. Analysis of two-dimensional linear field problems by scaled boundary finite element method. Dissertation for the Doctoral Degree. Bangkok: Chulalongkorn University, 2016Google Scholar
  28. 28.
    Chung N V, Jaroon R, Phoonsak P. Scaled boundary finite element method for two-dimensional linear multi-field media. Engineering Journal (Thailand), 2017, 21(7): 334–360Google Scholar
  29. 29.
    Ooi E T, Song C, Tin-Loi F, Yang Z J. Automatic modelling of cohesive crack propagation in concrete using polygon scaled boundary finite elements. Engineering Fracture Mechanics, 2012, 93: 13–33CrossRefzbMATHGoogle Scholar
  30. 30.
    Ooi E T, Shi C, Song C, Tin-Loi F, Yang Z J. Dynamic crack propagation simulation with scaled boundary polygon elements and automatic remeshing technique. Engineering Fracture Mechanics, 2013, 106: 1–21CrossRefGoogle Scholar
  31. 31.
    Dieringer R, Becker W. A new scaled boundary finite element formulation for the computation of singularity orders at cracks and notches in arbitrarily laminated composites. Composite Structures, 2015, 123: 263–270CrossRefGoogle Scholar
  32. 32.
    Natarajan S, Wang J, Song C, Birk C. Isogeometric analysis enhanced by the scaled boundary finite element method. Computer Methods in Applied Mechanics and Engineering, 2015, 283: 733–762MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Nguyen B H, Tran H D, Anitescu C, Zhuang X, Rabczuk T. Isogeometric symmetric Galerkin boundary element method for three-dimensional elasticity problems. Computer Methods in Applied Mechanics and Engineering, 2017, 323: 132–150MathSciNetCrossRefGoogle Scholar
  34. 34.
    Nguyen B H, Tran H D, Anitescu C, Zhuang X, Rabczuk T. An isogeometric symmetric Galerkin boundary element method for two-dimensional crack problems. Computer Methods in Applied Mechanics and Engineering, 2016, 306: 252–275MathSciNetCrossRefGoogle Scholar
  35. 35.
    Li P, Liu J, Lin G, Zhang P, Xu B. A combination of isogeometric technique and scaled boundary method for solution of the steady-state heat transfer problems in arbitrary plane domain with Robin boundary. Engineering Analysis with Boundary Elements, 2017, 82: 43–56MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Li F, Qiang T. The scaled boundary finite element analysis of seepage problems in multi-material regions. International Journal of Computational Methods, 2012, 9(1): 1240008MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Applied Mechanics and Structures Research Unit, Department of Civil Engineering, Faculty of EngineeringChulalongkorn UniversityBangkokThailand
  2. 2.Faculty of Civil EngineeringHo Chi Minh City of Technology and EducationHo Chi MinhVietnam

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