Frontiers of Structural and Civil Engineering

, Volume 13, Issue 1, pp 92–102

Numerical investigation of circle defining curve for two-dimensional problem with general boundaries using the scaled boundary finite element method

• Chung Nguyen Van
Research Article

Abstract

The scaled boundary finite element method (SBFEM) is applied to the static analysis of two dimensional elasticity problem, boundary value problems domain with the domain completely described by a circular defining curve. The scaled boundary finite element equations is formulated within a general framework integrating the influence of the distributed body force, general boundary conditions, and bounded and unbounded domain. This paper investigates the possibility of using exact geometry to form the exact description of the circular defining curve and the standard finite element shape function to approximate the defining curve. Three linear elasticity problems are presented to verify the proposed method with the analytical solution. Numerical examples show the accuracy and efficiency of the proposed method, and the performance is found to be better than using standard linear element for the approximation defining curve on the scaled boundary method.

Keywords

exact geometry circular defining curve general boundaries SBFEM

Notes

Acknowledgements

The author gratefully acknowledge the support provided by CU scholarship for ASEAN Countries 2013.

References

1. 1.
Wolf J P. The Scaled Boundary Finite Element Method. Chichester:John Wiley and Sons, 2003Google Scholar
2. 2.
Wolf J P, Song C. Finite-Element Modelling of Unbounded Domain. Chichester: Jonh Wiley and Sons, 1996
3. 3.
Wolf J P, Song C. Finite-element modelling of undounded media. In: Proceedings of Eleventh World Conference on Earthquake Engineering, 1996: Paper No. 70Google Scholar
4. 4.
Song C, Wolf J P. Body loads in scaled boundary finite-element method. Computer Methods in Applied Mechanics and Engineering, 1999, 180(1–2): 117–135
5. 5.
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): 329–355
6. 6.
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): 5551–5568
7. 7.
Deeks J A, Wolf J P. A virtual work derivation of the scaled boundary finite-element method for elastostatics. Computational Mechanics, 2002, 28(6): 489–504
8. 8.
Deeks A J. Prescribed side-face displacements in the scaled boundary finite-element method. Computers & Structures, 2004, 82(15–16): 1153–1165
9. 9.
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): 585–605
10. 10.
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): 1714–1733
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, 2005, 32(6): 436–444
12. 12.
Vu T H, Deeks A J. A p-adaptive scaled boundary finite element method based on maximization of the error decrease rate. Computational Mechanics, 2008, 41(3): 441–455
13. 13.
He Y, Yang H, Deeks A J. An Element-free Galerkin (EFG) scaled boundary method. Finite Elements in Analysis and Design, 2012, 62: 28–36
14. 14.
He Y, Yang H, Deeks A J. Use of Fourier shape functions in the scaled boundary method. Engineering Analysis with Boundary Elements, 2014, 41: 152–159
15. 15.
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): 641–657
16. 16.
Liu J, Lin G. A scaled boundary finite element method applied to electrostatic problems. Engineering Analysis with Boundary Elements, 2012, 36(12): 1721–1732
17. 17.
He Y, Yang H, Xu M, Deeks A J. A scaled boundary finite element method for cyclically symmetric two-dimensional elastic analysis. Computers & Structures, 2013, 120: 1–8
18. 18.
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: 13–33
19. 19.
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: 1–21
20. 20.
Chan C L, Anitescu C, Rabczuk T. Volumetric parametrization from a level set boundary representation with PHT-splines. Computer Aided Design, 2017, 82: 29–41
21. 21.
Nguyen V P, Anitescu C, Bordas S P A, Rabczuk T. Isogeometric analysis: an overview and computer implementation aspects. Mathematics and Computers in Simulation, 2015, 117: 89–116
22. 22.
Ghasemi H, Park H S, Rabczuk T. A level-set based IGA formulation for topology optimization of flexoelectric materials. Computer Methods in Applied Mechanics and Engineering, 2017, 313: 239–258
23. 23.
Nguyen B H, Zhuang X, Wriggers P, Rabczuk T, Mear ME, Tran H D. Isogeometric symmetric Galerkin boundary element method for three-dimensional elasticity problems. Computer Methods in Applied Mechanics and Engineering, 2017, 323: 132–150
24. 24.
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: 252–275
25. 25.
26. 26.
Karasudhi P. Foundation of Solid Mechanics. Kluwer Academic Publishers, 1991

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

Authors and Affiliations

1. 1.Department of Civil Engineering, Faculty of EngineeringChulalongkorn UniversityBangkokThailand
2. 2.Faculty of Civil EngineeringHo Chi Minh City of Technology and EducationHo Chi MinhViet Nam