# Frontiers of Structural and Civil Engineering

 Front. Struct. Civ. Eng.    2019, Vol. 13 Issue (1) : 92-102     https://doi.org/10.1007/s11709-018-0472-8
 RESEARCH ARTICLE |
Numerical investigation of circle defining curve for two-dimensional problem with general boundaries using the scaled boundary finite element method
Chung Nguyen VAN1,2()
1. Department of Civil Engineering, Faculty of Engineering, Chulalongkorn University, Thailand
2. Faculty of Civil Engineering, Ho Chi Minh City of Technology and Education, VietNam
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 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. Corresponding Authors: Chung Nguyen VAN Online First Date: 19 April 2018    Issue Date: 04 January 2019
 Cite this article: Chung Nguyen VAN. Numerical investigation of circle defining curve for two-dimensional problem with general boundaries using the scaled boundary finite element method[J]. Front. Struct. Civ. Eng., 2019, 13(1): 92-102. URL: http://journal.hep.com.cn/fsce/EN/10.1007/s11709-018-0472-8 http://journal.hep.com.cn/fsce/EN/Y2019/V13/I1/92
 Fig.1  Schematic of two-dimensional elasticity problem Fig.2  Schematic of a scaling center x0 and a defining curve C Fig.3  Schematic of a generic body $Ω$and its approximation$Ω h$ Fig.4  Schematics of (a) pressurized circular hole in linear elastic, infinite medium and (b) quarter of domain used in the analysis Fig.5  Relative percent error of displacement field versus number of elements for approximation by linear elements Fig.6  Normalized radial displacement along the radial direction Fig.7  Normalized radial and hoop stress components along the radial direction Fig.8  Schematics of (a) thick circular disk subjected to radial body force in linear elastic, finite medium and (b) quarter of domain used in the analysis Fig.9  Relative percent error of displacement field versus number of elements for approximation by linear elements Fig.10  Normalized radial displacement along the radial direction Fig.11  Normalized radial and hoop stress components along the radial direction Fig.12  Schematics of (a) pressurized circular hole in linear elastic, infinite medium and (b) quarter of domain used in the analysis Fig.13  Normalized stress component (s11/(P/r0) along the radial direction (θ=90°) Fig.14  Normalized stress component (s22/(P/r0) along the radial direction (θ=90°)
 1 J PWolf. The Scaled Boundary Finite Element Method. Chichester: John Wiley and Sons, 2003 2 J PWolf, C Song. Finite-Element Modelling of Unbounded Domain. Chichester: Jonh Wiley and Sons, 1996 3 J PWolf, C Song. Finite-element modelling of undounded media. In: Proceedings of Eleventh World Conference on Earthquake Engineering, 1996: Paper No. 70 4 CSong, J P Wolf. Body loads in scaled boundary finite-element method. Computer Methods in Applied Mechanics and Engineering, 1999, 180(1–2): 117–135 https://doi.org/10.1016/S0045-7825(99)00052-3 5 CSong, J P Wolf. 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 https://doi.org/10.1016/S0045-7825(97)00021-2 6 J PWolf, C Song. 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 https://doi.org/10.1016/S0045-7825(01)00183-9 7 J ADeeks, J P Wolf. A virtual work derivation of the scaled boundary finite-element method for elastostatics. Computational Mechanics, 2002, 28(6): 489–504 https://doi.org/10.1007/s00466-002-0314-2 8 A JDeeks. Prescribed side-face displacements in the scaled boundary finite-element method. Computers & Structures, 2004, 82(15–16): 1153–1165 https://doi.org/10.1016/j.compstruc.2004.03.024 9 A JDeeks, J P Wolf. An h-hierarchical adaptive procedure for the scaled boundary finite-element method. International Journal for Numerical Methods in Engineering, 2002, 54(4): 585–605 https://doi.org/10.1002/nme.440 10 T HVu, A J Deeks. 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 https://doi.org/10.1002/nme.1517 11 J PDoherty, A J Deeks. 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 https://doi.org/10.1016/j.compgeo.2005.07.001 12 T HVu, A J Deeks. A p-adaptive scaled boundary finite element method based on maximization of the error decrease rate. Computational Mechanics, 2008, 41(3): 441–455 https://doi.org/10.1007/s00466-007-0203-9 13 YHe, H Yang, A JDeeks. An Element-free Galerkin (EFG) scaled boundary method. Finite Elements in Analysis and Design, 2012, 62: 28–36 https://doi.org/10.1016/j.finel.2012.07.001 14 YHe, H Yang, A JDeeks. Use of Fourier shape functions in the scaled boundary method. Engineering Analysis with Boundary Elements, 2014, 41: 152–159 https://doi.org/10.1016/j.enganabound.2014.01.012 15 T HVu, A J Deeks. Using fundamental solutions in the scaled boundary finite element method to solve problems with concentrated loads. Computational Mechanics, 2014, 53(4): 641–657 https://doi.org/10.1007/s00466-013-0923-y 16 JLiu, G Lin. A scaled boundary finite element method applied to electrostatic problems. Engineering Analysis with Boundary Elements, 2012, 36(12): 1721–1732 https://doi.org/10.1016/j.enganabound.2012.06.010 17 YHe, H Yang, MXu, A JDeeks. A scaled boundary finite element method for cyclically symmetric two-dimensional elastic analysis. Computers & Structures, 2013, 120: 1–8 https://doi.org/10.1016/j.compstruc.2013.01.006 18 E TOoi, C Song, FTin-Loi, Z JYang. Automatic modelling of cohesive crack propagation in concrete using polygon scaled boundary finite elements. Engineering Fracture Mechanics, 2012, 93: 13–33 https://doi.org/10.1016/j.engfracmech.2012.06.003 19 E TOoi, C Shi, CSong, FTin-Loi, Z JYang. Dynamic crack propagation simulation with scaled boundary polygon elements and automatic remeshing technique. Engineering Fracture Mechanics, 2013, 106: 1–21 https://doi.org/10.1016/j.engfracmech.2013.02.002 20 C LChan, C Anitescu, TRabczuk. Volumetric parametrization from a level set boundary representation with PHT-splines. Computer Aided Design, 2017, 82: 29–41 https://doi.org/10.1016/j.cad.2016.08.008 21 V PNguyen, C Anitescu, S P ABordas, TRabczuk. Isogeometric analysis: an overview and computer implementation aspects. Mathematics and Computers in Simulation, 2015, 117: 89–116 https://doi.org/10.1016/j.matcom.2015.05.008 22 HGhasemi, H S Park, T Rabczuk. A level-set based IGA formulation for topology optimization of flexoelectric materials. Computer Methods in Applied Mechanics and Engineering, 2017, 313: 239–258 https://doi.org/10.1016/j.cma.2016.09.029 23 B HNguyen, X Zhuang, PWriggers, TRabczuk, M EMear, H DTran. Isogeometric symmetric Galerkin boundary element method for three-dimensional elasticity problems. Computer Methods in Applied Mechanics and Engineering, 2017, 323: 132–150 https://doi.org/10.1016/j.cma.2017.05.011 24 B HNguyen, H D Tran, C Anitescu, XZhuang, TRabczuk. An isogeometric symmetric Galerkin boundary element method for two-dimensional crack problems. Computer Methods in Applied Mechanics and Engineering, 2016, 306: 252–275 https://doi.org/10.1016/j.cma.2016.04.002 25 M HSadd. Elasticity: Theory, Application, and Numerics. Elsevier Academic Press, 2005 26 PKarasudhi. Foundation of Solid Mechanics. Kluwer Academic Publishers, 1991
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