|
|
Scaled boundary finite element method with exact defining curves for two-dimensional linear multi-field media |
Jaroon RUNGAMORNRAT1, Chung Nguyen VAN1,2() |
1. Applied Mechanics and Structures Research Unit, Department of Civil Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok 10330, Thailand 2. Faculty of Civil Engineering, Ho Chi Minh City of Technology and Education, Ho Chi Minh 721400, Vietnam |
|
|
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
|
Corresponding Author(s):
Chung Nguyen VAN
|
Just Accepted Date: 14 May 2018
Online First Date: 27 June 2018
Issue Date: 04 January 2019
|
|
1 |
J PWolf. The Scaled Boundary Finite Element Method. Chichester: John Wiley & Sons, 2003
|
2 |
J PWolf, C Song. Finite-Element Modelling of Unbounded Domain. Chichester: John Wiley & Sons, 1996
|
3 |
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
|
4 |
T ACruse. Boundary Element Analysis in Computational Fracture Mechanics. Dordrecht: Kluwer Academic Publishers, 1988
|
5 |
C ABrebbia, J Dominguez. Boundary Elements: An Introductory Course. 2nd ed. New York: McGraw-Hill, 1989
|
6 |
MBonnet, G Maier, CPolizzotto. Symmetric Galerkin Boundary Element Methods. Applied Mechanics Reviews, 1998, 51(11): 669–703
https://doi.org/10.1115/1.3098983
|
7 |
JLiu, G A 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
|
8 |
CLi, H Man, CSong, WGao. Fracture analysis of piezoelectric materials using the scaled boundary finite element method. Engineering Fracture Mechanics, 2013, 97: 52–71
https://doi.org/10.1016/j.engfracmech.2012.10.019
|
9 |
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
|
10 |
E TOoi, C Song, FTin-Loi. A scaled boundary polygon formulation for elasto-plastic analyses. Computer Methods in Applied Mechanics and Engineering, 2005, 268: 905–937
https://doi.org/10.1016/j.cma.2013.10.021
|
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, 2015, 32(6): 436–444
https://doi.org/10.1016/j.compgeo.2005.07.001
|
12 |
FLi, P Ren. A novel solution for heat conduction problems by extending scaled boundary finite element method. International Journal of Heat and Mass Transfer, 2016, 95: 678–688
https://doi.org/10.1016/j.ijheatmasstransfer.2015.12.019
|
13 |
MLi, H Zhang, HGuan. Study of offshore monopole behavior due to ocean waves. Ocean Engineering, 2011, 38(17–18): 1946–1956
https://doi.org/10.1016/j.oceaneng.2011.09.022
|
14 |
X NMeng, Z J Zou. Radiation and diffraction of water waves by an infinite horizontal structure with a sidewall using SBFEM. Ocean Engineering, 2013, 60: 193–199
https://doi.org/10.1016/j.oceaneng.2012.12.017
|
15 |
HGravenkamp, C Birk, CSong. The computation of dispersion relations for axisymmetric waveguides using the scaled boundary finite element method. Ultrasonics, 2014, 54(5): 1373–1385
https://doi.org/10.1016/j.ultras.2014.02.004
|
16 |
CLi, E T Ooi, C Song, SNatarajan. SBFEM for fracture analysis of piezoelectric composites under thermal load. International Journal of Solids and Structures, 2015, 52: 114–129
https://doi.org/10.1016/j.ijsolstr.2014.09.020
|
17 |
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
|
18 |
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
|
19 |
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
|
20 |
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
|
21 |
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
|
22 |
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
|
23 |
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
|
24 |
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
|
25 |
T HVu, A J Deeks. A p-adaptive scaled boundary finite element method based on maximization of the error decrease rate. Computational Mechanics, 2007, 41(3): 441–455
https://doi.org/10.1007/s00466-007-0203-9
|
26 |
A JDeeks, C E Augarde. A meshless local Petrov-Galerkin scaled boundary method. Computational Mechanics, 2005, 36(3): 159–170
https://doi.org/10.1007/s00466-004-0649-y
|
27 |
N VChung. Analysis of two-dimensional linear field problems by scaled boundary finite element method. Dissertation for the Doctoral Degree. Bangkok: Chulalongkorn University, 2016
|
28 |
N VChung, R Jaroon, PPhoonsak. Scaled boundary finite element method for two-dimensional linear multi-field media. Engineering Journal (Thailand), 2017, 21(7): 334–360
|
29 |
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
|
30 |
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
|
31 |
RDieringer, W Becker. 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: 263–270
https://doi.org/10.1016/j.compstruct.2014.12.036
|
32 |
SNatarajan, J Wang, CSong, CBirk. Isogeometric analysis enhanced by the scaled boundary finite element method. Computer Methods in Applied Mechanics and Engineering, 2015, 283: 733–762
https://doi.org/10.1016/j.cma.2014.09.003
|
33 |
B HNguyen, H D Tran, C Anitescu, XZhuang, TRabczuk. 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
|
34 |
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
|
35 |
PLi, J Liu, GLin, PZhang, BXu. 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: 43–56
https://doi.org/10.1016/j.enganabound.2017.05.006
|
36 |
FLi, T Qiang. The scaled boundary finite element analysis of seepage problems in multi-material regions. International Journal of Computational Methods, 2012, 9(1): 1240008
https://doi.org/10.1142/S0219876212400087
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
|
Shared |
|
|
|
|
|
Discussed |
|
|
|
|