# Frontiers of Structural and Civil Engineering

 Front. Struct. Civ. Eng.    2019, Vol. 13 Issue (1) : 201-214     https://doi.org/10.1007/s11709-018-0488-0
 RESEARCH ARTICLE |
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
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 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. Corresponding Authors: Chung Nguyen VAN Just Accepted Date: 14 May 2018   Online First Date: 27 June 2018    Issue Date: 04 January 2019
 Cite this article: Jaroon RUNGAMORNRAT,Chung Nguyen VAN. Scaled boundary finite element method with exact defining curves for two-dimensional linear multi-field media[J]. Front. Struct. Civ. Eng., 2019, 13(1): 201-214. URL: http://journal.hep.com.cn/fsce/EN/10.1007/s11709-018-0488-0 http://journal.hep.com.cn/fsce/EN/Y2019/V13/I1/201
 Fig.1  Schematic of two-dimensional, multi-field body subjected to external excitations Fig.2  Schematic of generic body $Ω$, corresponding boundary, and its approximation $Ωh$ Fig.3  Schematic of scaling center and defining curve of (a) 2-node isoparametric linear element and (b) 2-node circular-arc element Fig.4  Schematic of a quarter of a ring subjected to non-uniform heat source and mixed boundary conditions Tab.1  Normalized temperatures $u1/u1exact$ along the circular arc between AD and BC of two-dimensional domain associated with quarter of ring Fig.5  Relative errors of SBFE solutions versus number of degrees of freedom used in discretization of circular defining curve. DF: Defining curve Fig.6  Schematics of (a) plane-strain hollowed disk fully restrained against the movement on its outer boundary and subjected to uniform shear traction on its inner boundary and (b) equivalent quarter of body used in analysis Tab.2  Normalized displacements $u1/u1exact$ along circular arc between AD and BC of plane-strain hollowed disk Tab.3  Normalized displacements $u2/u2exact$ along circular arc between AD and BC of plane-strain hollowed disk Fig.7  Relative errors of SBFE solutions versus number of degrees of freedom used in discretization of circular defining curve. DF: Defining curve Tab.4  Normalized displacements $u1/u1exact$ along the line $x1=x2$ of quarter of hollowed circular plate Tab.5  Normalized displacements $u2/u2exact$ along the line $x1=x2$ of quarter of hollowed circular plate Tab.6  Normalized electric potential $u3/u3exact$ along the line $x1=x2$ of quarter of hollowed circular plate Fig.8  Relative errors of SBFE solutions versus number of degrees of freedom used in discretization of circular defining curve. DF: Defining curve
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