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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.

Keywords exact geometry      circular defining curve      general boundaries      SBFEM     
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
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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 Ωand 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°)
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