NEW TREATMENT OF ESSENTIAL BOUNDARY CONDITIONS IN EFG METHOD BY COUPLING WITH RPIM

One of major difficulties in the implementation of meshfree methods using the moving least square (MLS) approximation, such as element-free Galerkin method (EFG), is the imposition of essential boundary conditions as the approximations do not pass through the nodal parameter values. Another class of...

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Bibliographic Details
Published inActa mechanica solida Sinica Vol. 26; no. 3; pp. 302 - 316
Main Authors Cao, Yang, Yao, Linquan, Yin, Yu
Format Journal Article
LanguageEnglish
Published Singapore Elsevier Ltd 01.06.2013
Springer Singapore
School of Urban Rail Transportation, Soochow University, Suzhou 215006, China
School of Mathematical Sciences, Soochow University, Suzhou 215006, China%School of Mathematical Sciences, Soochow University, Suzhou 215006, China
Subjects
Approximation
Boundary conditions
Classical Mechanics
collocation approach
coupled method
EFG
Engineering
Galerkin methods
Interpolation
Joining
Mathematical analysis
Mathematical models
meshfree method
Meshless methods
moving least-squares (mls) approximation
radial point interpolation method (rpim)
Surfaces and Interfaces
Theoretical and Applied Mechanics
Thin Films
无网格伽辽金法
无网格方法
本质边界条件
治疗
移动最小二乘
耦合
逼近函数
meshfree method
coupled method
radial point interpolation method (rpim)
collocation approach
moving least-squares (mls) approximation
Online AccessGet full text
ISSN0894-9166
1860-2134
DOI10.1016/S0894-9166(13)60028-2

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Summary:One of major difficulties in the implementation of meshfree methods using the moving least square (MLS) approximation, such as element-free Galerkin method (EFG), is the imposition of essential boundary conditions as the approximations do not pass through the nodal parameter values. Another class of meshfree methods based on the radial basis point interpolation can satisfy the essential boundary conditions exactly since its approximation function passes through each node in an influence domain and thus its shape functions possess the properties of delta function. In this paper, a coupled element-free Galerkin(EFG)-radial point interpolation method (RPIM) is proposed to enhance their advantages and avoid their disadvantages. Discretized equations of equilibrium are obtained in the RPIM region and the EFG region, respectively. Then a collocation approach is introduced to couple the RPIM and the EFG method. This method satisfies the linear consistency exactly and can maintain the stiffness matrix symmetric. Numerical tests show that this method gives reasonably accurate results consistent with the theory.
Bibliography:meshfree method, moving least-squares （ntis） approximation, radial point inter-polation method （rpim）, coupled method, collocation approach
One of major difficulties in the implementation of meshfree methods using the mov- ing least square （MLS） approximation, such as element-free Galerkin method （EFG）, is the im- position of essential boundary conditions as the approximations do not pass through the nodal parameter values. Another class of meshfree methods based on the radial basis point interpola- tion can satisfy the essential boundary conditions exactly since its approximation function passes through each node in an influence domain and thus its shape functions possess the properties of delta function. In this paper, a coupled element-free Galerkin（EFG）-radial point interpola- tion method （RPIM） is proposed to enhance their advantages and avoid their disadvantages. Discretized equations of equilibrium are obtained in the RPIM region and the EFG region, respectively. Then a collocation approach is introduced to couple the RPIM and the EFG method. This method satisfies the linear consistency exactly and can maintain the stiffness matrix symmetric. Numerical tests show that this method gives reasonably accurate results consistent with the theory.
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ISSN:0894-9166
1860-2134
DOI:10.1016/S0894-9166(13)60028-2