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Acta Mechanica Solida Sinica

, Volume 26, Issue 3, pp 302–316 | Cite as

New Treatment of Essential Boundary Conditions in EFG Method by Coupling with RPIM

  • Yang Cao
  • Linquan Yao
  • Yu Yin
Article

Abstract

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.

Key Words

meshfree method moving least-squares (mls) approximation radial point interpolation method (rpim) coupled method collocation approach 

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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2013

Authors and Affiliations

  1. 1.School of Mathematical SciencesSoochow UniversitySuzhouChina
  2. 2.School of Urban Rail TransportationSoochow UniversitySuzhouChina

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