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

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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.

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Authors and Affiliations

  1. School of Mathematical Sciences, Soochow University, 215006, Suzhou, China

    Yang Cao, Linquan Yao & Yu Yin

  2. School of Urban Rail Transportation, Soochow University, 215006, Suzhou, China

    Linquan Yao

Authors
  1. Yang Cao
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  2. Linquan Yao
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  3. Yu Yin
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Corresponding author

Correspondence to Linquan Yao.

Additional information

This work is supported by the National Natural Science Foundation of China (No. 11172192), the College Postgraduate Research and Innovation Project of Jiangsu Province (No. CX10B_029Z) and the Nominated Excellent Thesis for PHD Candidates Program of Soochow University (No. 23320957).

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Cao, Y., Yao, L. & Yin, Y. New Treatment of Essential Boundary Conditions in EFG Method by Coupling with RPIM. Acta Mech. Solida Sin. 26, 302–316 (2013). https://doi.org/10.1016/S0894-9166(13)60028-2

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  • DOI: https://doi.org/10.1016/S0894-9166(13)60028-2

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