Structural Engineering and Mechanics

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An adaptive meshfree RPIM with improved shape parameter to simulate the mixing of a thermoviscoplastic material

  • Zouhair Saffah (LIMAT Laboratory, Faculty of Sciences of Ben M'Sik, Hassan II University of Casablanca) ;
  • Mohammed Amdi (Faculty of Sciences and Technology, University of Lille) ;
  • Abdelaziz Timesli (AICSE Laboratory, National Higher School of Arts and Crafts of Casablanca, Hassan II University of Casablanca) ;
  • Badr Abou El Majd (Faculty of Sciences and Technology, University of Lille) ;
  • Hassane Lahmam (LIMAT Laboratory, Faculty of Sciences of Ben M'Sik, Hassan II University of Casablanca)
  • Received : 2022.10.20
  • Accepted : 2023.10.11
  • Published : 2023.11.10
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Abstract

The Radial Point Interpolation Method (RPIM) has been proposed to overcome the difficulties associated with the use of the Radial Basis Functions (RBFs). The RPIM has the following properties: Simple implementation in terms of boundary conditions as in the Finite Element Method (FEM). A less expensive CPU time compared to other collocation meshless methods such as the Moving Least Square (MLS) collocation method. In this work, we propose an adaptive high-order numerical algorithm based on RPIM to simulate the thermoviscoplastic behavior of a material mixing observed in the Friction Stir Welding (FSW) process. The proposed adaptive meshfree RPIM algorithm adapts well to the geometric and physical data by choosing a good shape parameter with a good precision. Our numerical approach combines the RPIM and the Asymptotic Numerical Method (ANM). A numerical procedure is also proposed in this work to automatically determine an improved shape parameter for the RBFs. The efficiency of the proposed algorithm is analyzed in comparison with an iterative algorithm.

Keywords

Acknowledgement

The entire authors of this research are utterly grateful to the Arab Fund for Economic and Social Development (AFESD) for financial support for this work.

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