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Structural Engineering and Mechanics Volume 88, Number 3, November10 2023 , pages 239-249 DOI: https://doi.org/10.12989/sem.2023.88.3.239 |
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An adaptive meshfree RPIM with improved shape parameter to simulate the mixing of a thermoviscoplastic material |
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Zouhair Saffah, Mohammed Amdi, Abdelaziz Timesli, Badr Abou El Majd and Hassane Lahmam
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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. | ||
| Key Words | ||
| homotopy continuation method; meshless collocation method; optimization technique; radial point interpolation method; shape parameter; thermoviscoplastic material | ||
| Address | ||
| Zouhair Saffah: LIMAT Laboratory, Faculty of Sciences of Ben M | ||