 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 13427 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8178
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| In English (Mech. Solids): | | 5249 |
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| Xiao Ma, Changhe Li, Rui Xue, Mingqiang Zhang, Guang Wang, Yunfei Hu, Benkai Li, Min Yang, Yanbin Zhang, Xin Cui, and Mingzheng Liu, "Analysis of Geometric Nonlinear Problems Using Hermite Interpolation Meshless Method," Mech. Solids. 60 (6), 5018-5040 (2025) |
| Year |
2025 |
Volume |
60 |
Number |
6 |
Pages |
5018-5040 |
| DOI |
10.1134/S0025654425603623 |
| Title |
Analysis of Geometric Nonlinear Problems Using Hermite Interpolation Meshless Method |
| Author(s) |
Xiao Ma (School of Mechanical and Automotive Engineering, Qingdao University of Technology, Qingdao, 266520 China; Key Lab of Industrial Fluid Energy Conservation and Pollution Control (Ministry of Education), Qingdao University of Technology, Qingdao, 266520 China)
Changhe Li (School of Mechanical and Automotive Engineering, Qingdao University of Technology, Qingdao, 266520 China, sy_lichanghe@163.com)
Rui Xue (Tianjin Tanhas Technology Co., Ltd., Tianjin, 301000 China)
Mingqiang Zhang (Qingdao Jiuhe Heavy Industry Machinery Co., Ltd., Qingdao, 266213 China)
Guang Wang (Guohua (Qingdao) Intelligent Equipment Co., Ltd., Qingdao, 201620 China)
Yunfei Hu (Yutai County Huiyuan Planting Professional Cooperative, Jining, 272300 China)
Benkai Li (School of Mechanical and Automotive Engineering, Qingdao University of Technology, Qingdao, 266520 China)
Min Yang (School of Mechanical and Automotive Engineering, Qingdao University of Technology, Qingdao, 266520 China)
Yanbin Zhang (School of Mechanical and Automotive Engineering, Qingdao University of Technology, Qingdao, 266520 China)
Xin Cui (School of Mechanical and Automotive Engineering, Qingdao University of Technology, Qingdao, 266520 China)
Mingzheng Liu (School of Mechanical and Automotive Engineering, Qingdao University of Technology, Qingdao, 266520 China) |
| Abstract |
Geometric nonlinear problems are common in engineering, and it is very difficult to obtain
an analytical solution. Furthermore, mesh-based numerical methods suffer from high computational
complexity, low efficiency and poor accuracy in solving the geometric nonlinear problems due to mesh
constraints. To address this issue, this paper presents a nonlinear Hermite interpolation meshless
method (HIMM) for large deformation analysis of elastomers. This method utilizes a set of discrete
nodes to represent the problem domain, avoiding mesh generation and reconstruction. Firstly, the
governing equations of the geometric nonlinear problems are obtained based on the virtual displacement principle and full Lagrangian formulation. Secondly, the approximation function of the displacement field is derived using the Hermite approximation method and moving least squares method.
Then, the meshless formulation is obtained, and the HIMM model for the geometric nonlinear problems is established. Finally, the influence of the scale factor, load step and node density on the accuracy of the HIMM model is analyzed, and the effectiveness of the HIMM for solving geometric nonlinear problems is verified through several examples. The numerical results show that the computational accuracy of the HIMM is 3 to 6 times higher than that of the existing element-free Galerkin
method (EFGM). In addition, the HIMM reduces the computation time by approximately 50% compared to the EFGM. This work provides an effective numerical tool for geometric nonlinear problems,
and also provides a reference for applying meshless methods in the engineering field. |
| Keywords |
Hermite interpolation meshless method, geometric nonlinear problem, computational accuracy, computational efficiency |
| Received |
03 July 2025 | Revised |
31 July 2025 | Accepted |
04 September 2025 |
| Link to Fulltext |
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