ABSTRACTS OF ARTICLES OF THE JOURNAL "INFORMATION TECHNOLOGIES".
No. 5. Vol. 31. 2025

DOI: 10.17587/it.31.227-235

Raad M., PhD Student, Popov A. Y., Dr. of Tech. Sc., Professor,
BMSTU "Bauman Moscow State Technical University", Moscow, 105005, Russian Federation

The Improvement of the Mesh Generation Algorithm in the Finite Element Method for Accelerating the Calculation of Thermal Stresses in Solid Bodies

Received on July 14, 2024
Accepted on September 24, 2024

This study focuses on modeling the thermodiffusion process and thermal stresses using the finite element method (FEM). The paper examines algorithms for polygonal mesh generation and evaluates the influence of mesh quality on the accuracy of numerical methods in thermodiffusion calculations within solid bodies. An improved Delaunay algorithm is proposed to enhance mesh construction. Numerical experiments are presented, and the accuracy of the obtained results is analyzed to demonstrate the effectiveness of the proposed approach in accelerating thermal stress calculations.
Keywords: polygonal meshes, numerical methods, Delaunay, finite element method (FEM), FEM accuracy, thermal stresses, thermodiffusion, improved Delaunay algorithm

P. 227-235

Full text on eLIBRARY

References

1. Noda N. Thermal stresses in materials with temperature-dependent properties, Applied Mechanics Reviews, 1991, vol. 44, no. 9, pp. 383—397, available at: https://doi.org/10.1115/1.3119511.
2. Marousi A., Kokossis A. On the acceleration of global optimization algorithms by coupling cutting plane decomposition algorithms with machine learning and advanced data analytics, Computers & Chemical Engineering, 2022, vol. 163, pp. 107820.
3. Liu W. K., Li S., Park H. S. Eighty years of the finite element method: Birth, evolution, and future, Archives of Computational Methods in Engineering, 2022, vol. 29, no. 6, pp. 4431—4453.
4. Reddy J. N., Gartling D. K. The finite element method in heat transfer and fluid dynamics, Boca Raton, FL, CRC Press, 2010.
5. Hetnarski R. B. Encyclopedia of Thermal Stresses, Springer Netherlands, Dordrecht, 2014, doi: 10.1007/978-94-007-2739-7.
6. Peiro J., Sherwin S. Finite difference, finite element and finite volume methods for partial differential equations. Handbook of Materials Modeling, Methods, 2005, pp. 2415—2446.
7. Raad M., Popov A. Thermal stresses using Finite Element Method, 5th International Youth Conference on Radio Electronics, Electrical and Power Engineering (REEPE), IEEE, 2023, vol. 5, pp. 1—6.
8. Fang Q., Tsuchiya T., Yamamoto T. Finite difference, finite element and finite volume methods applied to two-point boundary value problems, Journal of Computational and Applied Mathematics, 2002, vol. 139, no. 1, pp. 9—19, doi: 10.1016/S0377-0427(01)00392-2.
9. Ho-Le K. Finite element mesh generation methods: A review and classification, Computer-Aided Design, 1988, vol. 20, no. 1, pp. 27—38.
10. Lei N., Li Z., Xu Z., Li Y., Gu X. What's the Situation with Intelligent Mesh Generation: A Survey and Perspectives, IEEE Transactions on Visualization and Computer Graphics, 2023, vol. 30, no. 8, pp. 4997—5017.
11. Lo D. S. H. Finite Element Mesh Generation, CRC Press, Boca Raton, FL, 2014, doi: 10.1201/b17713.
12. Cheng S.-W., Dey T. K., Shewchuk J., Sahni S. Delaunay Mesh Generation, Boca Raton, FL, CRC Press, 2013.
13. Raad M., Popov A. Y. Calculate the approximate volume of complex-shape solids, Materials Today: Proceedings, 2023, vol. 80, pp. 1214—1218.
14. Zhou G. How accurate is the streamline diffusion finite element method, Mathematics of Computation, 1997, vol. 66, no. 217, pp. 31—44.
15. Liu G., Nguyen-Xuan H. A theoretical study on the smoothed FEM (S-FEM) models: Properties, accuracy and convergence rates, International Journal for Numerical Methods in Engineering, 2010, vol. 84, no. 10, pp. 1222—1256.
16. Dekking F. M., Kraaikamp C., Lopuhaa H. P., Meester L. E. Why Probability and Statistics? A Modern Introduction to Probability and Statistics, London, Springer, 2005, 483 p.

To the contents