 | | 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: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| Guang Tao Xu and Shao Kang Wu, "Proper generalized decomposition method for stress analysis of functionally graded materials," Mech. Solids. 56 (3), 430-442 (2021) |
| Year |
2021 |
Volume |
56 |
Number |
3 |
Pages |
430-442 |
| DOI |
10.3103/S0025654421030146 |
| Title |
Proper generalized decomposition method for stress analysis of functionally graded materials |
| Author(s) |
Guang Tao Xu (School of Mechanical and Power Engineering, Zhengzhou University, Zhengzhou, Henan, 450001 China; Henan Key Engineering Laboratory for Anti-fatigue Manufacturing Technology, Zhengzhou University, Zhengzhou, Henan, 450001 China, xgtzzu@zzu.edu.cn)
Shao Kang Wu (School of Mechanical and Power Engineering, Zhengzhou University, Zhengzhou, Henan, 450001 China; Henan Key Engineering Laboratory for Anti-fatigue Manufacturing Technology, Zhengzhou University, Zhengzhou, Henan, 450001 China) |
| Abstract |
Proper generalized decomposition (PGD), an advanced numerical simulation method, has
been successfully used as a model reduction method in many fields. In this study, functionally graded materials are analyzed using the Airy stress function method, and a compatible equation representing the stress function is obtained. PGD is used to solve a compatible equation, which is a complex high-order partial differential equation, by decomposing it into two one-dimensional problems in space. The solution of the complex high-order partial differential equation is then obtained by solving the two one-dimensional problems using Chebyshev's method. The accuracy of the proposed method is verified by comparing the PGD solution with the analytical solution. Numerical examples show that highly accurate results can be obtained by using several iterative modes. Therefore, the PGD method is an effective numerical technique for the stress analysis of functionally graded materials. This paper provides a theoretical basis for future research on the stress concentrations of irregular shape and rough surface. |
| Keywords |
Functionally graded materials, Proper generalized decomposition, Airy stress function, High-order partial differential equation |
| Received |
05 November 2020 | Revised |
15 December 2020 | Accepted |
15 December 2020 |
| Link to Fulltext |
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