Body of Optimal Parameters in the Weighted Finite Element Method for the Crack Problem
In this paper, a high-accuracy weighted finite element method is constructed and investigated for finding an approximate solution of the crack problem. We consider an approximation of the Lamé system in the domain with the reentrant corner 2π at the boundary. A new concept of definition of the solut...
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| Format: | Article |
| Language: | English |
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Shahid Chamran University of Ahvaz
2021-10-01
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| Series: | Journal of Applied and Computational Mechanics |
| Subjects: | |
| Online Access: | https://jacm.scu.ac.ir/article_17020_e1df30242c6d8c3707a523a98d74ee9e.pdf |
| _version_ | 1818501379411410944 |
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| author | Viktor A. Rukavishnikov |
| author_facet | Viktor A. Rukavishnikov |
| author_sort | Viktor A. Rukavishnikov |
| collection | DOAJ |
| description | In this paper, a high-accuracy weighted finite element method is constructed and investigated for finding an approximate solution of the crack problem. We consider an approximation of the Lamé system in the domain with the reentrant corner 2π at the boundary. A new concept of definition of the solution of the problem is introduced. It allows us to suppress the influence of the singularity on the accuracy of finding an approximate solution, in contrast to the classical approach. We have introduced a weight function into the basis of the finite element method. The accuracy of finding an approximate solution by the weighted finite element method depends on three input parameters. We created an algorithm and establish the body of optimal parameters in the weighted finite element method for the crack problem. The choice of parameters from this set allows us to accurately and stability find an approximate solution with the smallest deviation from the best error. This is required to generate industrial codes. |
| first_indexed | 2024-12-10T20:55:19Z |
| format | Article |
| id | doaj.art-ebc78b77626e46d3ab1b58f336d8d877 |
| institution | Directory Open Access Journal |
| issn | 2383-4536 |
| language | English |
| last_indexed | 2024-12-10T20:55:19Z |
| publishDate | 2021-10-01 |
| publisher | Shahid Chamran University of Ahvaz |
| record_format | Article |
| series | Journal of Applied and Computational Mechanics |
| spelling | doaj.art-ebc78b77626e46d3ab1b58f336d8d8772022-12-22T01:33:58ZengShahid Chamran University of AhvazJournal of Applied and Computational Mechanics2383-45362021-10-01742159217010.22055/jacm.2021.38041.314217020Body of Optimal Parameters in the Weighted Finite Element Method for the Crack ProblemViktor A. Rukavishnikov0Computing Center of the Far Eastern Branch of the Russian Academy of Sciences, Kim Yu Chen St., 65, Khabarovsk, 680000, RussiaIn this paper, a high-accuracy weighted finite element method is constructed and investigated for finding an approximate solution of the crack problem. We consider an approximation of the Lamé system in the domain with the reentrant corner 2π at the boundary. A new concept of definition of the solution of the problem is introduced. It allows us to suppress the influence of the singularity on the accuracy of finding an approximate solution, in contrast to the classical approach. We have introduced a weight function into the basis of the finite element method. The accuracy of finding an approximate solution by the weighted finite element method depends on three input parameters. We created an algorithm and establish the body of optimal parameters in the weighted finite element method for the crack problem. The choice of parameters from this set allows us to accurately and stability find an approximate solution with the smallest deviation from the best error. This is required to generate industrial codes.https://jacm.scu.ac.ir/article_17020_e1df30242c6d8c3707a523a98d74ee9e.pdfelasticity problem with a crackweighted finite element methodbody of optimal parameters |
| spellingShingle | Viktor A. Rukavishnikov Body of Optimal Parameters in the Weighted Finite Element Method for the Crack Problem Journal of Applied and Computational Mechanics elasticity problem with a crack weighted finite element method body of optimal parameters |
| title | Body of Optimal Parameters in the Weighted Finite Element Method for the Crack Problem |
| title_full | Body of Optimal Parameters in the Weighted Finite Element Method for the Crack Problem |
| title_fullStr | Body of Optimal Parameters in the Weighted Finite Element Method for the Crack Problem |
| title_full_unstemmed | Body of Optimal Parameters in the Weighted Finite Element Method for the Crack Problem |
| title_short | Body of Optimal Parameters in the Weighted Finite Element Method for the Crack Problem |
| title_sort | body of optimal parameters in the weighted finite element method for the crack problem |
| topic | elasticity problem with a crack weighted finite element method body of optimal parameters |
| url | https://jacm.scu.ac.ir/article_17020_e1df30242c6d8c3707a523a98d74ee9e.pdf |
| work_keys_str_mv | AT viktorarukavishnikov bodyofoptimalparametersintheweightedfiniteelementmethodforthecrackproblem |