Nonlinear Structural Dynamic Finite Element Analysis Using Ritz Vector Reduced Basis Method
The large number of unknown variables in a finite element idealization for dynamic structural analysis is represented by a very small number of generalized variables, each associating with a generalized Ritz vector known as a basis vector. The large system of equations of motion is thereby reduced t...
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| Format: | Article |
| Language: | English |
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Wiley
1996-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.3233/SAV-1996-3404 |
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| _version_ | 1832551621092966400 |
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| author | M.S. Yao |
| author_facet | M.S. Yao |
| author_sort | M.S. Yao |
| collection | DOAJ |
| description | The large number of unknown variables in a finite element idealization for dynamic structural analysis is represented by a very small number of generalized variables, each associating with a generalized Ritz vector known as a basis vector. The large system of equations of motion is thereby reduced to a very small set by this transformation and computational cost of the analysis can be greatly reduced. In this article nonlinear equations of motion and their transformation are formulated in detail. A convenient way of selection of the generalized basis vector and its limitations are described. Some illustrative examples are given to demonstrate the speed and validity of the method. The method, within its limitations, may be applied to dynamic problems where the response is global in nature with finite amplitude. |
| format | Article |
| id | doaj-art-a7f8fe898d444f98ace9479d8b2c62f8 |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 1996-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-a7f8fe898d444f98ace9479d8b2c62f82025-02-03T06:01:05ZengWileyShock and Vibration1070-96221875-92031996-01-013425926810.3233/SAV-1996-3404Nonlinear Structural Dynamic Finite Element Analysis Using Ritz Vector Reduced Basis MethodM.S. Yao0Department of Mechanical Engineering, BruneI University, West London, UKThe large number of unknown variables in a finite element idealization for dynamic structural analysis is represented by a very small number of generalized variables, each associating with a generalized Ritz vector known as a basis vector. The large system of equations of motion is thereby reduced to a very small set by this transformation and computational cost of the analysis can be greatly reduced. In this article nonlinear equations of motion and their transformation are formulated in detail. A convenient way of selection of the generalized basis vector and its limitations are described. Some illustrative examples are given to demonstrate the speed and validity of the method. The method, within its limitations, may be applied to dynamic problems where the response is global in nature with finite amplitude.http://dx.doi.org/10.3233/SAV-1996-3404 |
| spellingShingle | M.S. Yao Nonlinear Structural Dynamic Finite Element Analysis Using Ritz Vector Reduced Basis Method Shock and Vibration |
| title | Nonlinear Structural Dynamic Finite Element Analysis Using Ritz Vector Reduced Basis Method |
| title_full | Nonlinear Structural Dynamic Finite Element Analysis Using Ritz Vector Reduced Basis Method |
| title_fullStr | Nonlinear Structural Dynamic Finite Element Analysis Using Ritz Vector Reduced Basis Method |
| title_full_unstemmed | Nonlinear Structural Dynamic Finite Element Analysis Using Ritz Vector Reduced Basis Method |
| title_short | Nonlinear Structural Dynamic Finite Element Analysis Using Ritz Vector Reduced Basis Method |
| title_sort | nonlinear structural dynamic finite element analysis using ritz vector reduced basis method |
| url | http://dx.doi.org/10.3233/SAV-1996-3404 |
| work_keys_str_mv | AT msyao nonlinearstructuraldynamicfiniteelementanalysisusingritzvectorreducedbasismethod |