Systematic Presentation of Ritz Variational Method for the Flexural Analysis of Simply Supported Rectangular Kirchhoff–Love Plates
In this work, the Ritz variational method for solving the flexural problem of Kirchhoff–Love plates under transverse distributed load has been presented systematically in matrix form. An illustrative application of the matrix presentation was done for simply supported rectangular Kirchhoff–Love plat...
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Sumy State University
2018-11-01
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| Series: | Журнал інженерних наук |
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| Online Access: | http://jes.sumdu.edu.ua/?page_id=27116 |
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| author | Ike C. C. |
| author_facet | Ike C. C. |
| author_sort | Ike C. C. |
| collection | DOAJ |
| description | In this work, the Ritz variational method for solving the flexural problem of Kirchhoff–Love plates under transverse distributed load has been presented systematically in matrix form. An illustrative application of the matrix presentation was done for simply supported rectangular Kirchhoff–Love plate under uniformly distributed load. The application used a one term Ritz approximating displacement (coordinate, or basis) function. A one term Ritz approximate solutions obtained for center displacement of square plates showed a difference of 1.9 % from the exact solution for displacement. Solution obtained for the bending moment at the center showed a difference of 7.9 % from the exact solution for bending moment. The one term Ritz approximation for the maximum shear force showed a difference of –10.7 % from the exact solution. The results obtained for a one term Ritz approximation of the displacement shape function was reasonably close for practical purposes. |
| format | Article |
| id | doaj-art-1a186d4c8f1b4c3d91c2eafbab0bea14 |
| institution | Kabale University |
| issn | 2312-2498 2414-9381 |
| language | English |
| publishDate | 2018-11-01 |
| publisher | Sumy State University |
| record_format | Article |
| series | Журнал інженерних наук |
| spelling | doaj-art-1a186d4c8f1b4c3d91c2eafbab0bea142025-08-20T03:49:03ZengSumy State UniversityЖурнал інженерних наук2312-24982414-93812018-11-0152D1D510.21272/jes.2018.5(2).d1Systematic Presentation of Ritz Variational Method for the Flexural Analysis of Simply Supported Rectangular Kirchhoff–Love PlatesIke C. C.0Enugu State University of Science and Technology, P.M.B. 01660, Enugu, NigeriaIn this work, the Ritz variational method for solving the flexural problem of Kirchhoff–Love plates under transverse distributed load has been presented systematically in matrix form. An illustrative application of the matrix presentation was done for simply supported rectangular Kirchhoff–Love plate under uniformly distributed load. The application used a one term Ritz approximating displacement (coordinate, or basis) function. A one term Ritz approximate solutions obtained for center displacement of square plates showed a difference of 1.9 % from the exact solution for displacement. Solution obtained for the bending moment at the center showed a difference of 7.9 % from the exact solution for bending moment. The one term Ritz approximation for the maximum shear force showed a difference of –10.7 % from the exact solution. The results obtained for a one term Ritz approximation of the displacement shape function was reasonably close for practical purposes.http://jes.sumdu.edu.ua/?page_id=27116Ritz variational methodKirchhoff–Love plateshape functiontotal potential energyprinciple of minimization |
| spellingShingle | Ike C. C. Systematic Presentation of Ritz Variational Method for the Flexural Analysis of Simply Supported Rectangular Kirchhoff–Love Plates Журнал інженерних наук Ritz variational method Kirchhoff–Love plate shape function total potential energy principle of minimization |
| title | Systematic Presentation of Ritz Variational Method for the Flexural Analysis of Simply Supported Rectangular Kirchhoff–Love Plates |
| title_full | Systematic Presentation of Ritz Variational Method for the Flexural Analysis of Simply Supported Rectangular Kirchhoff–Love Plates |
| title_fullStr | Systematic Presentation of Ritz Variational Method for the Flexural Analysis of Simply Supported Rectangular Kirchhoff–Love Plates |
| title_full_unstemmed | Systematic Presentation of Ritz Variational Method for the Flexural Analysis of Simply Supported Rectangular Kirchhoff–Love Plates |
| title_short | Systematic Presentation of Ritz Variational Method for the Flexural Analysis of Simply Supported Rectangular Kirchhoff–Love Plates |
| title_sort | systematic presentation of ritz variational method for the flexural analysis of simply supported rectangular kirchhoff love plates |
| topic | Ritz variational method Kirchhoff–Love plate shape function total potential energy principle of minimization |
| url | http://jes.sumdu.edu.ua/?page_id=27116 |
| work_keys_str_mv | AT ikecc systematicpresentationofritzvariationalmethodfortheflexuralanalysisofsimplysupportedrectangularkirchhoffloveplates |