Numerical analysis of a finite element method to compute the vibration modes of a reissner-mindlin laminated plate
This paper deals with the finite element approximation of the vibration modes of a laminated plate modeled by the Reissner-Mindlin equations; DL3 elements are used for the bending terms and standard piecewise linear continuous elements for the in-plane displacements. An a priori estimate of the regu...
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paper:paper_00255718_v80_n275_p1239_Duran2023-06-08T14:53:16Z Numerical analysis of a finite element method to compute the vibration modes of a reissner-mindlin laminated plate Duran, Ricardo Guillermo Laminated plates Reissner-Mindlin Spectral problems This paper deals with the finite element approximation of the vibration modes of a laminated plate modeled by the Reissner-Mindlin equations; DL3 elements are used for the bending terms and standard piecewise linear continuous elements for the in-plane displacements. An a priori estimate of the regularity of the solution, independent of the plate thickness, is proved for the corresponding load problem. This allows using the abstract approximation theory for spectral problems to study the convergence of the proposed finite element method. Thus, optimal order error estimates including a double order for the vibration frequencies are obtained under appropriate assumptions. These estimates are independent of the plate thickness, which leads to the conclusion that the method is locking-free. Numerical tests are reported to assess the performance of the method. © 2011 American Mathematical Society. Fil:Durán, R.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2011 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255718_v80_n275_p1239_Duran http://hdl.handle.net/20.500.12110/paper_00255718_v80_n275_p1239_Duran |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Laminated plates Reissner-Mindlin Spectral problems |
| spellingShingle |
Laminated plates Reissner-Mindlin Spectral problems Duran, Ricardo Guillermo Numerical analysis of a finite element method to compute the vibration modes of a reissner-mindlin laminated plate |
| topic_facet |
Laminated plates Reissner-Mindlin Spectral problems |
| description |
This paper deals with the finite element approximation of the vibration modes of a laminated plate modeled by the Reissner-Mindlin equations; DL3 elements are used for the bending terms and standard piecewise linear continuous elements for the in-plane displacements. An a priori estimate of the regularity of the solution, independent of the plate thickness, is proved for the corresponding load problem. This allows using the abstract approximation theory for spectral problems to study the convergence of the proposed finite element method. Thus, optimal order error estimates including a double order for the vibration frequencies are obtained under appropriate assumptions. These estimates are independent of the plate thickness, which leads to the conclusion that the method is locking-free. Numerical tests are reported to assess the performance of the method. © 2011 American Mathematical Society. |
| author |
Duran, Ricardo Guillermo |
| author_facet |
Duran, Ricardo Guillermo |
| author_sort |
Duran, Ricardo Guillermo |
| title |
Numerical analysis of a finite element method to compute the vibration modes of a reissner-mindlin laminated plate |
| title_short |
Numerical analysis of a finite element method to compute the vibration modes of a reissner-mindlin laminated plate |
| title_full |
Numerical analysis of a finite element method to compute the vibration modes of a reissner-mindlin laminated plate |
| title_fullStr |
Numerical analysis of a finite element method to compute the vibration modes of a reissner-mindlin laminated plate |
| title_full_unstemmed |
Numerical analysis of a finite element method to compute the vibration modes of a reissner-mindlin laminated plate |
| title_sort |
numerical analysis of a finite element method to compute the vibration modes of a reissner-mindlin laminated plate |
| publishDate |
2011 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255718_v80_n275_p1239_Duran http://hdl.handle.net/20.500.12110/paper_00255718_v80_n275_p1239_Duran |
| work_keys_str_mv |
AT duranricardoguillermo numericalanalysisofafiniteelementmethodtocomputethevibrationmodesofareissnermindlinlaminatedplate |
| _version_ |
1768546480809836544 |