Abstract: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.
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- Ricardo G. Durán
- Affiliation: Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428, Buenos Aires, Argentina
- ORCID: 0000-0003-1349-3708
- Email: firstname.lastname@example.org
- Rodolfo Rodríguez
- Affiliation: CI$^2$MA, Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile.
- Email: email@example.com
- Frank Sanhueza
- Affiliation: Escuela de Obras Civiles, Universidad Andres Bello, Autopista 7100, Concepción, Chile.
- Email: firstname.lastname@example.org
- Received by editor(s): August 24, 2009
- Received by editor(s) in revised form: June 9, 2010
- Published electronically: February 7, 2011
- Additional Notes: The first author was partially supported by Universidad de Buenos Aires under grant X070. Member of CONICET (Argentina).
The second author was partially supported by FONDAP and BASAL projects CMM, Universidad de Chile (Chile).
The third author was supported by a CONICYT fellowship (Chile).
All authors were partially supported by ANPCyT through grant PICT RAÍCES 2006, No. 1307 (Argentina).
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
- Journal: Math. Comp. 80 (2011), 1239-1264
- MSC (2010): Primary 65N25, 74K10, 65N30
- DOI: https://doi.org/10.1090/S0025-5718-2011-02456-7
- MathSciNet review: 2785457