IMAS   23417
INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Unidad Ejecutora - UE
artículos
Título:
Numerical analysis of a finite element method to compute the vibration modes of a Reissner-Mindlin laminated plate
Autor/es:
R. G. DURÁN; F. SANHUEZA; R. RODRÍGUEZ
Revista:
MATHEMATICS OF COMPUTATION
Editorial:
AMER MATHEMATICAL SOC
Referencias:
Lugar: Providence; Año: 2011 vol. 80 p. 1239 - 1264
ISSN:
0025-5718
Resumen:
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 \textit{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.