A locking-free finite element method for the buckling problem of a non-homogeneous Timoshenko beam
Carlo Lovadina; David Mora; Rodolfo Rodríguez
ESAIM: Mathematical Modelling and Numerical Analysis (2011)
- Volume: 45, Issue: 4, page 603-626
- ISSN: 0764-583X
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topLovadina, Carlo, Mora, David, and Rodríguez, Rodolfo. "A locking-free finite element method for the buckling problem of a non-homogeneous Timoshenko beam." ESAIM: Mathematical Modelling and Numerical Analysis 45.4 (2011): 603-626. <http://eudml.org/doc/276344>.
@article{Lovadina2011,
abstract = {
The aim of this paper is to develop a finite element method which allows computing
the buckling coefficients and modes of a non-homogeneous Timoshenko beam.
Studying the spectral properties of a non-compact operator,
we show that the relevant buckling coefficients correspond to isolated
eigenvalues of finite multiplicity.
Optimal order error estimates are proved for the eigenfunctions
as well as a double order of convergence for
the eigenvalues using classical abstract spectral approximation theory for non-compact operators.
These estimates are valid independently of the thickness of the beam, which
leads to the conclusion that the method is locking-free.
Numerical tests are reported in order to assess the performance of the method.
},
author = {Lovadina, Carlo, Mora, David, Rodríguez, Rodolfo},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Finite element approximation; eigenvalue problems; Timoshenko beams; finite element approximation},
language = {eng},
month = {1},
number = {4},
pages = {603-626},
publisher = {EDP Sciences},
title = {A locking-free finite element method for the buckling problem of a non-homogeneous Timoshenko beam},
url = {http://eudml.org/doc/276344},
volume = {45},
year = {2011},
}
TY - JOUR
AU - Lovadina, Carlo
AU - Mora, David
AU - Rodríguez, Rodolfo
TI - A locking-free finite element method for the buckling problem of a non-homogeneous Timoshenko beam
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2011/1//
PB - EDP Sciences
VL - 45
IS - 4
SP - 603
EP - 626
AB -
The aim of this paper is to develop a finite element method which allows computing
the buckling coefficients and modes of a non-homogeneous Timoshenko beam.
Studying the spectral properties of a non-compact operator,
we show that the relevant buckling coefficients correspond to isolated
eigenvalues of finite multiplicity.
Optimal order error estimates are proved for the eigenfunctions
as well as a double order of convergence for
the eigenvalues using classical abstract spectral approximation theory for non-compact operators.
These estimates are valid independently of the thickness of the beam, which
leads to the conclusion that the method is locking-free.
Numerical tests are reported in order to assess the performance of the method.
LA - eng
KW - Finite element approximation; eigenvalue problems; Timoshenko beams; finite element approximation
UR - http://eudml.org/doc/276344
ER -
References
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