We are interested in the asymptotic analysis of the eigenvalue problem of clamped cylindrical shells. We analyze the lowest eigenvalues as a function of the shell thickness t, the asymptotic behavior of the respective eigenfunctions, and show how the different displacement components and parts of the energy scale in t. As a consequence, we are able to single out the numerical difficulties of the problem, which, surprisingly for a formally bending inhibited problem, include the presence of locking. Extensive numerical tests are included. © 2008 World Scientific Publishing Company.
BEIRAO DA VEIGA, L., Hakula, H., Pitkaranta, J. (2008). Asymptotic and numerical analysis of the eigenvalue problem of a clamped cylindrical shell. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 18(11), 1983-2002 [10.1142/S0218202508003261].
Asymptotic and numerical analysis of the eigenvalue problem of a clamped cylindrical shell
BEIRAO DA VEIGA, LOURENCOPrimo
;
2008
Abstract
We are interested in the asymptotic analysis of the eigenvalue problem of clamped cylindrical shells. We analyze the lowest eigenvalues as a function of the shell thickness t, the asymptotic behavior of the respective eigenfunctions, and show how the different displacement components and parts of the energy scale in t. As a consequence, we are able to single out the numerical difficulties of the problem, which, surprisingly for a formally bending inhibited problem, include the presence of locking. Extensive numerical tests are included. © 2008 World Scientific Publishing Company.
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