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.
Asymptotic and numerical analysis of the eigenvalue problem of a clamped cylindrical shell / L. Beirao da Veiga, H. Hakula, J. Pitkaranta. - In: MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. - ISSN 0218-2025. - 18:11(2008), pp. 1983-2002.
Asymptotic and numerical analysis of the eigenvalue problem of a clamped cylindrical shell
L. Beirao da VeigaPrimo
;
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.Pubblicazioni consigliate
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