Multiparametric shell eigenvalue problems

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Multiparametric shell eigenvalue problems. / Laaksonen, Mikael; Hakula, Harri.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 343, 01.01.2019, p. 721-745.

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@article{2574dfb9cbd046f5a441fc63c9e5e102,
title = "Multiparametric shell eigenvalue problems",
abstract = "The eigenproblem for thin shells of revolution under uncertainty in material parameters is discussed. Here the focus is on the smallest eigenpairs. Shells of revolution have natural eigenclusters due to symmetries, moreover, the eigenpairs depend on a deterministic parameter, the dimensionless thickness. The stochastic subspace iteration algorithms presented here are capable of resolving the smallest eigenclusters. In the case of random material parameters, it is possible that the eigenmodes cross in the stochastic parameter space. This interesting phenomenon is demonstrated via numerical experiments. Finally, the effect of the chosen material model on the asymptotics in relation to the deterministic parameter is shown to be negligible.",
keywords = "Shells of revolution, Eigenvalue problems, Uncertainty quantification, Stochastic finite element methods",
author = "Mikael Laaksonen and Harri Hakula",
year = "2019",
month = "1",
day = "1",
doi = "10.1016/j.cma.2018.09.011",
language = "English",
volume = "343",
pages = "721--745",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",

}

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TY - JOUR

T1 - Multiparametric shell eigenvalue problems

AU - Laaksonen, Mikael

AU - Hakula, Harri

PY - 2019/1/1

Y1 - 2019/1/1

N2 - The eigenproblem for thin shells of revolution under uncertainty in material parameters is discussed. Here the focus is on the smallest eigenpairs. Shells of revolution have natural eigenclusters due to symmetries, moreover, the eigenpairs depend on a deterministic parameter, the dimensionless thickness. The stochastic subspace iteration algorithms presented here are capable of resolving the smallest eigenclusters. In the case of random material parameters, it is possible that the eigenmodes cross in the stochastic parameter space. This interesting phenomenon is demonstrated via numerical experiments. Finally, the effect of the chosen material model on the asymptotics in relation to the deterministic parameter is shown to be negligible.

AB - The eigenproblem for thin shells of revolution under uncertainty in material parameters is discussed. Here the focus is on the smallest eigenpairs. Shells of revolution have natural eigenclusters due to symmetries, moreover, the eigenpairs depend on a deterministic parameter, the dimensionless thickness. The stochastic subspace iteration algorithms presented here are capable of resolving the smallest eigenclusters. In the case of random material parameters, it is possible that the eigenmodes cross in the stochastic parameter space. This interesting phenomenon is demonstrated via numerical experiments. Finally, the effect of the chosen material model on the asymptotics in relation to the deterministic parameter is shown to be negligible.

KW - Shells of revolution

KW - Eigenvalue problems

KW - Uncertainty quantification

KW - Stochastic finite element methods

U2 - 10.1016/j.cma.2018.09.011

DO - 10.1016/j.cma.2018.09.011

M3 - Article

VL - 343

SP - 721

EP - 745

JO - Computer Methods in Applied Mechanics and Engineering

T2 - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

ER -

ID: 30332377