Multiparametric shell eigenvalue problems

Mikael Laaksonen, Harri Hakula

Research output: Contribution to journalArticleScientificpeer-review

6 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)721-745
Number of pages25
JournalComputer Methods in Applied Mechanics and Engineering
Publication statusPublished - 1 Jan 2019
MoE publication typeA1 Journal article-refereed


  • Shells of revolution
  • Eigenvalue problems
  • Uncertainty quantification
  • Stochastic finite element methods


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