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Finite element analysis of the Girkmann problem using the modern hp-version and the classical h-version

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Abstract

We perform finite element analysis of the so called Girkmann problem in structural mechanics. The problem involves an axially symmetric spherical shell stiffened with a foot ring and is approached (1) by using the axisymmetric formulation of linear elasticity theory and (2) by using a dimensionally reduced shell-ring model. In the first approach the problem is solved with a fully automatic hp-adaptive finite element solver whereas the classical h-version of the finite element method is used in the second approach. We study the convergence behaviour of the different numerical models and show that accurate stress resultants can be obtained with both models by using effective post-processing formulas.

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Authors and Affiliations

  1. Mathematical and Computer Sciences and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal, Kingdom of Saudi Arabia

    Antti H. Niemi

  2. Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin, Austin, TX, USA

    Ivo Babuška & Leszek Demkowicz

  3. Department of Mathematics and Systems Analysis, Aalto University School of Science and Technology, Espoo, Finland

    Juhani Pitkäranta

Authors
  1. Antti H. Niemi
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  2. Ivo Babuška
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  3. Juhani Pitkäranta
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  4. Leszek Demkowicz
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Corresponding author

Correspondence to Antti H. Niemi.

Appendix: Summary of challenge problem results

Appendix: Summary of challenge problem results

We reproduce here from [23] the results received in response to the Girkmann challenge problem. The four results based on the p-version and the eleven results based on the h-version are shown in Tables 5 and 6, respectively.

Table 5 Summary of the challenge problem results with the p-version
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Table 6 Summary of the challenge problem results with the h-version
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Niemi, A.H., Babuška, I., Pitkäranta, J. et al. Finite element analysis of the Girkmann problem using the modern hp-version and the classical h-version. Engineering with Computers 28, 123–134 (2012). https://doi.org/10.1007/s00366-011-0223-0

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  • DOI: https://doi.org/10.1007/s00366-011-0223-0

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