Best bilinear shell element: flat, twisted or curved?

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Doctoral thesis (article-based)
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Research reports / Helsinki University of Technology, Institute of Mathematics. A, 564
This thesis concerns the accuracy of finite element models for shell structures. The focus is on low-order approximations of layer and vibration modes in shell deformations with particular reference to problems with concentrated loads. It is shown that parametric error amplification, or numerical locking, arises in these cases when bilinear elements are used and the formulation is based on the so-called degenerated solid approach. Furthermore, an alternative way for designing bilinear shell elements is discussed. The procedure is based on a refined shallow shell model which allows for an effective coupling between the membrane and bending strain in the energy expression.
shell elements, locking, shell layers, shell vibration modes, asymptotic behavior
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  • [Publication 1]: Antti H. Niemi, Juhani Pitkäranta, and Harri Hakula. 2007. Benchmark computations on point-loaded shallow shells: Fourier vs. FEM. Computer Methods in Applied Mechanics and Engineering, volume 196, numbers 4-6, pages 894-907. © 2007 Elsevier Science. By permission.
  • [Publication 2]: Antti H. Niemi and Juhani Pitkäranta. 2008. Bilinear finite elements for shells: Isoparametric quadrilaterals. International Journal for Numerical Methods in Engineering, volume 75, number 2, pages 212-240.
  • [Publication 3]: Antti H. Niemi. 2008. Approximation of shell layers using bilinear elements on anisotropically refined rectangular meshes. Computer Methods in Applied Mechanics and Engineering, volume 197, numbers 45-48, pages 3964-3975. © 2008 Elsevier Science. By permission.
  • [Publication 4]: Antti H. Niemi, Harri Hakula, and Juhani Pitkäranta. 2008. Point load on a shell. In: Karl Kunisch, Günther Of, and Olaf Steinbach (editors). Numerical Mathematics and Advanced Applications. Proceedings of the 7th European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2007). Graz, Austria. 10-14 September 2007. Springer, pages 819-826. © 2008 by authors and © 2008 Springer Science+Business Media. By permission.
  • [Publication 5]: Antti H. Niemi. 2009. A bilinear shell element based on a refined shallow shell model. Espoo, Finland. 30 pages. Helsinki University of Technology Institute of Mathematics Research Reports, A562. International Journal for Numerical Methods in Engineering, submitted for publication. © 2009 by author and © 2009 John Wiley & Sons. By permission.