A smoothed finite element method for shell analysis

N. Nguyen-Thanh, Timon Rabczuk, H. Nguyen-Xuan, Stéphane P.A. Bordas

Research output: Contribution to journalArticlepeer-review

211 Citations (Scopus)


A four-node quadrilateral shell element with smoothed membrane-bending based on Mindlin-Reissner theory is proposed. The element is a combination of a plate bending and membrane element. It is based on mixed interpolation where the bending and membrane stiffness matrices are calculated on the boundaries of the smoothing cells while the shear terms are approximated by independent interpolation functions in natural coordinates. The proposed element is robust, computationally inexpensive and free of locking. Since the integration is done on the element boundaries for the bending and membrane terms, the element is more accurate than the MITC4 element for distorted meshes. This will be demonstrated for several numerical examples.

Original languageEnglish
Pages (from-to)165-177
Number of pages13
JournalComputer Methods in Applied Mechanics and Engineering
Issue number2
Publication statusPublished - 2008 Dec 1


  • MITC4 elements
  • Shell elements
  • Smoothed finite elements (SFEM)

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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