Assumed-metric spherically interpolated quadrilateral shell element

P. Areias, T. Rabczuk, D. Dias-Da-Costa

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


An alternative approach for the analysis of non-linear shells is adopted, based on mixed forms of the spatial metric (both enriched and assumed), spherical linear interpolation for quadrilaterals (for the first time) and covariant fixed frames to ensure the satisfaction of all patch tests (also an innovation). The motivation for the spherical interpolation was the work of Crisfield and Jelenić on geometrically exact beams. Shear deformation is included and rotations are defined relative to the Kirchhoff director. A systematic mixed method for deriving high-performance shell elements is presented in the sense that specific mixed shape functions can be inserted without altering the overall framework. A long-standing restriction of assumed-strain elements in FeFp plasticity is circumvented for metal plasticity by using the elastic left Cauchy-Green tensor. Enhanced-assumed metric is also included directly in the metric components. The forces are exactly linearized to obtain an asymptotically quadratic convergence rate in Newton's method. Verification tests of the formulation are performed with very good performance being observed. Applications to hyperelasticity and plasticity are shown with excellent robustness and accuracy.

Original languageEnglish
Pages (from-to)53-67
Number of pages15
JournalFinite Elements in Analysis and Design
Publication statusPublished - 2013


  • Kinematic constraints
  • Mixed method
  • Shells
  • Spherical interpolation

ASJC Scopus subject areas

  • Analysis
  • Engineering(all)
  • Computer Graphics and Computer-Aided Design
  • Applied Mathematics


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