Polynomial C1 shape functions on the triangle

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We derive generic formulae for all possible C1 continuous polynomial interpolations for triangular elements, by considering individual shape functions, without the need to prescribe the type of the degrees of freedom in advance. We then consider the possible ways in which these shape functions can be combined to form finite elements with given properties. The simplest case of fifth-order polynomial functions is presented in detail, showing how two existing elements can be obtained, as well as two new elements, one of which shows good numerical behaviour in numerical tests.

Original languageEnglish
Pages (from-to)53-58
JournalComputers and Structures
Early online date24 Jul 2012
Publication statusPublished - Mar 2013


  • Finite elements
  • C1 continuity
  • Shape functions
  • Triangular element
  • Gradient elasticity

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