Kirchhoff–Love shell theory based on tangential differential calculus

D. Schöllhammer*, T. P. Fries

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The Kirchhoff–Love shell theory is recasted in the frame of the tangential differential calculus (TDC) where differential operators on surfaces are formulated based on global, three-dimensional coordinates. As a consequence, there is no need for a parametrization of the shell geometry implying curvilinear surface coordinates as used in the classical shell theory. Therefore, the proposed TDC-based formulation also applies to shell geometries which are zero-isosurfaces as in the level-set method where no parametrization is available in general. For the discretization, the TDC-based formulation may be used based on surface meshes implying element-wise parametrizations. Then, the results are equivalent to those obtained based on the classical theory. However, it may also be used in recent finite element approaches as the TraceFEM and CutFEM where shape functions are generated on a background mesh without any need for a parametrization. Numerical results presented herein are achieved with isogeometric analysis for classical and new benchmark tests. Higher-order convergence rates in the residual errors are achieved when the physical fields are sufficiently smooth.

Original languageEnglish
Pages (from-to)113–131
Number of pages19
JournalComputational Mechanics
Issue number1
Publication statusPublished - Jul 2019


  • IGA
  • Isogeometric analysis
  • Manifolds
  • Shells
  • Tangential differential calculus
  • TDC

ASJC Scopus subject areas

  • Computational Mechanics
  • Ocean Engineering
  • Mechanical Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

Fields of Expertise

  • Advanced Materials Science


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