Kirchhoff–Love shell theory based on tangential differential calculus

Research output: Contribution to journalArticleResearchpeer-review

Abstract

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
Volume64
Issue number1
DOIs
Publication statusPublished - Jul 2019

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Differentiation (calculus)
Shell Theory
Differential Calculus
Parametrization
Shell
Geometry
Mesh
Isogeometric Analysis
Isosurface
Formulation
Mathematical operators
Level Set Method
Shape Function
Convergence Rate
Differential operator
Discretization
Higher Order
Benchmark
Finite Element
Numerical Results

Keywords

  • 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

Cite this

Kirchhoff–Love shell theory based on tangential differential calculus. / Schöllhammer, D.; Fries, T. P.

In: Computational mechanics, Vol. 64, No. 1, 07.2019, p. 113–131.

Research output: Contribution to journalArticleResearchpeer-review

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