Kirchhoff–Love shell theory based on tangential differential calculus

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 curvi...

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Bibliographic Details
Published in:Computational mechanics 2019-07, Vol.64 (1), p.113-131
Main Authors: Schöllhammer, D., Fries, T. P.
Format: Article
Language:English
Subjects:
Classical and Continuum Physics
Computational Science and Engineering
Computer graphics
Differential calculus
Differential equations
Engineering
Finite element method
Mathematical analysis
Operators (mathematics)
Original Paper
Parameterization
Shape functions
Shell theory
Theoretical and Applied Mechanics
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Summary: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.
ISSN:0178-7675
1432-0924
DOI:10.1007/s00466-018-1659-5