High Order Exact Geometry Finite Elements for Seven- Parameter Shells with Parametric and Implicit Reference Surfaces

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Abstract

We present high order surface finite element methods for the linear analysis of seven-parameter shells. The special feature of these methods is that they work with the exact geometry of the shell reference surface which can be given parametrically by a global map or implicitly as the zero level-set of a level set function. Furthermore, a special treatment of singular parametrizations is proposed. For the approximation of the shell displacement parameters we have implemented arbitrary order hierarchical shape functions on quadrilateral and triangular meshes. The methods are verified by a convergence analysis in numerical experiments.

Original languageEnglish
Pages (from-to)133-145
JournalComputational mechanics
DOIs
Publication statusPublished - 2019

Fingerprint

Shell
Higher Order
Finite Element
Level Set
Geometry
Quadrilateral Mesh
Zero set
Triangular Mesh
Shape Function
Convergence Analysis
Finite element method
Parametrization
Finite Element Method
Numerical Experiment
Experiments
Arbitrary
Approximation

Keywords

  • Exact geometry
  • Higher order
  • Implicit geometry
  • Shells
  • Surface finite elements

ASJC Scopus subject areas

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

Fields of Expertise

  • Information, Communication & Computing

Cite this

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abstract = "We present high order surface finite element methods for the linear analysis of seven-parameter shells. The special feature of these methods is that they work with the exact geometry of the shell reference surface which can be given parametrically by a global map or implicitly as the zero level-set of a level set function. Furthermore, a special treatment of singular parametrizations is proposed. For the approximation of the shell displacement parameters we have implemented arbitrary order hierarchical shape functions on quadrilateral and triangular meshes. The methods are verified by a convergence analysis in numerical experiments.",
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AB - We present high order surface finite element methods for the linear analysis of seven-parameter shells. The special feature of these methods is that they work with the exact geometry of the shell reference surface which can be given parametrically by a global map or implicitly as the zero level-set of a level set function. Furthermore, a special treatment of singular parametrizations is proposed. For the approximation of the shell displacement parameters we have implemented arbitrary order hierarchical shape functions on quadrilateral and triangular meshes. The methods are verified by a convergence analysis in numerical experiments.

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