A control volume based formulation of the discrete Kirchoff triangular thin plate bending element

A. J. Beveridge, M. A. Wheel

Research output: Contribution to conferencePaper

Abstract

A control volume method is presented for predicting the displacement and rotation of thin transversely loaded flat plates. The new procedure uses discrete Kirchoff triangle (DKT) elements but introduces a dual mesh of interconnected control volumes (CVs) centred on the finite element (FE) vertices. Discrete equations for the unknown degrees of freedom are subsequently derived by enforcing equilibrium on these CVs; as such this implementation is a quadrature free routine. To allow a comparison, a quadrature free implementation of the DKT element, using the standard finite element procedure, was developed using symbolic methematics. The CV based procedure is validated by patch tests for a state of pure bending and twist. Convergence tests for various loading types show enhanced performance for coarse meshes over the equivalent FE method.
LanguageEnglish
Pages287-290
Number of pages3
Publication statusPublished - 6 Apr 2009
EventThe 17th UK National Conference on Computational Mechanics in Engineering - Nottingham, UK
Duration: 6 Apr 20098 Apr 2009

Conference

ConferenceThe 17th UK National Conference on Computational Mechanics in Engineering
CityNottingham, UK
Period6/04/098/04/09

Fingerprint

Finite element method

Keywords

  • plate bending
  • finite element
  • control volume
  • symbolic mathematics

Cite this

Beveridge, A. J., & Wheel, M. A. (2009). A control volume based formulation of the discrete Kirchoff triangular thin plate bending element. 287-290. Paper presented at The 17th UK National Conference on Computational Mechanics in Engineering, Nottingham, UK, .
Beveridge, A. J. ; Wheel, M. A. / A control volume based formulation of the discrete Kirchoff triangular thin plate bending element. Paper presented at The 17th UK National Conference on Computational Mechanics in Engineering, Nottingham, UK, .3 p.
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Beveridge, AJ & Wheel, MA 2009, 'A control volume based formulation of the discrete Kirchoff triangular thin plate bending element' Paper presented at The 17th UK National Conference on Computational Mechanics in Engineering, Nottingham, UK, 6/04/09 - 8/04/09, pp. 287-290.

A control volume based formulation of the discrete Kirchoff triangular thin plate bending element. / Beveridge, A. J.; Wheel, M. A.

2009. 287-290 Paper presented at The 17th UK National Conference on Computational Mechanics in Engineering, Nottingham, UK, .

Research output: Contribution to conferencePaper

TY - CONF

T1 - A control volume based formulation of the discrete Kirchoff triangular thin plate bending element

AU - Beveridge, A. J.

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PY - 2009/4/6

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N2 - A control volume method is presented for predicting the displacement and rotation of thin transversely loaded flat plates. The new procedure uses discrete Kirchoff triangle (DKT) elements but introduces a dual mesh of interconnected control volumes (CVs) centred on the finite element (FE) vertices. Discrete equations for the unknown degrees of freedom are subsequently derived by enforcing equilibrium on these CVs; as such this implementation is a quadrature free routine. To allow a comparison, a quadrature free implementation of the DKT element, using the standard finite element procedure, was developed using symbolic methematics. The CV based procedure is validated by patch tests for a state of pure bending and twist. Convergence tests for various loading types show enhanced performance for coarse meshes over the equivalent FE method.

AB - A control volume method is presented for predicting the displacement and rotation of thin transversely loaded flat plates. The new procedure uses discrete Kirchoff triangle (DKT) elements but introduces a dual mesh of interconnected control volumes (CVs) centred on the finite element (FE) vertices. Discrete equations for the unknown degrees of freedom are subsequently derived by enforcing equilibrium on these CVs; as such this implementation is a quadrature free routine. To allow a comparison, a quadrature free implementation of the DKT element, using the standard finite element procedure, was developed using symbolic methematics. The CV based procedure is validated by patch tests for a state of pure bending and twist. Convergence tests for various loading types show enhanced performance for coarse meshes over the equivalent FE method.

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KW - finite element

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Beveridge AJ, Wheel MA. A control volume based formulation of the discrete Kirchoff triangular thin plate bending element. 2009. Paper presented at The 17th UK National Conference on Computational Mechanics in Engineering, Nottingham, UK, .