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

Beveridge, Andrew J. and Wheel, M. (2009) A control volume based formulation of the discrete Kirchoff triangular thin plate bending element. In: The 17th UK National Conference on Computational Mechanics in Engineering, 2009-04-06 - 2009-04-08.

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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.