Exact elasticity-based finite element for circular plates

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Date
2017
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Language
en
Pages
219-226
Series
Computers and Structures, Volume 182
Abstract
In this paper, a general elasticity solution for the axisymmetric bending of a linearly elastic annular plate is used to derive an exact finite element for such a plate. We start by formulating an interior plate problem by employing Saint Venant’s principle so that edge effects do not appear in the plate. Then the elasticity solution to the formulated interior problem is presented in terms of mid-surface variables so that it takes a form similar to conventional engineering plate theories. By using the mid-surface variables, the exact finite element is developed both by force- and energy-based approaches. The central, nonstandard feature of the interior solution, and the finite element based on it, is that the interior stresses of the plate act as surface tractions on the plate edges and contribute to the total potential energy of the plate. Finally, analytical and numerical examples are presented using the elasticity solution and the derived finite element.
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Karttunen , A , von Hertzen , R , Reddy , J & Romanoff , J 2017 , ' Exact elasticity-based finite element for circular plates ' , Computers and Structures , vol. 182 , pp. 219-226 . https://doi.org/10.1016/j.compstruc.2016.11.013