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A triangular plate element 2343 using second-order absolute-nodal-coordinate slopes: numerical computation of shape functions

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Abstract

In this paper, the process by which geometrical and structural matrices of plate finite elements employing absolute nodal coordinate formulation (ANCF) are constructed is studied. The kinematic and topological properties of an arbitrary plate finite element are described using universal digital code dncm that provides systematic enumeration of finite elements. This code is formed using the element’s dimension d, the number of nodes it possesses n, the number of scalar coordinates per node c, and a multiplier describing the process of transforming a conventional finite element to an ANCF element m. The detailed generation of a new type of triangular plate finite element 2343 using numerical computation of shape functions is also discussed in the paper. The new triangular element employs position vectors and slope vectors up to second-order mixed-derivative slope vector. A detailed derivation of the equations of motion of the element is also provided and examples of its numerical simulation and validation presented.

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Notes

  1. This problem can unambiguously be denoted by text line 0<{−l/2,−b/2:±b/2}[l×b×t,E×ν]{+l/2,±b/2}″(0,0,−P) for the further external references. This line contains all data mentioned above: geometry and material parameters of the plate are given in the square brackets […], application points (or intervals separated by a colon: symbol) for constraints and forces are given in the curly brackets {…} and are measured with respect to the plate’s center. The cantilever condition is denoted by combination 0< meaning attaching to the fixed reference frame indexed 0. The force vector is given in parenthesis ″(…). In the figure, the shortest notation is presented where the extreme points and intervals of the plate are shown just by signs −, +,: and ±, omitting numeric values l/2 and b/2.

  2. A short text description of this problem, [1×2×0.01×1e3,1e5×0.3]{±,±}.g, contains two new elements: the dot symbol . denotes the spherical joints at the four edges denoted by {±,±}, while symbol g introduces the default uniform gravity force.

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Acknowledgements

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology (2012R1A2A2A04047240 and 2012R1A1A2008870), Russian Foundation for Basic Research (11-01-00500-A), and Defense Acquisition Program Administration and Agency for Defense Development under the contract UD120037CD.

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Authors and Affiliations

  1. School of Mechanical Engineering, Konkuk University, 1 Hwanyang-Dong, Gwangjin-Gu, 143-701, Seoul, Korea

    Alexander Olshevskiy, Seoungsoo Lee & Chang-Wan Kim

  2. Department of Mechanical Engineering, Lappeenranta University of Technology, Skinnarilankatu 34, 53850, Lappeenranta, Finland

    Oleg Dmitrochenko

  3. Laboratory of Computational Mechanics, Bryansk State Technical University, Bulv. 50-let Oktyabrya, 7, 241035, Bryansk, Russia

    Alexander Olshevskiy & Oleg Dmitrochenko

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  1. Alexander Olshevskiy
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  4. Chang-Wan Kim
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Correspondence to Chang-Wan Kim.

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Olshevskiy, A., Dmitrochenko, O., Lee, S. et al. A triangular plate element 2343 using second-order absolute-nodal-coordinate slopes: numerical computation of shape functions. Nonlinear Dyn 74, 769–781 (2013). https://doi.org/10.1007/s11071-013-1004-7

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