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Element-Free Discretization Method with Moving Finite Element Approximation

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Computational and Experimental Simulations in Engineering (ICCES 2021)

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 98))

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Abstract

The popularity of standard Finite Element Method (FEM) results from its simplicity and wide applicability in engineering computations. The simplicity consists in polynomial interpolation of field variables within finite elements, while the wide applicability in rather close similarity of engineering problems based mostly on variational formulations. On the other hand, the standard FEM suffers from limited continuity on element intersections, global meshing difficulty in analysis of complex geometry, and global equations may not be parallelized efficiently. All these shortcomings can be removed in the mesh free formulations, where the arbitrary net of nodal points is used for discretization instead of subdivision of the analyzed domain into finite elements. The spatial approximations based on cluster of nodes are not expressed in terms of elementary functions and evaluation of the shape functions prolongs the computation. To get rid of disadvantages of the standard FEM and mesh free formulations, the moving finite element (MFE) method has been proposed. In this paper, we pay attention to explanation of the basis of the MFE approximation and to its combination with the strong as well as local weak formulations of boundary value problems for stationary heat conduction in solids with functionally graded heat conduction coefficient. Finally, in numerical test examples the reliability (accuracy and numerical stability) and computational efficiency are compared for three variants of the MFE method and the standard FEM.

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Acknowledgements

The authors acknowledge the support by the Slovak Science and Technology Assistance Agency registered under number SK-CN-RD-18-0005 and VEGA-2/0061/20.

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Authors and Affiliations

  1. Institute of Construction and Architecture, Slovak Academy of Sciences, Bratislava, 845 03, Slovakia

    Vladimir Sladek & Jan Sladek

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  1. Vladimir Sladek
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  2. Jan Sladek
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Correspondence to Vladimir Sladek .

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Editors and Affiliations

  1. Mechanical Engineering, Texas Tech University, Lubbock, TX, USA

    Satya N. Atluri

  2. Mechanical Engineering, University of Montenegro, Podgorica, Montenegro

    Igor Vušanović

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Sladek, V., Sladek, J. (2021). Element-Free Discretization Method with Moving Finite Element Approximation. In: Atluri, S.N., Vušanović, I. (eds) Computational and Experimental Simulations in Engineering. ICCES 2021. Mechanisms and Machine Science, vol 98. Springer, Cham. https://doi.org/10.1007/978-3-030-67090-0_30

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  • DOI: https://doi.org/10.1007/978-3-030-67090-0_30

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-67089-4

  • Online ISBN: 978-3-030-67090-0

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