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A cell-based smoothed finite element method for three dimensional solid structures

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Abstract

This paper extends further the strain smoothing technique in finite elements to 8-noded hexahedral elements (CS-FEM-H8). The idea behind the present method is similar to the cell-based smoothed 4-noded quadrilateral finite elements (CS-FEM-Q4). In CSFEM, the smoothing domains are created based on elements, and each element can be further subdivided into 1 or several smoothing cells. It is observed that: 1) The CS-FEM using a single smoothing cell can produce higher stress accuracy, but insufficient rank and poor displacement accuracy; 2) The CS-FEM using several smoothing cells has proper rank, good displacement accuracy, but lower stress accuracy, especially for nearly incompressible and bending dominant problems. We therefore propose 1) an extension of strain smoothing to 8-noded hexahedral elements and 2) an alternative CS-FEM form, which associates the single smoothing cell issue with multi-smoothing cell one via a stabilization technique. Several numerical examples are provided to show the reliability and accuracy of the present formulation.

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Authors and Affiliations

  1. Dept. of Mechanics, Faculty of Mathematics and Computer Science, University of Science, Vietnam National University — HCM, Hochiminh, 700000, Vietnam

    Hung Nguyen-Xuan

  2. Division of Computational Mechanics, Ton Duc Thang University, Hochiminh, 700000, Vietnam

    Hung Nguyen-Xuan

  3. Faculty of Civil Engineering, Ho Chi Minh City University of Transport, Hochiminh, 700000, Vietnam

    Hiep Vinh Nguyen

  4. School of Engineering, Institute of Theoretical, Applied and Computational Mechanics, Cardiff University, Wales, UK

    Stephane Bordas

  5. Institute of Structural Mechanics, Bauhaus-University Weimar, 99423, Weimar, Germany

    Timon Rabczuk

  6. CENAERO, Rue des Frres Wright 29, 6041, Gosselies, Belgium

    Marc Duflot

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  1. Hung Nguyen-Xuan
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  2. Hiep Vinh Nguyen
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  3. Stephane Bordas
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  4. Timon Rabczuk
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  5. Marc Duflot
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Correspondence to Hung Nguyen-Xuan.

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Nguyen-Xuan, H., Nguyen, H.V., Bordas, S. et al. A cell-based smoothed finite element method for three dimensional solid structures. KSCE J Civ Eng 16, 1230–1242 (2012). https://doi.org/10.1007/s12205-012-1515-7

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  • DOI: https://doi.org/10.1007/s12205-012-1515-7

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