KSCE Journal of Civil Engineering

, Volume 16, Issue 7, pp 1230–1242

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


    • Dept. of Mechanics, Faculty of Mathematics and Computer ScienceUniversity of Science, Vietnam National University — HCM
    • Division of Computational MechanicsTon Duc Thang University
  • Hiep Vinh Nguyen
    • Faculty of Civil EngineeringHo Chi Minh City University of Transport
  • Stephane Bordas
    • School of Engineering, Institute of Theoretical, Applied and Computational MechanicsCardiff University
  • Timon Rabczuk
    • Institute of Structural MechanicsBauhaus-University Weimar
  • Marc Duflot
Research Paper

DOI: 10.1007/s12205-012-1515-7

Cite this article as:
Nguyen-Xuan, H., Nguyen, H.V., Bordas, S. et al. KSCE J Civ Eng (2012) 16: 1230. doi:10.1007/s12205-012-1515-7


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.


3D elasticity cell-based smoothed finite element (CS-FEM) convergence stabilization

Copyright information

© Korean Society of Civil Engineers and Springer-Verlag Berlin Heidelberg 2012