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

Hung Nguyen-Xuan, Hiep Vinh Nguyen, Stephane Bordas, Timon Rabczuk, Marc Duflot

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1230-1242
Number of pages13
JournalKSCE Journal of Civil Engineering
Issue number7
Publication statusPublished - 2012 Nov

Bibliographical note

Funding Information:
The support of the Vietnam National Foundation for Science and Technology Development (NAFOSTED); (Grant No. 107.02-2012.17) is gratefully acknowledged.


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

ASJC Scopus subject areas

  • Civil and Structural Engineering


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