An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order

H. Nguyen-Xuan, G. R. Liu, S. Bordas, S. Natarajan, Timon Rabczuk

Research output: Contribution to journalArticle

125 Citations (Scopus)

Abstract

This paper presents a singular edge-based smoothed finite element method (sES-FEM) for mechanics problems with singular stress fields of arbitrary order. The sES-FEM uses a basic mesh of three-noded linear triangular (T3) elements and a special layer of five-noded singular triangular elements (sT5) connected to the singular-point of the stress field. The sT5 element has an additional node on each of the two edges connected to the singular-point. It allows us to represent simple and efficient enrichment with desired terms for the displacement field near the singular-point with the satisfaction of partition-of-unity property. The stiffness matrix of the discretized system is then obtained using the assumed displacement values (not the derivatives) over smoothing domains associated with the edges of elements. An adaptive procedure for the sES-FEM is proposed to enhance the quality of the solution with minimized number of nodes. Several numerical examples are provided to validate the reliability of the present sES-FEM method.

Original languageEnglish
Pages (from-to)252-273
Number of pages22
JournalComputer Methods in Applied Mechanics and Engineering
Volume253
DOIs
Publication statusPublished - 2013 Jan 1
Externally publishedYes

Fingerprint

Mechanics
Finite element method
finite element method
stress distribution
Stiffness matrix
stiffness matrix
Derivatives
smoothing
unity
mesh
partitions
near fields

Keywords

  • Adaptive finite elements
  • Crack propagation
  • Singular ES-FEM
  • Singularity
  • Smoothed finite element method

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)

Cite this

An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order. / Nguyen-Xuan, H.; Liu, G. R.; Bordas, S.; Natarajan, S.; Rabczuk, Timon.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 253, 01.01.2013, p. 252-273.

Research output: Contribution to journalArticle

Nguyen-Xuan, H. ; Liu, G. R. ; Bordas, S. ; Natarajan, S. ; Rabczuk, Timon. / An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order. In: Computer Methods in Applied Mechanics and Engineering. 2013 ; Vol. 253. pp. 252-273.
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