Strain smoothing in FEM and XFEM

  • Authors:

  • Stéphane P. A. Bordas;Timon Rabczuk;Nguyen-Xuan Hung;Vinh Phu Nguyen;Sundararajan Natarajan;Tino Bog;Do Minh Quan;Nguyen Vinh Hiep

  • Affiliations:

  • Department of Civil Engineering, University of Glasgow, G12 8LT Scotland, UK;Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand;Division of Computational Mechanics, Department of Mathematics and Informatics, University of Natural Sciences, VNU-HCM, 227 Nguyen Van Cu, Viet Nam;Delft University of Technology, Faculty of Civil Engineering and Geosciences, Stevinweg 1, 2628 CN Delft, The Netherlands;GE Aviation, India Technology Center, Bangalore, India;Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand;Division of Computational Mechanics, Department of Mathematics and Informatics, University of Natural Sciences, VNU-HCM, 227 Nguyen Van Cu, Viet Nam;Division of Computational Mechanics, Department of Mathematics and Informatics, University of Natural Sciences, VNU-HCM, 227 Nguyen Van Cu, Viet Nam

  • Venue:
  • Computers and Structures
  • Year:
  • 2010

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Abstract

We present in this paper recent achievements realised on the application of strain smoothing in finite elements and propose suitable extensions to problems with discontinuities and singularities. The numerical results indicate that for 2D and 3D continuum, locking can be avoided. New plate and shell formulations that avoid both shear and membrane locking are also briefly reviewed. The principle is then extended to partition of unity enrichment to simplify numerical integration of discontinuous approximations in the extended finite element method. Examples are presented to test the new elements for problems involving cracks in linear elastic continua and cracked plates. In the latter case, the proposed formulation suppresses locking and yields elements which behave very well, even in the thin plate limit. Two important features of the set of elements presented are their insensitivity to mesh distortion and a lower computational cost than standard finite elements for the same accuracy. These elements are easily implemented in existing codes since they only require the modification of the discretized gradient operator, B.