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Advances in Meshfree Techniques pp 1–26Cite as

A Global-Local Approach for the Construction of Enrichment Functions for the Generalized FEM and Its Application to Three-Dimensional Cracks

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Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 5))

Abstract

Existing generalized or extended finite element methods for modeling cracks in three-dimensions require the use of a sufficiently refined mesh around the crack front. This offsets some of the advantages of these methods specially in the case of propagating three-dimensional cracks. In this paper, a strategy to overcome this limitation is investigated. The approach involves the development of enrichment functions that are computed using a new global-local approach. This strategy allows the use of a fixed global mesh around the crack front and is specially appealing for non-linear or time dependent problems since it avoids mapping of solutions between meshes. The resulting technique enjoys the same flexibility of the so-called meshfree methods for this class of problem while being more computationally efficient.

The proposed generalized FEM with global-local functions, by numerically constructing the enrichment functions, brings the benefits of existing generalized FEM to a broader class of problems. The procedure is applied to the solution of three-dimensional linear elastic fracture mechanics problems. Numerical experiments demonstrating the computational efficiency and accuracy of the method are presented.

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Author information

Authors and Affiliations

  1. Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, 205 North Mathews Avenue, Urbana, IL, 61801, USA

    C. Armando Duarte & Dae-Jin Kim

  2. Institute for Computational Engineering and Sciences, The University of Texas at Austin, 1 University Station, C0200, Austin, TX, 78712, USA

    Ivo Babuška

Authors
  1. C. Armando Duarte
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  2. Dae-Jin Kim
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  3. Ivo Babuška
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Editor information

Editors and Affiliations

  1. Instituto Superior Técnico, Lisboa, Portugal

    V. M. A. Leitão  & C. J. S. Alves  & 

  2. University of Illinois at Urbana-Champaign, Urbana, IL, USA

    C. Armando Duarte

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Armando Duarte, C., Kim, DJ., Babuška, I. (2007). A Global-Local Approach for the Construction of Enrichment Functions for the Generalized FEM and Its Application to Three-Dimensional Cracks. In: Leitão, V.M.A., Alves, C.J.S., Armando Duarte, C. (eds) Advances in Meshfree Techniques. Computational Methods in Applied Sciences, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6095-3_1

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  • DOI: https://doi.org/10.1007/978-1-4020-6095-3_1

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-6094-6

  • Online ISBN: 978-1-4020-6095-3

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