Extended Finite Element Modeling of Large Deformation with Approprate Blending Elements

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Ehsaniardestani, Hedieh | 2012

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Type of Document: M.Sc. Thesis
Language: English
Document No: 43128 (53)
University: Sharif University of Technology, International Campus, Kish
Department: Science and Engineering
Advisor(s): Khoei, Amir Reza
Abstract:
In a classical finite element approach, interfaces are tracked and meshed. This mesh strategy introduces mesh distortions and difficulties to mesh the possibly complex interface shape. The Partition of Unity Method (PUM) alleviates these difficulties by allowing the discontinuities to be mesh-independent. This thesis concentrates on the blending elements in the eXtended Finite Element Method (XFEM).
The XFEM method enables local enrichments of approximation spaces. The standard finite elements are used in the major part of the domain and enriched elements are employed where special solution properties such as discontinuities and singularities shall be captured. In the extended finite element method (XFEM), errors are caused by parasitic terms in the approximation space of the blending elements at the edge of the enriched subdomain. These blending elements often require a special treatment in order to avoid a decrease in the overall convergence rate. Some modifications of the XFEM approximation are proposed in this work. The corrected XFEM is applied to problems in large deformation and optimal convergence rates are achieved
Keywords:
Large Deformation ; Extended Finite Element Method ; Enrichment ; Convergence

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