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Modeling of Arbitrary Interfaces with Extended Finite Element (XFEM)in Pressure-Sensitive Materials

RafieeRaad, Maryam | 2012

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  1. Type of Document: M.Sc. Thesis
  2. Language: English
  3. Document No: 43214 (53)
  4. University: Sharif University of Technology, International Campus, Kish Island
  5. Department: Science and Engineering
  6. Advisor(s): Khoei, Amir Reza
  7. Abstract:
  8. There are various physical phenomena involving discontinuities and interfaces. The finite element method (FEM) has become the most popular and influential analytical tool for solving these physical phenomena. In the analysis of progressive failures because of discontinuities and interfaces, the mesh adaptive refinement in diverse stages of process is of great importance and, at each stage the mesh conforming to the shape of the interfaces is not inconsiderable. Consequently, the requirement of mesh adaption may necessitate high expenses of time and capacity. In contrast, the extended finite element method (XFEM) has been developed to efficiently perform modeling of problems including discontinuity in the field of displacement or strain and interfaces. This method does not need fine nor special mesh structure besides the discontinuities surfaces and interfaces; because, the extended finite element method (XFEM) is of enrichment functions which are capable of representing these features. However, this method is more accurate than the standard FEM, when the enrichment functions are applied to the problems. The reported results of the previous research projects have shown the same convergence rate as the standard FEM, which is suboptimal. This degradation of the convergence rate is attributed to parasitic terms in the approximation space that arises in the blending elements, and these parasitic terms limit the accuracy of local PUM methods. In the present work, it is aimed to eliminate the parasitic terms by applying different methods in the blending elements. These methods are shown to be significantly more accurate than the standard XFEM for a given element size and to converge optimally
  9. Keywords:
  10. Extended Finite Element Method ; Finite Element Method ; Enrichment ; Partition Unity Method (PUM) ; Blending Elements

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