eXtended Finite Element Method (XFEM) | Mathematical and Numerical Study for Cracked Domains Computations

Elie Chahine

ISBN 10: 3639208781 / ISBN 13: 9783639208788

Published by VDM Verlag Dr. Müller, 2009

About this Item

eXtended Finite Element Method (XFEM) | Mathematical and Numerical Study for Cracked Domains Computations | Elie Chahine | Taschenbuch | Englisch | VDM Verlag Dr. Müller | EAN 9783639208788 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu.

Seller Inventory # 101428905

Bibliographic Details

• Title: eXtended Finite Element Method (XFEM) | Mathematical and Numerical Study for Cracked Domains Computations
• Publisher: VDM Verlag Dr. Müller
• Publication Date: 2009
• Language: English
• ISBN 10: 3639208781
• ISBN 13: 9783639208788
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 220W x 150H x 6D millimeters 220 millimeters width by 150 millimeters height by 6 millimeters depth
• Weight: 176 grams
• Seller catalogs:
  • Bücher

About this title

Synopsis

When modeling cracked domains, the classical FEM shows many drawbacks. The eXtended Finite Element method (XFEM) was introduced to overcome these difficulties. It allows modeling cracks and crack growth using a mesh independent of the crack path. Meanwhile, the optimal XFEM (with surface enrichment) is rather expensive. Also, the use of XFEM is limited to case where the singularity expansion at the crack tip is known. This work introduces XFEM variants that overcome these limitations and gives the first mathematical results for this type of methods. We introduce in the first part of this book, two XFEM variants (XFEM with a cutoff function and Integral Matching XFEM) allowing to obtain optimal convergence results for XFEM with a reduced computational cost. The second part presents two other XFEM methods (Spider XFEM and Reduced Basis XFEM) extending the application field of XFEM: they allow the use of XFEM when the singularity at the crack tip is partially or completely unknown, or even complicated. We prove the mathematical optimal convergence for these approaches and we perform numerical experiments validating the theoretical study.