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On Three-dimensional Modelling of Crack Growth Using Extended Isogeometric Method

Jalali Moghadam, Mohamad | 2014

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  1. Type of Document: M.Sc. Thesis
  2. Language: English
  3. Document No: 46505 (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. Isogeometric Analysis method is a newly introduced method for the analysis of problems governed by partial differential equations.The major difference between classic finite element method and isogeometric method is that FEA uses piecewise polynomial shape functions for analysis while the Non-Uniform Rational B-Splines (NURBS) functions are applied as basis function in isogeometric method. To model strong discontinuities like cracks in classical finite element method , very fine mesh near the crack tip must be used. Application of eXtended Finite Element Method (X-FEM) avoid making very fine mesh near crack tip which is a time consuming task. In the extended finite element method , a standard displacement based finite element approximation is enriched by additional (special) functions derived from fracture mechanics using the framework of partition of unity. The concept of eXtended Isogeometric Analysis (X-IGA) is similar to X-FEM for solving crack problems. In the X-IGA method basis functions are enriched isogeometrically around the crack tip. Nature of NURBS function increases the precision of calculations in comparison with the classical Lagrange shape function and makes refining and manipulating of the mesh more convenient. In the present work, X-IGA is used to model and analyze three-dimensional crack growth problems
  9. Keywords:
  10. Isogeometric Method ; Fracture Mechanics ; Crack Growth ; Three Dimentional Crack ; Non-Uniform Rational B-Splines (NURBS)Functions ; Extended Isogeometric Analysis

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