• Chapter 1 Introduction (13)
  • 1.1 Isogeometric Analysis (13)
  • 1.2 Fracture mechanics and eXtended Finite Element Method (13)
  • 1.3 eXtended Isogeometric Analysis (XIGA) (14)
• Chapter 2 Introduction to Isogeometric Analysis (15)
  • 2.1 Isogeometric Analysis Method (15)
    • 2.1.1 Computational Geometry (18)
  • 2.2 Basic Terminologies (18)
  • 2.3 B-splines (21)
    • 2.3.1 Knot vector (22)
    • 2.3.2 Basis Functions (24)
    • 2.3.3 Derivatives of B-spline basis functions (28)
    • 2.3.4 B-spline geometries (29)
      • 2.3.4.1 B-spline curves (29)
      • 2.3.4.2 B-spline surfaces (31)
      • 2.3.4.3 B-spline solids (33)
    • 2.3.5 Refinement (34)
      • 2.3.5.1 Knot insertion (34)
      • 2.3.5.2 Order Elevation (37)
  • 2.4 Non-Uniform Rational B-Splines (NURBS) (40)
  • 2.5 NURBS drawbacks (41)
    • 2.5.1 Local refinement (41)
    • 2.5.2 Patch Assembly (42)
  • 2.6 T-splines (43)
    • 2.6.1 PB-Splines (43)
    • 2.6.2 Defining T-splines (45)
      • 2.6.2.1 Anchors and T-mesh (45)
      • 2.6.2.2 Building a T-spline (47)
  • 2.7 Isoparametric concept (47)
  • 2.8 Obtaining weak form of BVPs (49)
  • 2.9 Similarities and differences for Isogeometric analysis and Finite element analysis (50)
• Chapter 3 Discretization and Linear Elasticity Problems (52)
  • 3.1 Formulating the equation (52)
    • 3.1.1 Strong form of BVP (53)
    • 3.1.2 Weak Form of Equilibrium equation (54)
      • 3.1.2.1 Galerkin’s method (55)
  • 3.2 One Dimensional Poisson’s Equation (58)
  • 3.3 Infinite plate with circular hole under constant in-plane tension (63)
• Chapter 4 Fracture Mechanics, A review (67)
  • 4.1 Historical perspective (67)
  • 4.2 Westergaard analysis of a sharp crack (69)
  • 4.3 Stress Intensity Factor (SIFs) (70)
  • 4.4 Griffith theory of strength (74)
  • 4.5 Brittle Materials (75)
  • 4.6 Mixed mode crack propagation (77)
  • 4.7 J-integral method for calculation of SIFs (78)
  • 4.8 Some numerical method based on J-integral method (81)
    • 4.8.1 Equivalent domain integral method (81)
    • Li et al [23] proposed the equivalent domain integral method as an alternative approach, which requires only one analysis. According to Fig. 2.17b, the J integral can be defined as ( [23,24]): (81)
    • 4.8.2 Interaction integral method (82)
• Chapter 5 Extended finite element method (84)
  • 5.1 A review of XFEM development (84)
  • 5.2 Basics of XFEM (86)
    • 5.2.1 Partition of unity (86)
    • 5.2.2 Enrichment (87)
      • 5.2.2.1 Intrinsic enrichment (88)
      • 5.2.2.2 Extrinsic enrichment (90)
  • 5.3 Enrichment in extended finite element method (91)
    • 5.3.1 The Heaviside function (93)
    • 5.3.2 Asymptotic functions (94)
  • 5.4 XFEM discretization (95)
  • 5.5 Element integration (97)
• Chapter 6 Extended isogeometric analysis for modeling crack growth problems (100)
  • 6.1 Introduction (100)
  • 6.2 Need for XIGA (100)
  • 6.3 Enrichment in XIGA (102)
  • 6.4 Numerical examples (103)
    • 6.4.1 A rectangular plate with an edge crack (103)
    • 6.4.2 An infinite plate with a middle crack under uniform uniaxial in-plane tension (107)
    • 6.4.3 Propagating crack through a T-spline patch of plate with a middle crack under uniform in-plane tension (110)
    • 6.4.4 A plate with two circular holes and two edge crack under displacement control state (116)
• Chapter 7 Conclusion and future works (120)
  • 7.1 Conclusion (120)
  • 7.2 Future works (121)