| Preface | xiii |
| Chapter 1 | Fundamental of plane elasticity crack problem | |
| 1 | Introduction | 1 |
| 2 | Cauchy integrals | 4 |
| 3 | Some elementary formulae for the calculation of Cauchy integrals | 5 |
| 4 | Poincare-Bertrand formula | 8 |
| 5 | Basic equations of complex variable function method in plane elasticity | 9 |
| 6 | Elementary solutions initiated by point sources | 10 |
| 7 | Elementary solutions for a single crack problem | 13 |
| 8 | Modified complex potentials for the case of bonded half-planes | 17 |
| 9 | Modified complex potentials for the case of circular boundary | 19 |
| 10 | Eigenfunction expansion form and singular stress field at the vicinity of crack tip | 24 |
| 11 | Logarithmic singularity at crack tip in plane elasticity | 27 |
| Chapter 2 | Multiple crack problems in an infinite plate | |
| 1 | Introduction | 35 |
| 2 | Singular integral equation for the multiple crack problem (type S1) | 36 |
| 3 | First type of Fredholm integral equation for the multiple crack problem (type R1A) | 41 |
| 4 | Alternative Fredholm integral equation for the multiple crack problem (type R1B) | 45 |
| 5 | Alternative singular integral equation for the multiple crack problem (type S2) | 48 |
| 6 | Third type of Fredholm integral equation for the multiple crack problem (type R2) | 51 |
| 7 | Hypersingular integral equation for the multiple crack problem (type HS) | 54 |
| 8 | General case of the multiple crack problem | 60 |
| 9 | Multiple semi-infinite crack problem in an elastic plane | 65 |
| 10 | Integral equations for the multiple crack problem in antiplane elasticity | 69 |
| 11 | T-stress analysis in the multiple crack problem | 78 |
| 12 | Interactions between main crack and microcracks | 81 |
| Chapter 3 | Multiple crack problems in more complicated cases | |
| 1 | Introduction | 87 |
| 2 | Multiple crack problems or circular regions | 87 |
| 3 | Multiple cracks in a pressurized cylinder | 98 |
| 4 | Multiple crack problems of circular region in antiplane elasticity | 103 |
| 5 | Multiple crack problems for two bonded half-planes in plane and antiplane elasticity | 106 |
| 6 | Multiple crack problem for an infinite strip | 113 |
| 7 | Multiple crack problem for a finite plate | 116 |
| 8 | Multiple crack problem for a rectangular region in antiplane elasticity | 118 |
| 9 | Periodic crack problem in plane elasticity | 121 |
| 10 | Doubly periodic crack problem in an infinite plate | 124 |
| 11 | Multiple branch crack problem in plane elasticity | 130 |
| 12 | Solution of multiple crack problem of elastic half-plane by using singular integral approach | 135 |
| 13 | Interaction between a hole edge crack and line crack | 139 |
| 14 | Interaction between an oblique edge crack and an internal crack in a cracked half-plane | 148 |
| 15 | Collinear crack problems in an infinite plate | 151 |
| 16 | An infinite plate containing hypocycloid hole with many cusps | 155 |
| 17 | Solution of antiplane elasticity crack problem using conformal mapping | 159 |
| 18 | Solutions of torsion crack problems of a rectangular bar | 163 |
| 19 | Solutions of torsion crack problems of a circular cross section bar | 168 |
| Chapter 4 | Miscellaneous problems | |
| 1 | Introduction | 175 |
| 2 | A rigid line problem in plane elasticity | 176 |
| 3 | Singular integral equation for the multiple rigid line problem and its regularization | 181 |
| 4 | Alternative singular integral equation for the multiple rigid line problem and its regularization | 188 |
| 5 | Collinear rigid line problems in an infinite plate | 191 |
| 6 | An infinite plate containing hypocycloid rigid inclusion with many cusps | 194 |
| 7 | Rigid line problems in antiplane elasticity | 196 |
| 8 | Multiple thermally insulated crack problem in an infinite plate | 200 |
| 9 | Multiple plate problem in two-dimensional potential flow | 209 |
| 10 | Multiple circular hole problems in plane elasticity | 213 |
| 11 | Elastic analysis of doubly periodic circular holes in an infinite plane | 222 |
| Chapter 5 | Three-dimensional multiple crack problem | |
| 1 | Introduction | 229 |
| 2 | Fundamental integral statement for the 3-D crack problem | 230 |
| 3 | Integral equations for the flat crack problem | 234 |
| 4 | Some particular solutions for penny-shaped crack problem by using hypersingular or differential-integral equation | 238 |
| 5 | Differential-integral equation for elliptical crack problem under normal loading | 246 |
| 6 | Differential-integral equation for elliptical crack problem under shear loading | 250 |
| 7 | Numerical solution of flat crack problem by using hypersingular integral equation | 257 |
| 8 | Hypersingular integral equation approach for multiple coplanar penny-shaped crack problems | 260 |
| 9 | Fredholm integral equation approach for multiple coplanar penny-shaped crack problems | 268 |
| 10 | Solution of multiple coplanar problems by using variational principle and differential-integral equation | 279 |
| Chapter 6 | Programs for multiple crack problems | |
| 1 | Introduction | 291 |
| 2 | Solution of problem of multiple crack problem by using the singular integral equation (Type S1) | 293 |
| 3 | Solution of problem of multiple crack problem by using the Fredholm integral equation (Type R1A) | 307 |
| 4 | Solution of problem of two cracks by using the Fredholm integral equation (Type R1B) | 308 |
| 5 | Solution of problem of multiple crack problem by using the Fredholm integral equation (Type R2) | 313 |
| 6 | Solution of problem of multiple crack problem in a circular plate by using the Fredholm integral equation (Type R1B) | 315 |
| 7 | Solution of the multiple crack problem in bonded half-planes by using the Fredholm integral equation (Type R1B) | 320 |
| 8 | Solution of multiple branch crack problem by using singular integral equation (Type S1) | 326 |
| 9 | Solution of the multiple coplanar penny-shaped crack problem by using Fredholm integral equation | 330 |
| 10 | Conclusion | 335 |
