| Contents | |
| Chapter 1 | Fundamental of plane elasticity crack problem |
| Introduction; Cauchy integrals; Some elementary formulae for the calculation of Cauchy integrals; Poincare-Bertrand formula; Basic equations of complex variable function method in plane elasticity; Elementary solutions initiated by point sources; Elementary solutions for a single crack problem; Modified complex potentials for the case of bonded half-planes; Modified complex potentials for the case of circular boundary; Eigenfunction expansion form and singular stress field at the vicinity of crack tip; Logarithmic singularity at crack tip in plane elasticity | |
| Chapter 2 | Multiple crack problems in an infinite plate |
| Introduction; Singular integral equation for the multiple crack problem (type S1); First type of Fredholm integral equation for the multiple crack problem (type R1A); Alternative Fredholm integral equation for the multiple crack problem (type R1B); Alternative singular integral equation for the multiple crack problem (type S2); Third type of Fredholm integral equation for the multiple crack problem (type R2); Hypersingular integral equation for the multiple crack problem (type HS); General case of the multiple crack problem; Multiple semi-infinite crack problem in an elastic plane; Integral equations for the multiple crack problem in antiplane elasticity; T-stress analysis in the multiple crack problem; Interactions between main crack and microcracks | |
| Chapter 3 | Multiple crack problems in more complicated cases |
Introduction; Multiple crack problems or circular regions; Multiple cracks in a pressurized cylinder; Multiple crack problems of circular region in antiplane elasticity; Multiple crack problems for two bonded half-planes in plane and antiplane elasticity; Multiple crack problem for an infinite strip; Multiple crack problem for a finite plate; Multiple crack problem for a rectangular region in antiplane elasticity; Periodic crack problem in plane elasticity; Doubly periodic crack problem in an infinite plate; Multiple branch crack problem in plane elasticity; Solution of multiple crack problem of elastic half-plane by using singular integral approach; Interaction between a hole edge crack and line crack; Interaction between an oblique edge crack and an internal crack in a cracked half-plane; Collinear crack problems in an infinite plate; An infinite plate containing hypocycloid hole with many cusps; Solution of antiplane elasticity crack problem using conformal mapping; Solutions of torsion crack problems of a rectangular bar; Solutions of torsion crack problems of a circular cross section bar |
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| Chapter 4 | Miscellaneous problems |
| Introduction; A rigid line problem in plane elasticity; Singular integral equation for the multiple rigid line problem and its regularization; Alternative singular integral equation for the multiple rigid line problem and its regularization; Collinear rigid line problems in an infinite plate; An infinite plate containing hypocycloid rigid inclusion with many cusps; Rigid line problems in antiplane elasticity; Multiple thermally insulated crack problem in an infinite plate; Multiple plate problem in two-dimensional potential flow; Multiple circular hole problems in plane elasticity; Elastic analysis of doubly periodic circular holes in an infinite plane | |
| Chapter 5 | Three-dimensional multiple crack problem |
| Introduction; Fundamental integral statement for the 3-D crack problem; Integral equations for the flat crack problem; Some particular solutions for penny-shaped crack problem by using hypersingular or differential-integral equation; Differential-integral equation for elliptical crack problem under normal loading; Differential-integral equation for elliptical crack problem under shear loading; Numerical solution of flat crack problem by using hypersingular integral equation; Hypersingular integral equation approach for multiple coplanar penny-shaped crack problems; Fredholm integral equation approach for multiple coplanar penny-shaped crack problems; Solution of multiple coplanar problems by using variational principle and differential-integral equation | |
| Chapter 6 | Programs for multiple crack problems |
Introduction; Solution of problem of multiple crack problem by using the singular integral equation (Type S1); Solution of problem of multiple crack problem by using the Fredholm integral equation (Type R1A); Solution of problem of two cracks by using the Fredholm integral equation (Type R1B); Solution of problem of multiple crack problem by using the Fredholm integral equation (Type R2); Solution of problem of multiple crack problem in a circular plate by using the Fredholm integral equation (Type R1B); Solution of the multiple crack problem in bonded half-planes by using the Fredholm integral equation (Type R1B); Solution of multiple branch crack problem by using singular integral equation (Type S1); Solution of the multiple coplanar penny-shaped crack problem by using Fredholm integral equation; Conclusion |
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