Multiple Crack Problems in Elasticity

"...a useful addition to the literature on computational methods for solving elastostatic crack problems." MATHEMATICAL REVIEWS

• 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 e 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 an tiplane 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. (part contents)