A general method of solution of two-dimensional problems in the theory of cracks

Interaction between Periodic System of Rigid Inclusions and Rectilinear Cohesive Cracks in an Isotropic Medium under Transverse Shear

“…In order to solve the problem in a natural way we combine the method worked out by solving the periodic elastic problem [2] with the method [23] for constructing in the explicit form the Kolosov-Muskhelishvili potentials, corresponding to unknown tangential displacements along cracks with the end zones. We represent the stresses and displacements [24] by the Kolosov-Muskheleshvili potentials…”

“…Using the quadrature formulas [23,25], we reduce main resolving equations (17), (18), (19), (20) to the totality of two infinite system of linear algebraic equation and to two finite algebraic systems with respect to approximate values ) ( …”

“…For constructing missing equations conditions (23) should be fulfilled at the nodal points. We use the finite differences method.…”

Mode Stresses for the Interaction between an Inclined Crack and a Curved Crack in Plane Elasticity

“…For two-dimensional crack, Panasyuk et al [1], Cotterell and Rice [2], Shen [3], and Martin [4] used perturbation method to obtain the elastic stress intensity factor for a variety of crack positions. Formulation in terms of singular, hypersingular, or Fredholm integral equations for solving single [5] and multiple cracks problems [6] in various sets of cracks positions was proposed later.…”

Interaction between inclined and curved cracks problem in plane elasticity

“…For two dimensional crack, perturbation method was used to obtain the elastic stress intensity factor for a variety of crack positions [1,2,3,4]. Formulation in terms of singular, hypersingular or Fredholm integral equations for solving single and multiple cracks problems in various set of cracks positions was proposed later [5].…”