Finite-part singular integral representation analysis in Lp of two-dimensional elasticity problems

A finite-part singular integral representation analysis in Lp is proposed for the solution of two-dimensional elasticity problems. The method consists of the reduction of the finite-part singular integral equations to the equivalent Fredholm equations. Nother theorems are generalized by using finite-part singular integral equations, by investigating the necessary and sufficient conditions for the solution of these equations in Lp, and by defining the index of such types of equations. A two-dimensional fracture mechanics application is given for the determination of the stress intensity factors in the neighborhood of a straight crack in a bimaterial infinite and isotropic solid under antiplane shear.