M. Denda et Yf. Dong, COMPLEX VARIABLE APPROACH TO THE BEM FOR MULTIPLE CRACK PROBLEMS, Computer methods in applied mechanics and engineering, 141(3-4), 1997, pp. 247-264
A boundary element method for straight multiple center and edge crack
problems is developed in this paper. The method is constructed upon th
e systematic use of the elastic singularity solutions in complex varia
bles. The crack opening is represented by the continuous distribution
of dislocation dipoles and the effect of the non-crack boundary by the
continuous distributions of point forces and dislocation dipoles. The
crack-tip singularity is embedded into the interpolation using orthog
onal polynomials (i.e. Chebyshev and Jacobi) and their associated sing
ular weight functions. The proposed analytical integration procedure o
f the Cauchy-type integrals defined over the crack eliminates the need
for the quadrature formulae for numerical integration, streamlines, a
nd enhances the accuracy of the traditional singular integral equation
method for crack problems. The stress intensity factors for the fifte
en problems analyzed in this paper have been accurate enough to substi
tute those given in stress intensity factor handbooks. Since non-crack
boundary of arbitrary shape can be introduced at will the method is e
xpected to give accurate stress intensity factors for complex rear lif
e problems.