Crack problems for three-dimensional elastostatics with collocation method

In this section we discuss an application of FM-BIEM to crack problems for three-dimensional elastostatics. Applications of FM-BIEM to ordinary problems in three-dimensional elastostatics are found in Fu et al.[18,19], Fukui and Kutsumi[27] and Takahashi et al.[78]. In our formulation we use 4 multipole moments for both ordinary problems and crack problems. On the other hand, Fu et al. use 12 multipole moments in their FMM formulation and Fukui and Kutsumi use the Neuber-Papkovich representation to obtain the same 4 multipole moment formulation as the present one. Also, Takahashi et al. use our formulation. In this section we use collocation method and piecewise constant shape functions for discretisation of BIEs. In elastostatics we can compute the multipole moments analytically in the regularised formulation. Although we have shown that FM-BIEM with the regularised integral equation is slower than FM-BIEM with the hypersingular integral equation in Laplace's equation, it is of interest to examine if the same conclusion is true in elasticity as well. Hence, we describe the regularised formulation as well as the non-regularised formulation once again.

The material in this section is from Yoshida et al.[84].