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#

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].

** Next:** Integral equation
** Up:** Applications of FMM to
** Previous:** Many penny-shaped cracks
*Ken-ichi Yoshida*

*2001-07-28*