COMBINATION OF REGIONS 207
and
[K'KfMf]
2 Ϊ
Pi;
= [M
2
]{P
2
} + D
2
(7.51)
Writing these two equations together, as a single matrix equation, we
have,
H
1
Hi
-G/
0
L 0 K
2
M
2
K
2
J
region 1 inter- region 2
face
U
1
u
2
M
2
r
B
^
>
+
<
(7.52)
Notice that on the boundary of the finite element region Ω
2
, only
the displacements on Γ
λ
have to be prescribed, whilst on the boundary
of Ω
2
we prescribe the displacements or tractions and consequently
need to reorder the equations.
The advantage of the second approach is that it does not require an
inversion.
REFERENCES
1.
Ungless, R. F., 'An Infinite Finite Element', M.Sc. Thesis, Department of Civil
Engineering, University of British Columbia, Canada (1973)
2.
Bettess, P., 'Infinite Elements', Int. J. Num. Meth. Engng, 11, 53-64 (1977)
3.
Lachat, J. C, Ά Further Development of the Boundary Integral Technique for
Elastostatics', Ph.D. Thesis, University of Southampton (1975)
4.
Brebbia, C. A. and Walker, S., 'Simplified Boundary Elements for Radiation
Problems', Res. Note,
Appl.
Math. Modelling, 2, No. 2, June (1978)
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in the Open Sea', Proc. 10th Symp. on Naval Hydrodynamics, London, 1974, pp.
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6. Shaw, R. P. and Falby, W., 'FEBIE—A Combined Finite Element-Boundary
Integral Equation Method', Proc. 1st Int. Symp.
on
Innovative Numerical Analysis
in Applied
Engineering
Science, Versailles, France, May 23-27, 1977
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Proc. 10th Symp. on Naval Hydrodynamics, London, 1974 (1975)
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Elements', Adv. Water Resources, 1, No. 3, June (1978)
208 COMBINATION OF REGIONS
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Symp., Atlas Computer Laboratory, Didcot, UK March 26-28, 1974
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Bettess, P. and Zienkiewicz, O. C, 'Diffraction and Refraction of Surface Waves
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Engng,
11,1271-40 (1977)
11.
Hommas, S., 'On the Behaviour of Seismic Sea Waves round Circular Island',
Geophys. Mag., 21, 199-208 (1950)
12.
Vastano, A. C. and Reid, R. O., Tsunami Response for Islands: Verificiation of a
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Osias, J. R., Wilson, R. B. and Seitelman, L. A., 'Combined Boundary Integral
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in
Applied Engineering Science,
Versailles,
France, May 23-27,
1977
15.
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Conf.
on Applied Mathematical Modelling, St. Louis, Missouri, August, 1977
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Appl.
Math. Modelling, 2, No. 1, March
(1978)
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