Civil Engineering Reference
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problem in Figure 11.4 where an additional circular impermeable isolator is specified on
the right hand side.
11
3
10
12
4
2
13
5
9
Region II, k
2
1
14
6
8
16
15
7
Region I, k
1
Figure 11.4
Problem with a circular inclusion and an isolator
Here only some of the nodes of region I are connected to region II. It is obviously
more efficient to consider in the calculation of the stiffness matrix only the interface
nodes, i.e. only of those nodes that are connected to a region. It is therefore proposed
that we modify our procedure in such a way that we first solve the problem with zero
values of
u
at the interface between region I and II and then solve the problem where
unit values of
u
are applied at each node in turn.
For partially coupled problems we therefore have to solve the following types of
problems (this is explained on a heat flow problem but can be extended to elasticity
problems by replacing
t
with
t
and
u
with
u
):
1.
Solution of system with “fixed” interface nodes
The first one is where boundary conditions are applied at the nodes which are not
connected to other regions (free nodes) and
Dirichlet
boundary conditions with
zero prescribed values are applied at the nodes which are connected to other
regions (coupled nodes). For each region we can write the following system of
equations:
>@
^`
^`
-
N
½
t
°
°
N
c
N
f
0
N
(11.7)
^`
B
F
®
¾
0
°
x
°
¯
¿
0
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