
170 Meshless methods and their numerical properties
4.3.5.4 Semi-infinite plate with a central hole
The RDQ method is applied to solve the problem of a semi-innite plate with
a central hole, as shown in Figure4.20a. Only one quarter of the plate is used
as the computation domain due to the axis-symmetric nature, as shown in
Figure4.20b. The analytical solutions in a Cartesian coordinate system are
given as
E
P
rb
r
b
r
b
r
1
1
cos( )
2
1
cos( )
2
cos3
2
cos(3)
0
00
22 4
3
()
=
+ν
+ν
θ+
+ν
θ+ θ− θ
(4.49)
v
E
P
rb
r
b
r
b
r
1
1
sin( )
1
1
sin( )sin(3 )
2
sin(3)
2
00
0
0
0
22 4
3
=
+ν
−ν
+ν
θ−
−ν
+ν
θ
+
θ
−
θ
(4.50)
–1
–0.5
0
0.5
1
1.5
0
2
4
6
8
–2.5
–2
–1.5
–1
–0.5
12
10 ...