
Recent developments of meshless methods 103
where K is the stiffness matrix, and f is the force vector, namely
=Ω−Γ
ΩΓ Γ
vDBwNDBwNDBKd
ij i
T
ji
j
ss
u
(3.138)
=Ω
fw
t
iii
s
ii
st
(3.139)
=
−
−
D
E
v
v
v
v
1
10
10
00
1
2
forplane stress
2
(3.140)
=
φ
φ
B
0
0
j
jx
jy
jy jx
,
,
(3.141)
=
v
w
w
0
0
i
ix
iy
iy ix
,
,
(3.142)
=
N
0
0
(3.143)
where w
i
, b
i
, and
i
are the weight function, body force, and traction
matrixes of the corresponding node i, respectively and E is the Young’s
modulus and ν the Poisson ratio.
The Gauss quadrature is employed here to perform the numerical
integrations in Equations (3.138) and (3.139). For ...