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Meshless Methods and Their Numerical Properties
book

Meshless Methods and Their Numerical Properties

by Hua Li, Shantanu S. Mulay
February 2013
Intermediate to advanced content levelIntermediate to advanced
447 pages
14h 16m
English
CRC Press
Content preview from Meshless Methods and Their Numerical Properties
Recent developments of meshless methods 103
where K is the stiffness matrix, and f is the force vector, namely
∫∫
=Ω−Γ
−Γ
ΩΓ Γ
vDBwNDBwNDBKd
dd
ij i
T
ji
ji
j
ss
is
u
(3.138)
∫∫
=Ω
ΩΓ
fw
bw
t
dd
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
φφ
B
0
0
j
jx
jy
jy jx
,
,
,,
(3.141)
=
v
w
w
ww
0
0
i
ix
iy
iy ix
,
,
,,
(3.142)
=
N
nn
nn
0
0
xy
yx
(3.143)
where w
i
, b
i
, and
t
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 ...
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Publisher Resources

ISBN: 9781466517462