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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
118 Meshless methods and their numerical properties
where Γ
w
, Γ
θ
, Γ
M
and Γ
v
are the boundaries of w, θ, M, and V imposed,
respectively, and t is the time and t
0
is the initial time. The local weak
form of the differential Equation (3.166) over a local support domain Ω
s
bounded by Γ
s
can be constructed by the weighted residual method as
ρ
∂∂
∂∂
Ω=
ρ
∂θ
∂∂
∂θ
+
Ω=
vA
w
tx
GAk
w
x
fd
vI
tx
EI
x
GAk
w
x
d
0
0
s
s
2
2
2
2
s
s
(3.171)
where v is the weight function. Integrating Equation (3.171) by parts, one
can have
∫∫
∫∫
ρ
Ω+
Ω−
=
ρ
∂θ
Ω+
∂θ
+
Ω−
∂θ
=
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Publisher Resources

ISBN: 9781466517462