Civil Engineering Reference
In-Depth Information
Table 3.11.
Gaussian quadrature
x
i
w
i
One point
0
2
Two points
-0.577350269
1
0.577350269
1
Three points
-0.774596669
0.555555556
0
0.888888889
0.774596669
0.555555556
Four points
-0.861136312
0.347854845
-0.339981044
0.652145155
0.339981044
0.652145155
0.861136312
0.347854845
Five points
-0.906179846
0.236926885
-0.538469310
0.478628670
0
0.568888889
0.538469310
0.478628670
0.906179846
0.236926885
Six points
-0.932469514
0.171324492
-0.661209386
0.360761573
-0.238619186
0.467913935
0.238619186
0.467913935
0.661209386
0.360761573
0.932469514
0.171324492
Two points are shown in Table 3.12:
Table 3.12.
Example 3.5 Gaussian quadrature
x
i
-0.577350269
2-points
0.577350269
w
i
1
1
s
1
+sx
i
2.90192379
8.098076211
f(s
1
+sx
i
)
0.462686003
0.90838186
f(s
1
+sx
i
)w
i
0.462686003
0.90838186
1.371067862
S
6.169805381
S*s
