Civil Engineering Reference
In-Depth Information
1
2
0
2
1
1
141
000
14 1
1
121
000
12 1
−
−
−
1
2
1
1
2
+
=
3
3
3
h
2
h
h
−
−
−
−
−
−
1
141
000
14 1
1
−
QD
z
dx dy
d
3
d
3
z
=
1
y
=−
+
(3.18)
2
3
3
dy
2
h
−
−
−
3.11
nuMERic MODELing WitH PARtiAL
DiffEREncE OPERAtORS
The differential equation and the difference operators from Section 3.10
are used in the following example to solve for plate bending. The forces
on a middle surface plate are shown in Figure 3.10.
Example 3.19
Plate bending
Calculate the shear, moment, rotation, and deflection for a 1 inch thick,
20 inch square, fixed end steel plate with a uniformly distributed load
of 100 psi using central difference operator of order of error
h
2
at 1/10th
points. The plate has
E
= 29,000 ksi and
u
= 0.25.
dx
dy
My +
δMy
δy
δMx
δx
dy
Mx
+
dx
Myx +
δMyx
δy
δMxy
dy
Mxy
+
+
δQx
dx
δx
+
δQy
δy
Qx
dx
Qy
dy
δx
Figure 3.10.
Numeric modeling with partial difference operators.
