Civil Engineering Reference
In-Depth Information
equations you simply add the location of the operator at
i
, known as the
pivot point. To take the product of two differential equations, you must
multiply the value of the operator at
i
of one differential to each of the
terms in the other differential. Partial differentials also require both
the
x
and
y
direction, so they will be written horizontally and vertically.
The following are six examples of creating partial difference operators for
the equation used to solve plate bending. The partial differential equation
is listed first in each of the six examples followed by the basic operators
that represent the equation.
Example 3.13
Partial difference operator
d
4
z
z
dx dy
d
4
d
4
z
1
14641
(
)
+
2
+
=
−
−
4
22
4
4
dx
dy
h
1
4
6
4
1
1
2
1
−
1
121
1
1
(
)
+
2
*
−
*
−
+
2
2
4
h
h
h
−
1
4
6
4
1
121
24 2
121
−
−
1
146412
1
1
+
(
)
+
=
−
−
*
−
−
h
4
h
4
h
4
−
−
1
282
1820
−
1
=
−
−
8
1
4
h
282
1
−
1
282
1820 81
282
1
−
4
4
4
q
D
d
z
z
dx dy
d
d
z
1
=+ +=
2
−
−
(3.12)
dx
4
22
dy
4
h
4
−
