Civil Engineering Reference
In-Depth Information
y
h
,
T
a
y
h
,
T
a
h
,
T
a
2
b
x
Q
b
2
a
h
,
T
a
a
x
(a)
(b)
(c)
y
q
y
0
Insulated
y
q
x
0
h
,
T
a
h
,
T
a
2
b
Insulated
a
h
,
T
a
x
x
(d)
(e)
(f )
Figure 7.12
Illustrations of symmetry dictated by boundary conditions.
symmetric conditions about the
x
axis but symmetry about the
y
axis exists. For
these conditions, we can use the “half-symmetry” model shown in Figure 7.12f,
using the symmetry (boundary) condition
q
x
=
0
across
x
=
0
and apply the
internal heat generation term
Q
/
2
.
Symmetry can be used to reduce the size of finite element models signifi-
cantly. It must be remembered that symmetry is not simply a geometric occur-
rence. For symmetry, geometry, loading, material properties, and boundary
conditions must all be symmetric (about an axis, axes, or plane) to reduce the
model.
7.4.4 Element Resultants
In the approach just taken in heat transfer analysis, the primary nodal variable
computed is temperature. Most often in such analyses, we are more interested in
the amount of heat transferred than the nodal temperatures. (This is analogous to
structural problems: We solve for nodal displacements but are more interested in
stresses.) In finite element analyses of heat transfer problems, we must back sub-
stitute the nodal temperature solution into the “reaction” equations to obtain
global heat transfer values. (As in Example 7.5, when we solved the partitioned
matrices for the heat flux values at the constrained nodes.) Similarly, we can back
