24 2. LET’S GET STARTED
2.4.1 THE LIMIT OF THE THIN (PLANE STRESS AND PRESSURE
VESSELS)
ere are many problems of practical importance in which the stress conditions are ones of plane
stress. is occurs often in thin members, as shown in Fig. 2.11. In this limit:
1. e stress components
x
,
y
, and
z
do not vary through the thickness, i. e., they are
functions of x and y only.
2. Externally applied forces are functions of x and y only.
3. e out-of-plane stress components are identically zero, i. e.,
z
D 0
xz
D
zx
D 0
yz
D
zy
D 0:
For such cases in FEA, a two-dimensional solid or continuum plane stress element is used.
x
y y
z
y
x
)
(
xy
O
T
y
T
x
Figure 2.11: A state of plane stress will often result in thin sections with loads applied in the plane.
2.4.2 THE LIMIT OF THE THICK (PLANE STRAIN)
ere are many problems of practical importance in which the strain conditions are ones of plane
strain. For long, prismatic members subject to lateral loading in the x-y plane, as shown in
Fig. 2.12, a state of plane strain will result. In this limit:
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