26 2. LET’S GET STARTED
Table 2.1: Conversions of two-dimensional assumptions
Solution To convert to E is is
replaced by replaced by
Plane stress Plane strain E=.1
2
/ =.1 /
Plane strain Plane stress E.1 C 2/=.1 C /
2
=.1 C /
2.4.4 THE LIMIT OF THE ROUND (AXISYMMETRY)
Finally, many practical problems exhibit azimuthal symmetry about an axis. When there is no
dependence of the deformation on the angle, , in Fig. 2.13, the state of stress will not vary
in this direction and the stress and deformation fields reduce to functions of .r; z/ only. Such
conditions arise whenever:
1. all cross sections in the r-z-plane experience identical deformations;
2. externally applied forces are functions of r and z only; and
3. there is no -variation of the deformation in the body, i. e., points in the transverse .r; z/
plane always remain in their respective transverse planes following application of the loads.
r
z
Figure 2.13: An axisymmetric geometry results when there is no variation in the azimuthal () direc-
tion.
For such cases in FEA, the body is meshed in the r-z plane and an axisymmetric, two-dimensional
continuum element is chosen for the analysis.
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