Introduction 7
Consider a at plate with a hole, as shown in Figure 1.7. A tensile pressure is
applied at the left and right sides. It is only necessary to consider one-quarter of the
problem. This type of symmetry is called the planar. The boundary condition should
be modi ed at the surfaces of symmetry. For the example shown in Figure 1.7, the
vertical line of symmetry should have zero displacement in the x-direction, and
the horizontal line of symmetry should have a zero displacement in the y-direction.
The cyclic symmetry is similar to the planar symmetry except that it is described
in a cylindrical rather than a rectangular coordinate system. The common problem
found in practice is a washer under stress, as shown in Figure 1.8.
When the geometry and boundaries of the model are repeated in a particular
direction, then the model has a repetitive symmetry. The repetitive symmetry is also
called a periodic. For example, the simulation of a ow in a wavy channel can be eas-
ily modeled using the repetitive symmetry, as shown in Figure 1.9. Special periodic
boundary conditions should be imposed. In addition, the size of a long beam with
holes under a distributed pressure can be signi cantly reduced using the repetitive
symmetry. In this case, the vertical line of symmetry should have a zero displacement
in the x-direction, as shown in Figure 1.9.
FIGURE 1.6 Type of symmetry: axial.
T = 25°C
T = 25°C
T = 95°C
T = 95°C
FIGURE 1.7 Type of symmetry: planar.
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