Symmetry

You do not need to model the whole section of this axisymmetric component because the problem is symmetric about a horizontal line through the center of the mount. By modeling only half of the section, you can use half as many elements and, hence, approximately half the number of degrees of freedom. This significantly reduces the run time and storage requirements for the analysis or, alternatively, allows you to use a more refined mesh.

Many problems contain some degree of symmetry. For example, mirror symmetry, cyclic symmetry, axisymmetry, or repetitive symmetry (shown in Figure 1) are common. More than one type of symmetry may be present in the structure or component that you want to model.

Figure 1. Various forms of symmetry.

When modeling just a portion of a symmetric component, you have to add boundary conditions to make the model behave as if the whole component were being modeled. You may also have to adjust the applied loads to reflect the portion of the structure actually being modeled. Consider the portal frame in Figure 2.

Figure 2. Symmetric portal frame.

The frame is symmetric about the vertical line shown in the figure. To maintain symmetry in the model, any nodes on the symmetry line must be constrained from translating in the 1-direction and from rotating about the 2- or 3-axes.

In the frame problem the load is applied along the model's symmetry plane; therefore, only half of the total value should be applied to the portion you are modeling.

In axisymmetric analyses using axisymmetric elements, such as this rubber mount example, we need model only the cross-section of the component. The element formulation automatically includes the effects of axial symmetry.