2.4. Finding Ways to Take Advantage of Symmetry

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Many objects have some kind of symmetry, be it repetitive symmetry (such as evenly spaced cooling fins on a long pipe), reflective symmetry (such as a molded plastic container), or axisymmetry (such as a light bulb). When an object is symmetric in all respects (geometry, loads, constraints, and material properties), you can often take advantage of that fact to reduce the size and scope of your model.

Figure 2.7  Examples of Symmetry

2.4.1. Some Comments on Axisymmetric Structures

Any structure that displays geometric symmetry about a central axis (such as a shell or solid of revolution) is an axisymmetric structure. Examples would include straight pipes, cones, circular plates, domes, and so forth.

Models of axisymmetric 3-D structures may be represented in equivalent 2-D form. You may expect that results from a 2-D axisymmetric analysis will be more accurate than those from an equivalent 3-D analysis.

By definition, a fully axisymmetric model can only be subjected to axisymmetric loads. In many situations, however, axisymmetric structures will experience non-axisymmetric loads. You must use a special type of element, known as an axisymmetric harmonic element, to create a 2-D model of an axisymmetric structure with nonaxisymmetric loads. See Axisymmetric Elements with Nonaxisymmetric Loads in the Elements Reference for details.

2.4.1.1. Some Special Requirements for Axisymmetric Models

Special requirements for axisymmetric models include:

  • The axis of symmetry must coincide with the global Cartesian Y-axis.

  • Negative nodal X-coordinates are not permitted.

  • The global Cartesian Y-direction represents the axial direction, the global Cartesian X-direction represents the radial direction, and the global Cartesian Z-direction corresponds to the circumferential direction.

  • Your model should be assembled using appropriate element types:

    • For axisymmetric models, use applicable 2-D solids with KEYOPT(3) = 1, and/or axisymmetric shells. In addition, various link, contact, combination, and surface elements can be included in a model that also contains axisymmetric solids or shells. (The program will not realize that these "other" elements are axisymmetric unless axisymmetric solids or shells are present.) If the Elements Reference does not discuss axisymmetric applications for a particular element type, do not use that element type in an axisymmetric analysis.

    • For axisymmetric harmonic models, use only axisymmetric harmonic elements.

  • The SHELL61 element cannot lie on the global Y-axis.

  • For models containing 2-D solid elements in which shear effects are important, at least two elements through the thickness should be used.

2.4.1.2. Some Further Hints and Restrictions

If your structure contains a hole along the axis of symmetry, don't forget to provide the proper spacing between the Y-axis and the 2-D axisymmetric model. (See Figure 2.8: "An X-direction Offset Represents an Axisymmetric Hole".) See "Loading" in the Basic Analysis Guide for a discussion of axisymmetric loads.

Figure 2.8  An X-direction Offset Represents an Axisymmetric Hole

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