Machine Design

FEA Update: How to add joints to beam structures

Many mechanical structures are modeled with beam elements because they can represent any material and cross section, as well as transmit axial loads, moments, and torques. "But what if a designer must model a structure that transmits only torque -- not moments?

The office chair shows that more than structural towers can be modeled with the FEA program GBW32 from Grape Software. A user has released translation along the Y axis and rotation about the Z axis of element 75, effectively creating a hinge.
A beam element consists of two nodes and can be of any cross section or material. There are six degrees of freedom (dof) per node. Elements joined at a node behave as if welded. Relesaing one or more dofs transforms the connection.
Release the local X axis degree of freedom at the node that joins two beam elements.
To model a hinge, release the rotation about the appropriate local axis at the node. Releasing rotation about the Z axis, for example, lets the beams on either side of the node rotate about the Z axis.
To create a ball and socket joint, release all three rotational degrees of freedom about the local beam element axis at the node.
Place more and shorter beam elements near the released degree of freedom. Elements further away from the release should be progressively longer. Short elements at the release point give correct displacement and rotation information.
Local y and Ry dofs have been released at the beam-element connection. The result will be a pinned joint that also translates along the vertical beam, which may not have the user's intended affect on the model.

Or include a slider joint? What then?" asks Erik Luczak, director of Grape Software Inc., Winnipeg, Man., Canada ( The answer: Release nodes.

Proper use of release nodes requires a good understanding of beam-element characteristics. That is why designers sometimes overlook them. "Each beam element has two nodes with six degrees of freedom per node: translation in the X, Y, and Z axis and rotations about these three axes," says Luczak. "Translations allow transmitting shear loads in two directions and an axial load. Rotations allow bending about two axes perpendicular to each other and a torque along the axis. When two elements join at a node, the connection is treated as if it's welded because it transmits loads and moments. Release nodes, however, let designers model a number of real-world structures that are actually a combination of welded, slider, pinned, and ball-and-socket joints.

To model a pin, slider, or ball connection, the analyst releases appropriate degrees of freedom. "This is where knowledge of beam elements and user-friendly software play important roles" he adds.The hazard is that releasing the wrong degree of freedom can have unwanted and diverse effects on the model. "This is one reason designers shy away from release nodes and go with less-refined solutions. When using release nodes, designers must anticipate a particular result. For instance, if designers require accurate displacement or rotation, or both, then a number of short elements must be used at the point of release.

If not, analysts may interpret translation results as being incorrect or assume the release is not having the desired effect. If internal-member loads and stress results are unimportant, then adding short elements is not required.

Designers should also consider the effects release nodes will have on applied loads and moments. If one or more degrees of freedom are released, the applied loading can have different affects. For example, a moment cannot be applied to a rotational degree of freedom that is no longer there.

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