Understanding Degrees of Freedom

For finite element analysis (FEA) users, it's important to keep in mind that some types of elements might not transmit all types of loads through their nodes. For example, two structural beam elements connected together behave like a fully welded connection because the beam elements will transmit three forces (axial and two shears) and three moments (torsion and two bending). However, a beam element connected to a truss element behaves like a pinned joint because the truss element can only transmit axial forces. The concept of what forces are transmitted and consequently what loads and restraints can be applied is known as degree of freedom (DOF).

The DOF is important to understand in determining how loads can be applied, how boundary conditions restrain the model and how different element types need to be connected together. A translational DOF indicates that forces are transmitted through the nodes and a rotational DOF indicates that moments are transmitted through the nodes.

For example, two-dimensional (2-D) elements only have translational DOFs. Thus, you cannot apply a nodal moment to a 2-D element; mathematically, the element cannot react to the moment.

Figure 1: 2D Elements (Triangular)		Figure 2: 2D Elements (Quadrilateral)

In addition, a "fully fixed" boundary condition cannot provide a moment restraint to a brick element because brick elements only have translational DOFs.

Figure 3: Brick Elements (8 noded)

Finally, the beam to truss element connections could be unstable because the truss element will not prevent the beam element from rotating; if the other end of the beam is free to translate, then the connection behaves like a ball joint.

Figure 4: Beam Element to Truss Element connection

The last two examples may result in model stability messages (such as "model not tied down enough") during a linear static stress analysis.

Table 1: DOFs for common structural element types.

Element	Degrees of Freedom
Truss	translation in X, Y, Z
Beam	translation in X, Y, Z; rotation in X, Y, Z
2-D	translation in Y, Z
Brick	translation in X, Y, Z
Plate	translation in X, Y, Z; Two in-plane rotation DOFs (The out-of-plane rotational DOF is not considered for plate elements)

Note: This is a small subset of the available element types in Autodesk Simulation Mechanical software, see the User's Guide for a full list.