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Active Degrees Of Freedom

Before the stiffness matrix is assembled it is necessary to decide which degrees of freedom need to be included in the solution.

The nodes can be categorised as follows:

  • Inactive the node does not exist.
  • Non-structural the node is not part of the structure (e.g. orientation node).
  • Active the node is part of the structure.

Likewise the degrees of freedom can be categorised as:

  • Non-existent this degree of freedom does not exist. The node is undefined.
  • Inactive this degree of freedom exists but is not used (considered like a restrained node).
  • Restrained the degree of freedom exists and is part of the structure but it is restrained and so it is not active in the stiffness matrix.
  • Constrained the degree of freedom is constrained (through being in a rigid constraint, or by a repeat freedom) to move relative to a primary degree of freedom and so it is not active in the stiffness matrix.
  • Active this degree of freedom is active in the stiffness matrix.

In setting up a list of degrees of freedom the following operations are carried out:

  1. All the nodes are assumed to be inactive.
  2. Look at elements attached to nodes to see which degrees of freedom are required.
  3. Remove the degrees of freedom that are restrained by single point constraints or global constraints.
  4. Remove the degrees of freedom that are constrained.
  5. Remove degrees of freedom that have no local stiffness.
  6. Number the degrees of freedom.

The degrees of freedom are made active based on the elements attached at the nodes. The degrees of freedom will depend on the element type: These are summarised in the table below:

ElementActive degrees of freedom per node
Bar, Cable1 translational
Rod1 translational + 1 rotational
Beam3 translational + 3 rotational
General spring3 translational + 3 rotational
Mass3 translational
Mass with inertia3 translational + 3 rotational

2D plane stress

2D plane strain


2 translational (Bilinear)

2 translational + 1 rotational (Allman-Cook)

2D bending

1 translational + 2 rotational (Mindlin)

1 translational + 3 rotational (MITC)

2D shell

3 translational + 2 rotational (Mindlin)

3 translational + 3 rotational (MITC)

3D solid3 translational