Skew Frame Properties

Beam type spring elements are best defined using three nodes (Figure 1). Nodes 1 and 2 are the two ends of the element and define the local X axis. Node 3 allows the local Y and Z axes to be defined. However, this node does not need to be supplied.

If all three nodes are defined, the local reference frame is calculated by:(1)

\vec{x} = \bar{n_{1} n_{2}}

(2)

\vec{z} = \vec{x} \times \bar{n_{1} n_{3}}

(3)

\vec{y} = \vec{z} \times \vec{x}

If node 3 is not defined, the local skew frame that can be specified for the element is used to define the Z axis. The X and Y axes are defined in the same manner as before.(4)

\vec{z} = \vec{x} \times {\vec{y}}_{s k e w}

If no skew frame and no third node are defined, the global Y axis is used to replace the Y skew axis. If the Y skew axis is collinear with the local X axis, the local Y and Z axes are placed in a totally arbitrary position. The local Y axis is defined at time zero, and is corrected at each cycle, taking into account the mean X axis rotation.