The global link element is formulated in the global coordinate system and acts like a spring between two nodes. The stiffness of the link is defined by the user in the global coordinate system. It is intended to link two nodes with X, Y, or Z stiffness even if the link element is drawn at an angle to the global axes. It does not generate moments due to out-of-plane offsets.

Degrees of Freedom

The global link element contains six degrees-of-freedom (DoFs) at each node:

1. x-translation
2. y-translation
3. z-translation
4. rotation about x
5. rotation about y
6. rotation about z

There are six nodes defined for this formulation. These nodes are numbered from 1 to 6 in a counter-clockwise direction, bottom surface first, then top surface. This element formulation does not contain rotational degrees of freedom.

The local stiffness matrix is formulated with the following degree-of-freedom order:

$\begin{bmatrix}u_1 & v_1 & w_1 & \theta_{1,x} & \theta_{1,y} & \theta_{1,z} & u_2 & v_2 & w_2 & \theta_{2,x} & \theta_{2,y} & \theta_{2,z} \end{bmatrix}$

Where:

$u_k=$ x-translation at node $k$

$v_k=$ y-translation at node $k$

$w_k=$ z-translation at node $k$

$\theta_{k,x}=$ rotation about x at node $k$

$\theta_{k,y}=$ rotation about y at node $k$

$\theta_{k,z}=$ rotation about z at node $k$

Stiffness Matrix