Two-node 3-dimensional spring (SPRING2)

This is a spring element which is attached to two nodes (Figure 83). The directions $\boldsymbol{n_1}$ and $\boldsymbol{n_2}$ determining the action of the spring have to be defined by the user underneath the *SPRING keyword card by specifying the appropriate degrees of freedom. These degrees of freedom can be local if the ORIENTATION parameter is used on the *SPRING card. Usually, it does not make sense to take a different degree of freedom in node 1 and node2. If $\boldsymbol{u_1}$ is the displacement in node 1 (and similar for node 2) and $K$ is the spring constant, the force in node 1 is obtained by:

$$\boldsymbol{F_1}=K [(\boldsymbol{u_1} \cdot \boldsymbol{n_1}) \boldsymbol{n_1} - (\boldsymbol{u_2} \cdot \boldsymbol{n_2}) \boldsymbol{n_1}],$$ (12)

and the force in node 2 by:

$$\boldsymbol{F_2}=- K [(\boldsymbol{u_1} \cdot \boldsymbol{n_1}) \boldsymbol{n_2} - (\boldsymbol{u_2} \cdot \boldsymbol{n_2}) \boldsymbol{n_2}].$$ (13)

A nonlinear spring can be defined by specifying a piecewise linear force versus elongation relationship (underneath the *SPRING card).