MDO does not have nonlinear spring.
Also, relations are not linked/updated to measures during analysis. (limited usage)
The proper way is with a force/torque motor with the math necessary.
This is linear spring example. You should be able to apply similarly to torsion spring.
Setup measures: Lengthofspring(L), Velocityofspringjoint(VelX)
user defined measures:
FreeLength(FreeL) = 5.0 (just a number to capture the free length)
Sign = ((FreeL-L)*VelX)/abs(((FreeL-L)*VelX))
Make force/torque Motor with primary variable Sign.
Set domain for sign positive and one for negative.
Each with force based on spring length
(L-FreeL) * 30 Domain(-1.0 <= Sign < 0.0)
(L-FreeL) * 20 Domain(0.0 <= Sign <= 1.0)
Note: The signs of measures matter, check simulation and reverse Rate1 Rate2 if necessary.
If visualization of the spring is desired, place a very low stiffness spring, otherwise only the force motor applies the representation of the spring.
Also, as a pro tip, many things like friction, aerodynamic drag, etc. can be applied as equations within force motors.


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