In the Abaqus manual the velocity for a dashpota element is defined like this and multiplied with a factor for any change in the reference system
opposite to the Calculix manual where the reference factor has been lifted to the power of 2 like this
can anyone confirm that this just is an error in the Calculix manual or alternative maybe explain the reason for this difference.
Note that the Abaqus manual formula defines the velocity difference, while the formula in the CalculiX manual defines the force. Those are different things.
If you combine the formulae (ignoring the difference in notation) you get:
F₂ = -c·Δv·(x₂-x₁)/L.
That is, the force depends linearly on the velocity difference; which makes sense.
@rsmith I believe we misunderstand each other but can agree on that a common definition of damper force would be F = c·Δv or F = -c·Δv depending on how the local directions are defined so by substitution the Δv from Abaqus will give the same formula as you have written
F₂ = -c·Δv·(x₂-x₁)/L
but in the Calculix manual is written
F₂ = -c·(v₂-v₁)·(x₂-x₁)/L·(x₂-x₁)/L or F₂ = -c·Δv·(x₂-x₁)/L·(x₂-x₁)/L
and I simply cannot understand how you can get this last part "·(x₂-x₁)/L " to disappear from the formula
Where I think you are led astray is that Δv is not simply (v₂-v₁).
As defined in the Abaqus formula, Δv = (v₂-v₁)·(x₂-x₁)/L. Also note that this part is shown within square brackets in the CalculiX formula for F₂ even though that is not strictly necessary.
@rsmith I respect your answer but in that case i just don’t understand the meaning of the formulation in the Calculix manual.
v and x are vectors, not scalars, so in CCX the force magnitude is F=cΔv and the direction is defined by the unit vector along the line of action (x2-x1/L), the Δv also has to be evaluated in the direction of action, therefore using the dot product of the velocity vector and the unit vector along the direction of action. Same for Abaqus.
@JuanP74 , That makes sense. Thanks for the explanation.