Damping in a dynamic model?

[jd90]

In a static analysis we are solving: [K]{x}={F}
In a dynamic analysis we are solving: [M]{x''}+[C]{x'}+[K]{x}={F}

Now by introducing a quasi static problem, the initial acceleration at the beginning of each iteration is 0. so we are left with: [C]{x'}+[K]{x}={F}

As I have not specified damping in my model is this now:[K]{x}={F} or is damping used somehow in the model to counteract the [M]{x''} ?

I'm rather confused about this and struggling to find a clear definition.

 

[Mustaine3]

Why is x" zero at the beginning of an iteration?

 

[jd90]

im assuming that because in the step 'other' tab the "initial acceleration calculation at begining of step" is set to "Bypass".

Now i may be incorrect on this, because I've just been looking through the Abaqus manual and it says Quasi static applications introduce inertia to stabalise the system. So im guessing it is counteracting inertia with inertia!?

I'm hoping someone can clear this up?

 

[Mustaine3]

Beginning of a step is only one time beginning of an increment.

You're using *Dynamic, application=Quasi-Static? There is a lot of numerical damping in this method.

 

[jd90]

And is that how it is achieving the quasi-static behavior? By introducing damping?

Here is a quote from the Abaqus theory manual, the section in bold is what is confusing me, as you say damping is being introduced, affecting the inertia (increasing it?)

•Quasi-static applications are primarily interested in determining a final static response. These problems typically show monotonic behavior, and inertia effects are introduced primarily to regularize unstable behavior. For example, the statically unstable behavior may be due to temporarily unconstrained rigid body modes or “snap-through” phenomena. Large time increments are taken when possible to obtain the final solution at minimal computational cost. Considerable numerical dissipation may be required to obtain convergence during certain stages of the loading history.

 

[Mustaine3]

The highlighted section explains, why a dynamic procedure can handle unstable situations. A static procedure can't do that, since the released strain energy can not transform into kinetic energy. A dynamic procedure can do that, even if there is no damping.

 

[jd90]

I see what you mean, and i appreciate your comments but I'm still confused regarding how the program is actually implementing a quasi static application, you say it is increasing the damping but the section taken from the manual clearly states it is introducing inertia into the system.
Is the inertia being introduced a product of the numerical damping you speak of?

 

[Mustaine3]

The method in general is dynamic, so you have inertia. But at the same time the numerical way it is done (Backward Euler) adds a large amount of numerical damping.