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K matrix

gfraulini
17-Peridot

K matrix

Hi all,

do you know how to read the stiffness matrix?
I've read of a method for understand whether the K matrix is ill-conditioned.
It consist in the calculus of the condition number of K expressed as the ration between the max and min value of the eigenvalues of K.

How can I do this? (also utilizing Mathcad)

1 ACCEPTED SOLUTION

Accepted Solutions
ehaenen
4-Participant
(To:gfraulini)

Giulio

You're not wrong, but a) you can come close to K eigenvalues if you choose M small --> use a very low specific mass.

2) if you go for normal modes (even with correct mass) and you look at modeshapes, they should deform your structure in a natural way.

A poorly conditioned mesh would clearly show up in strange mechanisms that seem to appear in your structure. I can trigger this in Nastran by making an ugly mesh. I've not been able to trigger this in  simulate.

The other answer is: I do not know how to get the stiffness matrix as output.

Erik

View solution in original post

6 REPLIES 6
ehaenen
4-Participant
(To:gfraulini)

Hi Giulio

It's always been my understanding that Simulate does not use a regular stiffness matrix. The relevant matrix does not contain true stifnesses, it is filled with data derived from the coefficients of the P-method displacement functions. The nice thing here is that very small coefficients simply do not develop. The K-matrix in Simulate is only ill-conditioned for an insufficiently constrained model. I use this to my advantage to develop bearing elements in assemblies, with an extremely low stiffness in the sliding direction of the bearing. This works great in modal analysis models.

Erik

gfraulini
17-Peridot
(To:ehaenen)

Hi Erik,
but do you know the file where I can find the Matrix? And how can I open it?

In truth I would the eigenvalues. Is there another method for get them?

ehaenen
4-Participant
(To:gfraulini)

Giulio

I do not know where and in what format the Matrix is stored, eigenvalues (and eigenvectors) is easy, run a modal analysis.

Erik

gfraulini
17-Peridot
(To:ehaenen)

I've read that a way to determine if the "numerical quality" of the mesh, is calculating the conditioning number expressed as the ration between the max and min of the eigenvalues.
More this ratio is distant from 1 and more sensible will be the problem respect of the numerical stability: small variations within K cause big variations in the results.

The modal analysis gives out the natural frequencies, resolving a matricial equation like
det(M^-1 * K - w^2 * M^-1 * M) = 0.
where lambda = w^2 are the eigenvalues of the matrix
A = [M^-1 * K].

So the natural frequencies are equal to the eigenvalues of A, and not K.

I'm wrong?

ehaenen
4-Participant
(To:gfraulini)

Giulio

You're not wrong, but a) you can come close to K eigenvalues if you choose M small --> use a very low specific mass.

2) if you go for normal modes (even with correct mass) and you look at modeshapes, they should deform your structure in a natural way.

A poorly conditioned mesh would clearly show up in strange mechanisms that seem to appear in your structure. I can trigger this in Nastran by making an ugly mesh. I've not been able to trigger this in  simulate.

The other answer is: I do not know how to get the stiffness matrix as output.

Erik

View solution in original post

gfraulini
17-Peridot
(To:ehaenen)

Hi Erik,

I guess your tip of using a very low density to bring closer the matrix K to the matrix "A" is the better way to get a numeric validation.

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