Fwd: Regarding Step 60 tutorial of deal.ii

[Ramprasad R]

Dear Sir/Madam,

I am a student in Technical University of Braunschweig, Germany. I am trying to work on a project for the aerospace department of my university. In this project I am trying to extend the step 60 tutorial into buckling analysis. I am trying to find a function to calculate the geometric stiffness matrix. It would be of great help if I could find some help regarding this issue. 

Hoping to hear from you soon.

Thank you.

Best regards,

Ramprasad Raghunath

[Wolfgang Bangerth]

On 6/22/19 3:46 AM, Ramprasad R wrote:
>
> I am a student in Technical University of Braunschweig, Germany. I am trying
> to work on a project for the aerospace department of my university. In this
> project I am trying to extend the step 60 tutorial into buckling analysis. I
> am trying to find a function to calculate the geometric stiffness matrix.

Can you describe how exactly the "geometric stiffness matrix" is defined?

Best
W.

--
------------------------------------------------------------------------
Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/

[peterrum]

Do you mean something like these lines in step 44:

```cpp

if (component_i == component_j)

  data.cell_matrix(i, j) += grad_Nx[i][component_i] * tau *grad_Nx[j][component_j] * JxW;

```

Peter 

[Ramprasad R]

Hello all,

The following image has the exact formulation of the geometric stiffness matrix. Which is denoted by G in the image.

Thank you for your reply.

Warm regards,

Ramprasad

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[Wolfgang Bangerth]

On 6/24/19 9:24 AM, Ramprasad R wrote:
>
> The following image has the exact formulation of the geometric stiffness
> matrix. Which is denoted by G in the image.

Ramprasad,
I don't think I quite understand the connection step-60. In the context
of that problem, for which of the two variables (u and lambda) do you
want to compute that matrix? Assuming you mean that it is supposed to be
for u, it is not difficult to write down what you need to do based on
what you already learn in step-3 or step-4, for example. In fact, these
two early programs already implement the first two terms of G_ij if you
assume that N_x=N_y=N_xy=1.

I am not familiar with the terms used in the page you show. Are the N_*
factors constants? Are they functions of space?

[Ramprasad R]

Hello Bangerth,

The terms N_* are the resultant forces in the * direction and these forces are calculated using the strains which in turn are calculated using the displacements u. So the terms N_* are not constants, rather change with each element. And these values directly depend on u.

Thank you.

Regards,

Ramprasad

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[Daniel Garcia-Sanchez]

On Monday, June 24, 2019 at 11:36:32 PM UTC+2, Ramprasad R wrote:

Hello Bangerth,

The terms N_* are the resultant forces in the * direction and these forces are calculated using the strains which in turn are calculated using the displacements u. So the terms N_* are not constants, rather change with each element. And these values directly depend on u.

Hi Ramprasad,

I think that you want to do an eigenvalue calculation (step-36)

I think that first you have to do an static calculation before your eigenvalue calculation in order to obtain the values for N_* (step-8)

As discussed in your paper, the typical eigenvalue problem for the elastic equation takes this form, where omega^2 is your eigenvalue and Phi the eigenvector

(K - omega^2 M)*Phi = 0

For the buckling case lambda is your eigenvalue.

(K - lambda G)*Phi = 0

The calculation of K can be found in step-8, step-62 (or other tutorials).

I think that in order to calculate G you need the resulting strain of an static calculation. You can do the static calculation, store the strain in a temporary buffer and use that data to calculate G. step-18 shows you how to do this.

Once you have K and G, you can do an eigenvalue calculation. step-36 shows you how to do an eigenvalue calculation. Note that in step36 the stiffness matrix is called A.

The equation in step36 is 

(D-epsilon M)*Phi=0

which is very similar to the buckling equation. 

Best,

Daniel 

[Ramprasad R]

Hi Daniel,

Thank you so much for your detailed Explanation. As you said earlier, I have to do the eigen value analysis.  You explanation has given me an approach to start with. I can not thank you enough.

Warm regards

Ramprasad

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[Ramprasad R]

Hello all,

I would like to know if I can use one name space (step-x) in another name space (step-y). So that I can couple the 2 or more steps.

Thank you.

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[Wolfgang Bangerth]

On 7/25/19 8:12 AM, Ramprasad R wrote:
>
> I would like to know if I can use one name space (step-x) in another name
> space (step-y). So that I can couple the 2 or more steps.

Yes, of course. These are just different namespaces. You can combine them in
one program in the same way as you can copy a class with one name to a file in
which you already have a class with a different name.