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 

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