Stiffness matrix of simple shell element (Simple reasoning?)

[BennyS]

Hi together,
I struggle a lot with the task to set-up a stiffness matrix for a simple shell element.
In Nastran, I have a 5x5mm flat shell with 1mm thickness (isotropic), represented by a CQUAD4 element.

Can somebody explain an easy way to setup the corresponding stiffness matrix? I already read that its a 24x24 matrix, 12x12 from bending and 8x8 from membrane stiffness, the rotational degrees of freedom are usually 0 but are given a small value to make the matrices invertible. Unfortunately, Ive not found an easy way to create these submatrices, thus the element matrix.

Any advice would be really appreciated

Cheers
Benny

 

[WARose]

... like TET4s ?

No, I am talking the 8-node solid ["brick"] element. STAAD has never had anything but that for solid elements (that I am aware of).

 

[BennyS]

Thank you all so far for your responses.

@gravityandinertia :
Okay I think i used "analytical" in a wrong way.

To summarize it:
I have a structure (does not matter how it exactly looks).
I want to stiffen it by factorising the e-modul by 10%.
The other approach I want to compare to, is that I am not varying the young's modulus, but applying a factor to the stiffness matrix itself (so factorising each element of the matrix by 10%).
Now, I want to understand or to prove that both ways lead to the same result.
That's why I wanted to have a correlation between beam/QUAD stiffness matrix to the young's modulus.
According to my current understanding, there is a difference as the inplane rotational degree of freedom (r3) is not part of the element formulation ( in Nastran), and has to be therefore defined by the "K6ROT" parameter. This DOF stiffness is not influence by varying the young's modulus, but by varying the matrix itself.
Are my conclusion correct so far?

 

[rb1957]

it's my understanding that K6ROT won't seriously affect your model's results.

increase E by 10% should increase the model stiffness 10%.

no idea how to practically factor element stiffness 10%, unless you're doing this by hand. In which case you should clearly see the role of E, and so the self-fulfilling prophesy of what you're trying to do.

another day in paradise, or is paradise one day closer ?

 

[IDS]

There is a good short description of how the K6ROT parameter works here:

http://www.eng-tips.com/viewthread.cfm?qid=169523

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[BennyS]

So,
to sum up my latest information.

I analysed a simple CQUAD4 and I realized that varying Young's Modulus or Plate thickness IS influencing also the in-plane rotational DOF. So my previous statement that changing the young's modulus is not influencing these stiffness matrix entries but the direct matrix modification does, is wrong.

For the shell theory itself:
In the Nastran theoretical manual, there's a depiction of the material property matrix which is behind the "MAT1" card. In this case, the linear proportionality to the young's modulus is shown.

I found some information that a simple quadrilateral shell element can be superpositioned by membrane and plate-bending stiffness. The membrane stiffness is of shape 8x8 and the plate-bending is of shape 12x12. The K6Rot fills the last 4x4 to get the 24x24.
When I am focussing on Reissner-Mindlin plates ( =CQUAD4), I find some "different" matrices:
A 3x3 for the plate-bending and a 2x2 for shearing. For 4 grids, this would also result in a 20x20. But is this an identical approach to the previously mentioned one?
For this approach, the Bending stiffness (e*h^3)/(12*(1+v)) would lead to the the linear proportionality conclusion as well and the shear stiffness 5/6 * G * h as well (with G ~ E).