Are shell elements available in deal.II?

[Yuxiang Wang]

Hi,

Sorry for the spam.

I tried to search but did not find an implementation of shell elements in deal.II. Since this is a commonly used element, I'd like to make sure that it's not me missing it. Could you please help confirm?

Best,

Shawn

[Wolfgang Bangerth]

Shawn,

> I tried to search but did not find an implementation of shell elements in
> deal.II. Since this is a commonly used element, I'd like to make sure that
> it's not me missing it. Could you please help confirm?

That depends on how exactly you define "shell elements". But if you mean
"elements that are not only continuous but also have continuous derivatives,
for use in problems with fourth derivatives", then the answer is "no".

Of course, there are other approaches to solve shell problems -- maybe even
better ones than using shell elements -- that are available in deal.II. This
includes using mixed methods.

Best
W.

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

[Yuxiang Wang]

Thank you Professor Bangerth for your response! Yes that's exactly what I am interested in.

I am excited to learn that there are arguably better methods (mixed methods) to solve shell problems. I am not familiar with those; could you please kindly provide some pointers for me to start (anything, either example, code, or paper)?

Best,

Shawn

[Wolfgang Bangerth]

> I am excited to learn that there are arguably better methods (mixed methods)
> to solve shell problems. I am not familiar with those; could you please kindly
> provide some pointers for me to start (anything, either example, code, or paper)?

That all depends on what equation exactly you're looking at solving. For the
biharmonic equation, you could for example start looking here:

https://scholar.google.co.jp/scholar?hl=en&as_sdt=0%2C5&q=mixed+methods+biharmonic+equation&btnG=
https://scholar.google.co.jp/scholar?hl=en&as_sdt=0%2C5&q=discontinuous+galerkin+biharmonic+equation&btnG=

Beyond that, you'd have to be more specific about what you want to do.

[Yuxiang Wang]

Hi Professor Bangerth,

Thank you for the pointer! Those are very helpful. I just realized that Mindlin-Reissner plate theory can be expressed in forms of mixed elements.

My current need for shell element is for solid mechanics problem (Mindlin-Reissner plates). A simple example could be that a thick square plate, with all its edges fixed, under a force loading at the center. The dimensions of the plate are around 10x of its thickness; so, as one can note, there is 1) only in-plate stress in this problem, 2) the plate thickness remains constant during the deformation, and 3) there is an approximately linear variation of displacement across the thickness direction.

Do you happen to be aware of any examples in deal.ii, that solves shell problems for solid mechanics application? If not, I can also try to start from scratch; but I figured it'd be nice that if I know someone who did this already and wouldn't need to reinvent the wheels.

Thank you!

Shawn

[Wolfgang Bangerth]

On 03/25/2018 11:44 AM, Yuxiang Wang wrote:
>
> My current need for shell element is for solid mechanics problem
> (Mindlin-Reissner plates). A simple example could be that a thick square
> plate, with all its edges fixed, under a force loading at the center. The
> dimensions of the plate are around 10x of its thickness; so, as one can note,
> there is 1) only in-plate stress in this problem, 2) the plate thickness
> remains constant during the deformation, and 3) there is an approximately
> linear variation of displacement across the thickness direction.
>
> Do you happen to be aware of any examples in deal.ii, that solves shell
> problems for solid mechanics application? If not, I can also try to start from
> scratch; but I figured it'd be nice that if I know someone who did this
> already and wouldn't need to reinvent the wheels.

I don't know of any that would be publicly available. I know that Baerbel
Janssen's diploma thesis was on biharmonic problems (or at least had them as
part). You can get it from here but it is in German:
http://www.csc.kth.se/~barbel/link/en/publications.shtml

I am certain that others have done similar work, but I don't know the details.
Of course, we are always grateful to anyone willing to share their codes
through the code gallery!

Best
Wolfgang

[Andrew McBride]

Hi

I’ve hesitated to add this link as it predates many of the features in deal.II that would have made the implementation a lot more elegant and simple. Nevertheless have a look at https://open.uct.ac.za/handle/11427/5552 It’s a fully nonlinear shell theory due to Simo & Fox implemented in deal.II. 

There is no reason why you can’t implement Mindlin-Reissner  plate theory in deal.II. I would start with Timoshenko beam theory and then build up to plates. 

A

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[Yuxiang Wang]

Thank you again Professor Bangerth and mac!

As you can understand, implementing a Mindlin-Reissner element along with appropriate shear-locking relieves (MITC7/MITC9) indeed seems daunting at a first glance (at least for me). I was hoping that I can get some example code for a head start, but since those are not available, I'll just jump in and try my best to implement one. If I would be able to make it, I'd be happy to share my code!

Best,

Shawn

On Monday, March 26, 2018 at 6:59:33 AM UTC-7, mac wrote:

Hi

I’ve hesitated to add this link as it predates many of the features in deal.II that would have made the implementation a lot more elegant and simple. Nevertheless have a look at https://open.uct.ac.za/handle/11427/5552 It’s a fully nonlinear shell theory due to Simo & Fox implemented in deal.II. 

There is no reason why you can’t implement Mindlin-Reissner  plate theory in deal.II. I would start with Timoshenko beam theory and then build up to plates. 

A

On 26 Mar 2018, at 14:40, Wolfgang Bangerth <bang...@colostate.edu> wrote:

On 03/25/2018 11:44 AM, Yuxiang Wang wrote:

My current need for shell element is for solid mechanics problem (Mindlin-Reissner plates). A simple example could be that a thick square plate, with all its edges fixed, under a force loading at the center. The dimensions of the plate are around 10x of its thickness; so, as one can note, there is 1) only in-plate stress in this problem, 2) the plate thickness remains constant during the deformation, and 3) there is an approximately linear variation of displacement across the thickness direction.
Do you happen to be aware of any examples in deal.ii, that solves shell problems for solid mechanics application? If not, I can also try to start from scratch; but I figured it'd be nice that if I know someone who did this already and wouldn't need to reinvent the wheels.

I don't know of any that would be publicly available. I know that Baerbel Janssen's diploma thesis was on biharmonic problems (or at least had them as part). You can get it from here but it is in German:
 http://www.csc.kth.se/~barbel/link/en/publications.shtml

I am certain that others have done similar work, but I don't know the details. Of course, we are always grateful to anyone willing to share their codes through the code gallery!

Best
Wolfgang

--
------------------------------------------------------------------------

Wolfgang Bangerth          email:         ...@colostate.edu

[fea...@gmail.com]

Dear Prof. Bangerth,

May I continue this topic, for shell problems, shall we better use IGA (more faster & more robust ... vs Mixed formulation)?

 
Best,

Yaakov

[Wolfgang Bangerth]

On 04/25/2018 04:31 PM, fea...@gmail.com wrote:
>
> May I continue this topic, for shell problems, shall we better use*IGA* (more

> faster & more robust ... vs Mixed formulation)?

I suspect that everyone will have their own opinion on this question. You will
have to read through the literature to find out what people think works best!