Best way and practices to implement new elements

[Diego Magela]

Dear deal.II users,

I would like to implement new elements, namely 3D beam element and 8-node shell element.

As far as I know, these elements are not available on deal.II.

I appreciate any tip on how to implement these two finite elements.

Thank you all in advance.

Best regards,
Diego Magela

[Wolfgang Bangerth]

On 10/8/21 10:54 AM, Diego Magela wrote:
>
>
> I would like to implement new elements, namely 3D beam element

> <https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.mm.bme.hu%2F~gyebro%2Ffiles%2Fans_help_v182%2Fans_elem%2FHlp_E_BEAM188.html&data=04%7C01%7CWolfgang.Bangerth%40colostate.edu%7C77a0c86c437a4b6e298308d98a7c416b%7Cafb58802ff7a4bb1ab21367ff2ecfc8b%7C0%7C0%7C637693089308694897%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000&sdata=x2lVi0X3VyEdoWPnWotoRwvqpz3ziOu79OlLDjHe2lQ%3D&reserved=0> and
> 8-node shell element
> <https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.mm.bme.hu%2F~gyebro%2Ffiles%2Fans_help_v182%2Fans_elem%2FHlp_E_SHELL281.html&data=04%7C01%7CWolfgang.Bangerth%40colostate.edu%7C77a0c86c437a4b6e298308d98a7c416b%7Cafb58802ff7a4bb1ab21367ff2ecfc8b%7C0%7C0%7C637693089308694897%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000&sdata=iJKp1bSwP9MFUMnPCHuWt2cNreYS%2BKqHAXPQGKsM%2Bko%3D&reserved=0>.

>
> As far as I know, these elements are not available on deal.II.
>
> I appreciate any tip on how to implement these two finite elements.

Diego -- these are difficult to implement as far as I know. I can't find
this from the pages you link to, but my understanding is that for these
elements, one needs not only ensure continuity of the solution across
interfaces between cells, but also continuity of the derivative. Is that
right?

Best
W.

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

[Diego Magela]

Dear Wolgang,

Yes, it is right. These are C^1 finite elements.

Best regards,

Diego Magela

[Wolfgang Bangerth]

On 10/8/21 2:19 PM, Diego Magela wrote:
>
> Yes, it is right. These are C^1 finite elements.

These elements are difficult to implement. Maybe not for the 1d case, but
certainly for the 2d case. Have you taken a look at the existing step-47 and
the new step-82 (in the dev version)? They show how one can work around the
issues of C^1 elements by using regular Lagrange elements and ensuring C^1
continuity in other ways.

Shell and beam elements have, over the years, fallen out of favor in the
finite element community. That's because they are difficult to implement on
unstructured meshes, and because alternative methods are no worse in accuracy
and cost.

Best
Wolfgang

[Diego Magela]

Dear Wolfgang,

Thanks for pointing out these tutorials.

I will take a look.

Best regards,

Diego Magela