Others may also be interested in this, but I have a keen interest. I'd be
happy to look at the patch, but, even better, would be for you to open a
pull request on GitHub (https://github.com/libMesh/libmesh) so that, if we
decide to integrate the patch, we have a commit history of your development
since it sounds like it's not a small patch.
Best,
Paul
On Fri, Feb 21, 2014 at 8:53 AM, Roman Vetter <vette...@ethz.ch> wrote:
> Dear libMesh devs,
>
> the roots of the finite element method lie in structural analysis and
> the need to solve elasticity problems. Thin shells with a stretching and
> a bending rigidity are an extremely important special case. The bending
> term requires C1 finite elements which have been hard to construct for
> arbitrary surface topologies until the subdivision surface paradigm
> found its way to the FEM a few years ago (Int. J. Numer. Meth. Engng.
> 47, 2039-2072 (2000), more than 300 citations!). Ever since, subdivision
> surfaces are the way to go in thin shell finite element analysis, as they
>
> 1) require only the three nodal displacement dofs, no rotational or
> other auxiliary dofs,
> 2) require only one Gauss point per element (very efficient), although
> more still work of course,
> 3) greatly simplify the implementation of thin shells with arbitrary
> topology.
>
> Still, they have not made it into most finite element packages, perhaps
> because they somewhat deviate from conventional FE principles:
>
> a) the shape functions don't interpolate the mesh nodes, instead they
> approximate them,
> b) the solution on an element is determined not only by the nodal
> solutions of its nodes, but also of nodal solutions at the neighboring
> nodes
> c) the number of shape functions per element depends on the mesh
> connectivity,
> d) the conventional h-refinement and p-refinement techniques can't be
> applied
> e) they require special treatment of boundaries and constraints.
>
> I have prepared a patch that adds the most popular, versatile and
> widely-used type of subdivision surface elements to libMesh: Loop
> subdivision surface elements. Everything is readily Doxygen-commented
> like all of libMesh. I've also prepared a new example
> (miscellaneous_ex11) showing how to use the new element on a loaded thin
> elastic plate.
>
> This is a joint effort initiated by Norbert Stoop in 2008. The related
> discussions can be looked up at:
> http://sourceforge.net/mailarchive/message.php?msg_id=20778890
> http://sourceforge.net/mailarchive/message.php?msg_id=20808509
>
> Why didn't I attach the patch already? I'd first like to know if you're
> interested at all. Why wouldn't you, you're asking? Bear in mind the
> unconventional nature of subdivision surface finite elements. (b)
> requires a more general treatment of the number of shape functions in
> DofMap, as it is no longer constant. (c) requires a new integer stored
> in each Node instance, holding the node valence. (d) means some of the
> nice features of libMesh like AMR won't work with the new element. (e)
> means that libMesh's built-in boundary and constraint handling won't
> work with the new element. Furthermore the new element supports only 2D
> triangular meshes in 3D space, so it is a far cry from being as general
> as other elements implemented in libMesh.
>
> Why would you be interested despite all this? First of all, subdivision
> surfaces seem to be the future of two-dimensional C1 elements. They
> would give libMesh an advantage over other FEM packages. Moreover,
> recent advances in finite element research suggest that more new
> elements of this general kind (isogeometric analysis) are on the way.
> Some of them similarly generalize the way we traditionally think about
> element shape functions and even work with less than one quadrature
> point per element [sic!].
>
> This extension of libMesh adds five new source code files and modifies
> 22 more (mostly small additions like enums etc.). I've tried to keep the
> patch minimal. It has been in successful operation for a few years now
> at our labs, and I think it's about time it's committed to the official
> libMesh repository. It would make a great added value to libMesh for all
> those who use it for thin shell analysis (and I know that there are a
> few of them around). I'm happy to send you the patch and further
> explanations on it if you're willing to give it a closer look.
>
> Best regards,
> Roman
>
>
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