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 ------------------------------------------------------------------------------ Managing the Performance of Cloud-Based Applications Take advantage of what the Cloud has to offer - Avoid Common Pitfalls. Read the Whitepaper. http://pubads.g.doubleclick.net/gampad/clk?id=121054471&iu=/4140/ostg.clktrk _______________________________________________ Libmesh-devel mailing list Libmesh-devel@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/libmesh-devel
