I am working with a mesh generated from subdivided_cylinder, and am wondering whether the area and volume should be assumed to match that of a true cylinder, or if it only converges to that when many refinements are made. I would like to calculate the total energy of the system by integrating over the whole volume, as well as calculate shear forces by integrating over faces on the surface.
I am trying to compare the results of the FEM code to that of Euler-Bernoulli beam theory, similarly to how was done in this question. <https://groups.google.com/g/dealii/c/K-lMxbtZUdQ/m/fnWlwrRxBgAJ> Basically, I use Dirichlet conditions and hold one end in place, while the other end is displaced by small amount in the positive y direction. In this case, I use a radius of 1, a total length of 20, and a displacement of 0.1. When I ran this calculation with a regular flat manifold (i.e., a standard rectangular cuboid beam), I found that I only needed to refine along the beam axis (x) in order to converge to the analytical results from beam theory. However, here I am finding that no matter how much I refine along the beam axis, the result does not converge, and in fact barely changes at all. When I refine in all directions, then the energy and shear force increase, although they then overshoot the analytical result. [image: cylinder_shear-force_refined.png] To be clear, for calculating the beam theory result, I used the same expression as for the rectangular cuboid beam, but with a different second moment of area, and this was in agreements with the FEM calculations with the rectangular cuboid beam. I am using quadratic elements. Any thoughts would be greatly appreciated, Alex -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/8053cd87-91a2-4c36-8bc9-c9cc6a905dfan%40googlegroups.com.
