Discussion Forum

Posted: 1 decade ago May 24, 2011, 10:34 a.m. EDT

Hi I cannot find back the equation just like that and just now but you have all ingrediants in COMSOl, in "solid" the small deformation angle Thx = 0.5*solid.curlUX, etc, also the the uX,uY,uZ, vX,VY,Vz etc Pls report back, that is one of these formulas I regularly need, but alwys have to rebuild ;) It wuld be nice to have it on clear here on the Forum -- Good luck Ivar

Posted: 1 decade ago Feb 29, 2012, 3:41 a.m. EST

Dear Ivar, I would like to compute the curvature as well. Using shell elements, this worked fine. However, in the solid mechanics module I do have problems computing the curvature. What way did you go to get the curvature of the boundary of a solid? (Did you introduce variables that are only defined on the surface/boundary of a solid domain?) One point I struggle is that using uX etc. only gives the deformation curvature and in my case was zero in the initial state despite the initial state is a sphere. Kind regards, Stefan

Posted: 1 decade ago Feb 29, 2012, 4:36 a.m. EST

Hi Pertinent question/remark, there is the way I have posted on the Model Exchange, with the Zernike polynomials, you can reduce the optimising to the "z20" = piston, tip, tilt, and sphericity. But Zernike polynomials are only normalised correctly on round circular shapes (use mostly in optics for mirror deformations andeer mounting or gravity load) there is also the thread, still unanswered, of http://www.comsol.eu/community/forums/general/thread/26075/ I must say I have started a few times, normally we have all info with the normals etc in COMSOL, it's just that I have never had the time to finish it up. The uY-vX ... gives the (small) deformation angles not really the curvature (you need the second order derivatives Iif I remember right -- Good luck Ivar

Posted: 1 decade ago Feb 29, 2012, 9:31 a.m. EST

Maybe this link can help: http://www.intmath.com/applications-differentiation/8-radius-curvature.php With that equation you should be able to create a global equation in your solver?

Posted: 1 decade ago Feb 29, 2012, 10:55 a.m. EST

HI Yes the equation of the curvature of a line is well known, now express that simply for any portion of a boundary (surface or edge 3D resp. 2D) from the COMSOL FEM internal variables is where I have failed so far Indeed it looks simple and trivial, so I must have missed something so far ;) -- Good luck Ivar

Posted: 1 decade ago Mar 1, 2012, 9:57 a.m. EST

Dear colleagues, since using uX, p(n,x) and ptang(x,x) didn't worked that fine for me I asked the support. There are normal derivatives already implemented. nxcTy for solids or shell.anxty for shells gives the derivation of the surface normal. The mean curvature then is the trace of that matrix elements: (nxcTx+nycTy+nzcTz) gives the mean curvature (or shell.anxTx+shell.anyTy+shell.anzTz) of my surface. Thank you for your help and your explanations! Kind regards, Stefan Wolf

Posted: 1 decade ago Mar 1, 2012, 10:17 a.m. EST

Hi thanks for the feed back, remains for me to dig into the 3D once, still ;) -- Good luck Ivar