On Fri, Apr 22, 2016 at 6:58 PM, Bhalla, Amneet Pal S <amne...@live.unc.edu> wrote:
> Hi Folks, > > How difficult would it be for the developers to extend ex7 of system of > equations for nonlinear elasticity to include variation in surface traction > in the > Jacobian formation? > > https://github.com/libMesh/libmesh/blob/master/examples/systems_of_equations/systems_of_equations_ex7/systems_of_equations_ex7.C#L230-L256 > > In theory its straightforward (I think), but for the life of me I cannot > figure out how to play with the indices to get terms like > > D traction [u] = (D F[u] S N). V + (F(u) D S[u] N). V > = (D F[u] S N). V + (F(u) (C : D E[u]) N). V > > in which D [u] is the linearization in the direction u, F is deformation > gradient, S is PK2 tensor, N is normal vector in reference frame, E is > Green strain > C is elasticity tensor, and V is a test function. > I worked on this example, but I don't have time to look into this in detail at the moment. In any case, I'm not sure I fully understand what you're asking. I would suggest you have a look at the weak form of the PDE in the comments at the top, and note that it includes a surface traction term: \int_\Gamma g_i v_i ds. That term is omitted in the code, but it should be easy to add in by adding a surface integral term to the residual. Also, note that the traction term \int_\Gamma g_i v_i ds will not contribute to the Jacobian (similar to how the volumetric load doesn't contribute to the Jacobian). But I'm not sure if the formulation above is what you're asking about? > Also, how bad is the nonlinear convergence if one leaves traction part > from Jacobian in general? > You're asking how bad convergence will be if your Jacobian is not correct? Hard to say in general. It's best to just make sure your Jacobian is correct :) David ------------------------------------------------------------------------------ Find and fix application performance issues faster with Applications Manager Applications Manager provides deep performance insights into multiple tiers of your business applications. It resolves application problems quickly and reduces your MTTR. Get your free trial! https://ad.doubleclick.net/ddm/clk/302982198;130105516;z _______________________________________________ Libmesh-users mailing list Libmesh-users@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/libmesh-users
