On Friday, February 17, 2017 at 1:48:54 PM UTC+1, Luca Heltai wrote:
>
> Dear Franco,
>
> I think there is a problem in your formulation…
>
> You are integrating
>
> u_i n_i f_i
>
>
I agree I have a translation problem here. In practice, I am integrating a
weak problem as this (in Fenics' UFL terms, but easy to recognize):
inner( sigma(u), eps(v) ) * dx = inner(f, v) * dx + inner(f1, v) * ds(1)
where f is a bulk force (zero in my code), f1 is a (distributed) force
applied to the top boundary. The dx and ds terms refer to the integral on
the domain and boundary; u is the displacement, and v is the test function.
Sigma and eps are functions that compute, obviously, stress and strain
tensors.
As I said, Fenics hid everything as you see above, but I am very eager to
let it go as soon as possible.
> and while you can certainly come up with good reasons for this to work
> out, I’m unsure about what you want to achieve. If your boundary conditions
> are
>
> ((grad(u)).n,v) = u_i,j n_j v_i
>
> and you impose
>
> (grad(u).n)_i = f_i
>
> on the boundary, then you should have
>
> cell_rhs(i) += ( fe_face_values.shape_value(i, f_q_point) *
> rhs_face_values[f_q_point][component_i]) *
> fe_face_values.JxW(f_q_point);
>
>
My question here is this: why am I not using the normal to the face?
> on the other hand, if you want to have, for example, for a scalar function
> p,
>
> u_i,j n_j = p n_i
>
> then you should have
>
> cell_rhs(i) += ( fe_face_values.shape_value(i, f_q_point) *
> rhs_scalar_function[f_q_point]
> fe_face_values.normal_vector(f_q_point)[component_i]
> ) * fe_face_values.JxW(f_q_point);
>
>
> What is the exact term you want to integrate?
>
> L.
>
Thanks for your help, Luca!
Franco
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