Hi Shaqir,
So, I have a short question to clarify something: By commenting out the calls
to VectorTools::interpolate_boundary_values() and
MatrixTools::apply_boundary_values(), are you implying that you do not impose
equation 4 (the Dirichlet boundary conditions) anywhere on the boundary of the
domain? If so then your problem is indeterminate, and I bet you’d get a
non-trivial solution once you constrain at least one boundary surface.
Best,
Jean-Paul
> On 31 Aug 2018, at 10:09, shaxrodg...@gmail.com wrote:
>
> Hi all, I am quite new to deal.ii and have been tasked with making use of it
> for my Honours project.
>
> I am trying to implement a traction boundary condition for a steady state
> linear elasticity type problem. I am therefore using step-8 from the
> tutorials as the base for my project and have attempted a Neumann boundary
> implementation by making use
> of a combination of the step-44 traction boundary and lecture 21.55 by Prof
> Bangerth. The code that I added is as follows:
>
>
> for (unsigned int f=0; f<GeometryInfo<dim>::faces_per_cell; ++f)
> if (cell->face(f)->at_boundary() == true
> && cell->face(f)->boundary_id() == 3)
> {
> fe_face_values.reinit (cell, f);
>
> for (unsigned int fq_point=0; fq_point<n_face_q_points;
> ++fq_point)
> {
> const Tensor<1, dim> &N =
> fe_face_values.normal_vector(fq_point);
> static const double T = 7.0e6; // arbitraty magnitude of
> traction
> const Tensor<1,dim> traction = (T * N);
>
> for (int i = 0; i<dofs_per_cell; ++i)
> {
> const unsigned int component_i =
> fe.system_to_component_index(i).first;
>
> cell_rhs(i) += traction[component_i]
> * fe_face_values.shape_value(i,fq_point)
> * fe_face_values.JxW(fq_point);
> }
>
> }
> }
>
> The code runs without any errors, however when I set my body force to zero to
> check for the traction contribution I noticed that there seems to be no
> displacement at all. I have also commented out the interpolate boundary
> values as follows:
>
> // std::map<types::global_dof_index,double> boundary_values;
> // VectorTools::interpolate_boundary_values (dof_handler,
> 0,
>
> Functions::ZeroFunction<dim>(dim),
> boundary_values);
>
> // MatrixTools::apply_boundary_values (boundary_values,
> system_matrix,
> solution,
> system_rhs);
>
>
> I have also tried increasing the magnitude of my traction but that doesn’t
> make a difference either. I am currently at my wits end as to why this would
> be the case for there being zero displacement. I have attached the
> formulation with regards to the weak form of my problem
> as to give more insight into what I am trying to implement. Any form of help
> or insight as to what the cause of the issue might be would be greatly
> appreciated.
>
> Kind regards
> Shaqir
>
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> <weak_form(1).pdf>
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