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
Description: Adobe PDF document
