I have solve a thermoelastic problem using block matrices and block vectors
and a same dofhandler for the displacement and temperature fields.
Fully coupled thermal-stress analysis is needed when the stress analysis is
dependent on the temperature distribution and the temperature distribution
depends on the stress solution. For example, metalworking problems may
include significant heating due to inelastic deformation of the material
which, in turn, changes the material properties. Some problems require a
fully coupled analysis in the sense that the mechanical and thermal
solutions evolve simultaneously, but with a weak coupling between the two
solutions. In other words, the components in the off-diagonal submatrices
are small compared to the components in the diagonal submatrices. For the
thermoelastic problem the off-diagonal terms are zero and solution is
straight and stable. You can solve the block systems simultaneously or
using staggered solution technique.
Setup system as follow:
dof_handler.distribute_dofs (fe);
DoFRenumbering::Cuthill_McKee(dof_handler);
BlockDynamicSparsityPattern dsp(2, 2);
std::vector<*unsigned* *int*> block_component(3, 0);
block_component[*dim*] = 1; // temperature
DoFRenumbering::component_wise(dof_handler, block_component);
DoFTools::count_dofs_per_block(dof_handler, dofs_per_block,block_component);
*const* types::global_dof_index n_dofs_u = dofs_per_block[0];
// determine number of temperature DOFs if requested.
types::global_dof_index n_dofs_temp;
n_dofs_temp = dofs_per_block[1];
dsp.block(0, 0).*reinit*(n_dofs_u, n_dofs_u);
dsp.block(0, 1).*reinit*(n_dofs_u, n_dofs_temp);
dsp.block(1, 0).*reinit*(n_dofs_temp, n_dofs_u);
dsp.block(1, 1).*reinit*(n_dofs_temp, n_dofs_temp);
dsp.collect_sizes();
...
use the following approach for system matrix and RHS:
*for* (*unsigned* *int* q=0; q<n_q_points; ++q)
{
// extract temperature gradient and value
*for* (*unsigned* *int* k = 0; k < dofs_per_cell; ++k){
temp_grads_N[k] = fe_values[temp_fe].gradient (k, q);
temp_N[k] = fe_values[temp_fe].value (k, q);
}
*for* (*unsigned* *int* i=0; i<dofs_per_cell; ++i)
*for* (*unsigned* *int* j=0; j<dofs_per_cell; ++j)
{
*const* *unsigned* *int* comp_j = fe.system_to_component_index(j).first;
*if* (comp_j < *dim*){
cell_matrix(i,j) += determine block(0,0)
}*else* *if* (comp_j == *dim*){
// temperature
cell_matrix(i,j) += determine block(1,1)
}
}
}
cell->get_dof_indices (local_dof_indices);
*for* (*unsigned* *int* i=0; i<dofs_per_cell; ++i)
{
*for* (*unsigned* *int* j=0; j<dofs_per_cell; ++j)
system_matrix.add (local_dof_indices[i],local_dof_indices[j],
cell_matrix(i,j));
}
for rhs:
loop over cells:
PointHistory<*dim*> *local_quadrature_points_data
= *reinterpret_cast*<PointHistory<*dim*>*>(cell->user_pointer());
// extract nodal total and incremental displacement
// will be used for strain and delta_strain calculation
fe_values[u_fe].get_function_gradients (solution_delta,
displacement_increment_grads);
fe_values[u_fe].get_function_gradients (solution, displacement_grads);
// extract temperature values and gradients
*if*(parameters.is_temperature){
fe_values[temp_fe].get_function_values (solution, temp_value);
fe_values[temp_fe].get_function_values (solution_n, temp_n_value);
fe_values[temp_fe].get_function_gradients (solution, temp_grads);
}
// Then we can loop over all degrees of freedom on this cell and
// compute local contributions to the right hand side:
*for* (*unsigned* *int* q=0; q<n_q_points; ++q)
{
*for* (*unsigned* *int* i=0; i<dofs_per_cell; ++i){
*const* *unsigned* *int* comp_i = fe.system_to_component_index(i).first;
*if* ((comp_i < *dim*) ){
cell_rhs(i) +=
}*else* *if* (comp_i == *dim*)
{
// temperature
cell_rhs(i) +=
}
}
}
cell->get_dof_indices (local_dof_indices);
*for* (*unsigned* *int* i=0; i<dofs_per_cell; ++i)
system_rhs(local_dof_indices[i]) += cell_rhs(i);
On Tuesday, August 26, 2014 at 5:51:25 PM UTC+4:30, Lisa Collins wrote:
>
> Hi,
>
> I want to start deal.ii and model a thermoelastic problem in 2D & 3D.
>
> Can you please guide me which steps I should study.
> Which step should be considered as the base of my work and by modifying it
> I can model a thermoelastic problem?
>
> Best regards
> Lisa
>
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