Re: [deal.II] Queries on calculation on average stress.
On 3/2/23 22:57, Deepika Kushwah wrote:
Kindly suggest if there is any other method to calculate avg strain/stress
using composite material where the size of elements in matrix and inclusion
are different.
DataPostprocessor is the wrong approach to the problem. It is used to generate
graphical output, but that is not what you want.
The average strain is
s_avg = \int_\Omega s(x) dx / \int_\Omega 1 dx
where the second integral is simply the volume. You can approximate both
integrals by a sum over all cells and then applying quadrature. For example,
the first integral is computed via a loop that will look roughly like this:
double s_integral = 0;
for (cell=)
{
fe_values.reinit(cell);
fe_values.get_function_gradients (solution, solution_grads);
for (q=...)
s_integral += (compute strain/stress from solution_grads[q]) *
fe_values.JxW(q);
}
The volume of the domain is computed similarly, but you can also use
GridTools::volume() for that.
Best
W.
--
Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
--
The deal.II project is located at http://www.dealii.org/
For mailing list/forum options, see
https://groups.google.com/d/forum/dealii?hl=en
---
You received this message because you are subscribed to the Google Groups "deal.II User Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to dealii+unsubscr...@googlegroups.com.
To view this discussion on the web visit
https://groups.google.com/d/msgid/dealii/6e1029dc-cc8f-b8d5-145a-3afa23326eb9%40colostate.edu.
Re: [deal.II] Queries on calculation on average stress.
Hello Everyone,
Thanks for your response.
The problem is how to calculate the average strain and stress values using
Area Average Method (for the geometry attached in previous mail)?
I am using this formula *Avg Strain = (A1E1+A2E2.AnEn/A)* for the
calculation. I have calculated the values of E1,E2.. En using
DataPostProcedure Class but now the problem is how to calculate A1,A2An
in the same class as active.cell_iterator showing the error?
*What I have done so far:*
*1. I have calculated strain and stress using DataPostProcedure Class*
template
class StrainPostprocessor : public DataPostprocessorTensor
{
public:
StrainPostprocessor ()
:
DataPostprocessorTensor ("strain",
update_gradients)
{}
virtual
void
evaluate_vector_field
(const DataPostprocessorInputs::Vector &input_data,
std::vector > &computed_quantities) const override
{
AssertDimension (input_data.solution_gradients.size(),
computed_quantities.size());
for (unsigned int p=0; p::n_independent_components));
for (unsigned int d=0; d::component_to_unrolled_index(TableIndices<2>(d,e))]
= (input_data.solution_gradients[p][d][e]
+
input_data.solution_gradients[p][e][d]) / 2;
}
}
};
*2. I have calculated area of each cell using active.cell_iterator
separately *
Triangulation<2> triangulation;
std::vector x(4);
std::vector y(4);
std::vector A(4);
GridGenerator::hyper_cube(triangulation,-1,1);
//double A;
// double B;
// double C;
triangulation.refine_global(1);
int j =0;
for (const auto &cell : triangulation.active_cell_iterators())
{
int i =0;
for (const auto v : cell->vertex_indices())
{
x[i] = cell->vertex(v)(0);
y[i] = cell->vertex(v)(1);
std::cout<< "cord_x" << x[i]< wrote:
> Daniel,
>
> Side question:
> If I have to output gradients of a variable, the straightforward approach
> would be to evaluate the gradients over quadrature points and then average.
> This gives me an average value of my gradient per cell.
> Do you know how does data DataPostProcessor evaluates the value of the
> gradient at the mesh nodes? How does it it work under the hood? Do you mind
> explaining?
>
> Deepika,
>
> This is a strain post processor. Create a function that does this:
> template
> class StrainPostprocessor : public DataPostprocessorTensor
> {
> public:
> StrainPostprocessor()
> : DataPostprocessorTensor("strain",
> update_gradients)
> {
> }
>
> virtual void evaluate_vector_field(const DataPostprocessorInputs::Vector<
> dim> &input_data, std::vector> &computed_quantities) const
> override
> {
> AssertDimension(input_data.solution_gradients.size(),
> computed_quantities.size());
>
> for (unsigned int p = 0; p < input_data.solution_gradients.size(); ++p)
> {
> AssertDimension(computed_quantities[p].size(),
> (Tensor<2, dim>::n_independent_components));
>
> for (unsigned int d = 0; d < dim; ++d)
> for (unsigned int e = 0; e < dim; ++e)
> computed_quantities[p][Tensor<2, dim>::component_to_unrolled_index(
> TableIndices<2>(d, e))] = (input_data.solution_gradients[p][d][e] +
> input_data.solution_gradients[p][e][d]) /
> 2;
> }
> }
> };
>
> Then in data output you can do this:
> void CG_Elasticity_Linear::output_results(unsigned int
> refinement_level, unsigned int cycle) const
> {
>
> std::vector
> interpretation(dim,
> DataComponentInterpretation::component_is_part_of_vector);
> std::vector solution_names(dim, "u");
>
> DataOut data_out;
>
> data_out.add_data_vector(dof_handler, solution, solution_names,
> interpretation);
> const StrainPostprocessor strain;
> data_out.add_data_vector(dof_handler, solution, strain);
> data_out.build_patches();
>
> std::ofstream output("solution" + std::to_string(refinement_level) + "_" +
> std::to_string(cycle) + ".vtu");
>
> data_out.write_vtu(output);
>
> }
> For averages you'll have to loop in the DataPostProcessor derived class
> and average your quantity.
>
>
> Best,
> Abbas
>
> On Thursday, March 2, 2023 at 12:42:46 PM UTC+1 d.arnd...@gmail.com wrote:
>
>> Deepika,
>>
>> > How can I calculate the average stress and strain values for the
>> following geometry (Where element size is not uniform) using the Data
>> PostProcedure?
>>
>> Can you describe what you are trying to do in a formula?
>> DataPostProcessor typically gives you a result per grid point in the output
>> step.
>>
>> > 2. Is it possible to make a uniform mesh so the size of elements in
>> both (inclusion and matrix) will be the same?
>>
>> If you can draw a mesh that you would like to use, you should also be
>> able to create that in deal.II to use. Of course, it will be very difficult
>> to achieve the same size for all elements since you will need more cells to
>> describe the inclusions anyway.
>>
>> Best,
>> Daniel
>>
>> On Wed, Mar 1, 2023 at 6:38 PM Deepika Kushwah
>> wrote:
>>
>>> Hello Ever
Re: [deal.II] Queries on calculation on average stress.
Daniel,
Side question:
If I have to output gradients of a variable, the straightforward approach
would be to evaluate the gradients over quadrature points and then average.
This gives me an average value of my gradient per cell.
Do you know how does data DataPostProcessor evaluates the value of the
gradient at the mesh nodes? How does it it work under the hood? Do you mind
explaining?
Deepika,
This is a strain post processor. Create a function that does this:
template
class StrainPostprocessor : public DataPostprocessorTensor
{
public:
StrainPostprocessor()
: DataPostprocessorTensor("strain",
update_gradients)
{
}
virtual void evaluate_vector_field(const DataPostprocessorInputs::Vector
&input_data, std::vector> &computed_quantities) const
override
{
AssertDimension(input_data.solution_gradients.size(),
computed_quantities.size());
for (unsigned int p = 0; p < input_data.solution_gradients.size(); ++p)
{
AssertDimension(computed_quantities[p].size(),
(Tensor<2, dim>::n_independent_components));
for (unsigned int d = 0; d < dim; ++d)
for (unsigned int e = 0; e < dim; ++e)
computed_quantities[p][Tensor<2, dim>::component_to_unrolled_index(
TableIndices<2>(d, e))] = (input_data.solution_gradients[p][d][e] +
input_data.solution_gradients[p][e][d]) /
2;
}
}
};
Then in data output you can do this:
void CG_Elasticity_Linear::output_results(unsigned int
refinement_level, unsigned int cycle) const
{
std::vector
interpretation(dim,
DataComponentInterpretation::component_is_part_of_vector);
std::vector solution_names(dim, "u");
DataOut data_out;
data_out.add_data_vector(dof_handler, solution, solution_names,
interpretation);
const StrainPostprocessor strain;
data_out.add_data_vector(dof_handler, solution, strain);
data_out.build_patches();
std::ofstream output("solution" + std::to_string(refinement_level) + "_" +
std::to_string(cycle) + ".vtu");
data_out.write_vtu(output);
}
For averages you'll have to loop in the DataPostProcessor derived class and
average your quantity.
Best,
Abbas
On Thursday, March 2, 2023 at 12:42:46 PM UTC+1 d.arnd...@gmail.com wrote:
> Deepika,
>
> > How can I calculate the average stress and strain values for the
> following geometry (Where element size is not uniform) using the Data
> PostProcedure?
>
> Can you describe what you are trying to do in a formula? DataPostProcessor
> typically gives you a result per grid point in the output step.
>
> > 2. Is it possible to make a uniform mesh so the size of elements in both
> (inclusion and matrix) will be the same?
>
> If you can draw a mesh that you would like to use, you should also be able
> to create that in deal.II to use. Of course, it will be very difficult to
> achieve the same size for all elements since you will need more cells to
> describe the inclusions anyway.
>
> Best,
> Daniel
>
> On Wed, Mar 1, 2023 at 6:38 PM Deepika Kushwah
> wrote:
>
>> Hello Everyone,
>>
>> I have the following queries :
>> 1. How can I calculate the average stress and strain values for the
>> following geometry (Where element size is not uniform) using the Data
>> PostProcedure?
>>
>> [image: image.png]
>> 2. Is it possible to make a uniform mesh so the size of elements in both
>> (inclusion and matrix) will be the same?
>>
>> Thanks & Regards
>> Deepika
>>
>>
>> **
>> This e-mail is for the sole use of the intended recipient(s) and may
>> contain confidential and privileged information. If you are not the
>> intended recipient, please contact the sender by reply e-mail and destroy
>> all copies and the original message. Any unauthorized review, use,
>> disclosure, dissemination, forwarding, printing or copying of this email
>> is strictly prohibited and appropriate legal action will be taken.
>>
>>
>>
>> --
>> The deal.II project is located at http://www.dealii.org/
>> For mailing list/forum options, see
>> https://groups.google.com/d/forum/dealii?hl=en
>> ---
>> You received this message because you are subscribed to the Google Groups
>> "deal.II User Group" group.
>> To unsubscribe from this group and stop receiving emails from it, send an
>> email to dealii+un...@googlegroups.com.
>> To view this discussion on the web visit
>> https://groups.google.com/d/msgid/dealii/CAKTdrpp2Ckswjqi8RsU9DDwm6AkT-d05Cin-D33bWmfLv20Ytw%40mail.gmail.com
>>
>>
>> .
>>
>
--
The deal.II project is located at http://www.dealii.org/
For mailing list/forum options, see
https://groups.google.com/d/forum/dealii?hl=en
---
You received this message because you are subscribed to the Google Groups
"deal.II User Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to
