Dear James,
I'm not 100% sure in this specific case, but I would expect that Getfem
computes gradients not by finite differences, but by using the analytical
gradients of the
shape functions. Doing per element something like this: Grad U = Grad Shape
Func X U. This is a very common practice in FE if I'm not mistaken.
Best regards,
Andriy
On 13 May 2012 14:26, James Zhou <[email protected]> wrote:
> Thank you Andriy. The linear operator I meant is global. The code you
> provided is very clear, but I am still wondering how the gradient of
> displacement is computed? In your code, it corresponds to
> "getfem::compute_gradient(mf_u,
> mf_strain, U, GRAD);".
>
> I have looked the method compute_gradient in
> src/getfem/getfem_derivatives.h, but didn't quite figure out what it is
> doing. Since I am using tri-linear element in 3D, I thought the gradient
> of displacement could be computed with finite difference (using center
> difference). However, it gives different result than GetFEM++. So I am
> wondering how GetFEM++ computes the gradients.
>
> best,
> James
>
>
> On Fri, May 11, 2012 at 5:24 AM, Andriy Andreykiv <
> [email protected]> wrote:
>
>> Dear James,
>>
>> When you speak about this linear ooperator, do you imply element level
>> or the global mesh level?
>> Basically, there are several ways to do this.
>> If you want to calculate strain in integration points (element by
>> element) please see calculation in
>> getfem_nonlinear_elasticty.h elasticity_nonlinear_term::compute.
>>
>> Below there is simple function, that extracts individual linear strain
>> components into a global vector that can be postprocessed.
>>
>> The code:
>>
>> //
>> gefem::mesh m; //
>> getfem::mesh_fem mf_u(m); // the mesh_fem used to describe the
>> approximation of the displacements
>> set_classical_finite_element(approximation_order_U);
>> ...
>>
>> // compute displacement U from elastic problem
>>
>> ....
>> getfem::mesh_fem mf_strain(m);
>> mf_strain.set_classical_discontinuous_finite_element(approximation_order_U
>> -1);
>> //approximation of strain has to be discontinous and one order lower
>> plain_vector STRAIN_VECTOR(mf_strain.nb_dof()*6); /assuming 3D with 6
>> components of strain in Voight notation
>> compute_strain(mf_u,mf_strain,U,STRAIN_VECTOR);
>>
>> // now STRAIN_VECTOR can be exported to VTK component by component on
>> mf_strain if you want to
>>
>>
>> .......
>> //function compute_strain
>> void compute_strain(const getfem::mesh_fem& mf_u, const getfem::mesh_fem&
>> mf_strain, const plain_vector& U,
>> plain_vector& strain)
>> {
>> unsigned N = mf_u.linked_mesh().dim();
>> GMM_ASSERT1(N==3,"This function is written as a demo only for 3D");
>> GMM_ASSERT1(gmm::vect_size(strain) == 6*mf_strain.nb_dof(),
>> "compute_strain: wrong size");
>>
>> plain_vector GRAD(mf_strain.nb_dof() * N * N);
>>
>> //compute gradient of displacement on the whole mesh
>> getfem::compute_gradient(mf_u, mf_strain, U, GRAD);
>>
>> base_matrix E(N, N), gradU(N, N);
>> for (size_type i = 0; i < mf_strain.nb_dof(); i+=6)
>> {
>> //extract the gradient in the node
>> std::copy(GRAD.begin() + i * N*N, GRAD.begin()+(i + 1) * N*N,
>> gradU.begin());
>>
>> // compute strain from the gradient
>> gmm::add(gradU,gmm::transposed(gradU),E);
>> gmm::scale(E, scalar_type(0.5));
>>
>> //using Voight notation to convert the strain tensor into a vector
>> // in 3D
>> strain[6*i ]=E(0,0);
>> strain[6*i+1]=E(1,1);
>> strain[6*i+2]=E(2,2);
>> strain[6*i+3]=E(0,1);
>> strain[6*i+4]=E(1,2);
>> strain[6*i+5]=E(0,2);
>> }
>> }
>>
>>
>>
>>
>>
>>
>> On 10 May 2012 21:26, James Zhou <[email protected]> wrote:
>>
>>> Dear GetFEM++ users,
>>>
>>> In the context of solving a linear elasticity problem, is there a way to
>>> extract the linear operator that converts displacement into strain tensor?
>>> For example, if there are n nodes, we would have a displacement vector of
>>> size 3*n, if the strain tensors are reshaped into a 6*n vector (assuming
>>> isotropic material), I would like to build the 6*n x 3*n matrix that
>>> convert displacement into strain.
>>>
>>> I have tried a finite difference approach where strain is written as the
>>> symmetric gradient of displacement, and the gradient of displacement is
>>> approximated by finite difference. However, this does not yield the same
>>> result as the stress tensor computed in src/getfem/getfem_derivatives.h
>>>
>>> Thanks!
>>>
>>> James
>>>
>>> _______________________________________________
>>> Getfem-users mailing list
>>> [email protected]
>>> https://mail.gna.org/listinfo/getfem-users
>>>
>>>
>>
>
>
>
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