Re: [Libmesh-users] Store the finite element matrices for post-processing of stresses/strains?

[David K. <dav...@ak...>]

On Sat, Nov 3, 2018 at 11:46 PM Yuxiang Wang <yw...@vi...> wrote:

> Hi David,
>
> Greetings again.
>
> I found the answer from this link
> <http://www.joinville.udesc.br/portal/professores/pablo/materiais/CIL26_0053.pdf>
> and yes, we will get a globally smooth distribution at the cost of much
> more computation.
>

That looks like a good reference. I think the most common approach to
getting a smooth stress plot is to compute element-based stress and then do
nodal averaging. But there are obviously many different approaches that one
can use.

David



>
> On Fri, Nov 2, 2018 at 10:01 PM Yuxiang Wang <yw...@vi...> wrote:
>
>> Hi David,
>>
>> Thank you for your response! Yes I was indeed reading your example and
>> thinking about it. Your insight helps a lot. Thank you so much!
>>
>> Since we are discussing on this topic, if you wouldn't mind, I'd like to
>> ask one more question:
>>
>> During the L2 projection process, we solved the system per element. If we
>> assemble the element mass matrices and the RHS to a global one with all
>> elements, and similarly solve the global equation, would we be getting a
>> globally smoothed stress distribution?
>>
>> I'd really love to hear your comment. Thanks in advance!
>>
>> Best,
>> Shawn
>>
>> On Fri, Nov 2, 2018 at 7:27 PM David Knezevic <dav...@ak...>
>> wrote:
>>
>>> On Fri, Nov 2, 2018 at 9:50 PM Yuxiang Wang <yw...@vi...> wrote:
>>>
>>>> Dear all,
>>>>
>>>> I have been using the matrix notation (following the Bathe textbook)
>>>> with
>>>> libmesh recently to code finite element solutions for basic continuum
>>>> structural elements. I realized that I need to compute those matrices
>>>> twice
>>>> - once when I assemble the global stiffness matrix, and another time
>>>> when I
>>>> get the solutions and need to post-process to compute the
>>>> stresses/strains.
>>>> Being curious, do we have any best practices (or special
>>>> considerations) to
>>>> save those matrices so that we don't have to compute them twice? For
>>>> example, should I just create a huge vector of DenseMatrix, and each
>>>> matrix
>>>> for each quadrature point? Or that libmesh has some tools for this book
>>>> keeping?
>>>>
>>>> Explanation for what I meant by "matrix notation" and what are those
>>>> finite
>>>> element matrices: for example, for each quadrature point I have an
>>>> interpolation matrix [H], a strain-displacement matrix [B] (constructed
>>>> from derivatives of [H]). With the constitutive tensor matrix being
>>>> [C], we
>>>> can easily get the element stiffness matrix by [K] =
>>>> integrate([B]^T[C][B]). After the solution [uhat] is obtained, we can
>>>> also
>>>> get the strain and stress by again [strain] = [B][uhat] or [stress] =
>>>> [C][B][uhat].
>>>>
>>>> Just wondering whether anyone else has done this before and whether
>>>> there
>>>> would be a better practice to do it more elegantly. Thanks :)
>>>>
>>>> Best,
>>>> Shawn
>>>
>>>
>>> See systems_of_equations_ex6 for an example of computing stresses in
>>> libMesh. In that case we do not store and re-use the per-element strain and
>>> stress matrices (C and B in your notation) You could store and reuse that
>>> data, but it's not clear to me whether it'd be worth it. You'd presumably
>>> get some speedup in the evaluation of the stress at the cost of extra
>>> storage, so you'd have to decide if you want that or not (in my experience
>>> I would not want that since memory is usually more of a limiting factor
>>> than speed).
>>>
>>> Best,
>>> David
>>>
>>
>>
>> --
>> Yuxiang "Shawn" Wang, PhD
>> yw...@vi...
>> +1 (434) 284-0836
>>
>
>
> --
> Yuxiang "Shawn" Wang, PhD
> yw...@vi...
> +1 (434) 284-0836
>