Hi David, Thank you for your comment! Yes - for example, I found that ABAQUS mostly use the average nodal values. In the mean time, it can have the user to suppress averaging between domains of different materials or section properties (e.g. cross-section of a beam/shell), in order to emphasize on the discontinuities at the boundaries. I guess after all this is left to user interpretation based on the actual physical problem being solved.
One of my friend also said that this is "not that critical" because it does not impact the solving process. For the most important analyses, he usually just uses quadrature stresses as the most "ground-truth" answer :) Thank you again for the help David! Best, Shawn On Sun, Nov 4, 2018 at 6:34 AM David Knezevic <david.kneze...@akselos.com> wrote: > On Sat, Nov 3, 2018 at 11:46 PM Yuxiang Wang <yw...@virginia.edu> 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...@virginia.edu> 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 < >>> david.kneze...@akselos.com> wrote: >>> >>>> On Fri, Nov 2, 2018 at 9:50 PM Yuxiang Wang <yw...@virginia.edu> 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...@virginia.edu >>> +1 (434) 284-0836 >>> >> >> >> -- >> Yuxiang "Shawn" Wang, PhD >> yw...@virginia.edu >> +1 (434) 284-0836 >> > -- Yuxiang "Shawn" Wang, PhD yw...@virginia.edu +1 (434) 284-0836 _______________________________________________ Libmesh-users mailing list Libmesh-users@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/libmesh-users
