search

kai5z / Chladni-patterns

A short script for chladni patterns using FEM
46 stars 9 forks source link

An issue on pull request #9

Open juninagaki1975 opened 1 year ago

juninagaki1975 commented 1 year ago 
    Hi Jun. Could you please provide a picture / outtake on where this is

opened up in the textbook? Or how you derived this result using e.g. Galerkin. Looking then at the shear force part of the stiffness matrix. To be honest I do not directly remember how I calculated this since it was almost 10 years ago.

On Sun, Dec 18, 2022 at 4:33 PM Jun @.***> wrote:

@.**** commented on this pull request.

In sweep.py https://github.com/kai5z/Chladni-patterns/pull/7#discussion_r1051613830:

@@ -59,7 +59,7 @@ def Bb(ix): return Matrix([[0,dNNx[ix],0],[0,0,dNNy[ix]],[0,dNNy[ix],dNNx[ix]]]) def Bs(ix):

  • return Matrix([[dNNx[ix],-NN[ix],0],[dNNy[ix],0,-NN[ix]]])
  • return Matrix([[dNNx[ix],-dNNy[ix],0],[dNNy[ix],0,-dNNx[ix]]])

Components of B matrix must be derivatives all? Replace NN with dNNx or dNNy based on some textbooks.

— Reply to this email directly, view it on GitHub https://github.com/kai5z/Chladni-patterns/pull/7#pullrequestreview-1222037502, or unsubscribe https://github.com/notifications/unsubscribe-auth/ABJBNK7UNEN7MRYIVUYMTKTWN4OD7ANCNFSM6AAAAAATCJOD5Y . You are receiving this because you commented.Message ID: @.***>

Originally posted by @kai5z in https://github.com/kai5z/Chladni-patterns/issues/7#issuecomment-1356814751

juninagaki1975 commented 1 year ago

As you mentioned on your blog, sweep.py is employing Reissner Mindlin model. And it is not what I want that violate the way. A series of unnecessary modification on my pull request is caused by my misunderstanding.

I belive sweep.py is working well on your design on my side, with a little issue I opened another.

◆

I tempted to change Bs (shear?) matrix based on below Chap. of textbooks.

  1. C. Kittel "Introduction to Solid State Physics" 8th ed. Chap.3 p.74 In there, Taylor expansion for displacement vector R is described with R(0) = 0.

  2. "Programming the Finite Element Method" 3rd and 5th ed. Chap.2 In there, [B] = [A][N] where [A] is differentiation operators, [N] is shape functions.

So I think it is not not appropriate that shape function it self (in this case, -NN[ix]) exiist in B matrix. But I have never seen formalism for Reissner-Mindlin plate model on that part directly.

Rather I would like to know what the Ds on sweep.py is based on.

Best Regards, Jun