9
votes
Accepted
FEM for vector valued problems: reference request
Short answer: Just replicate the vector of interpolation functions into a block-diagonal matrix, as showed e.g. on page 5 in this lecture note.
Detailed answer:
Mathematically oriented texts typically ...
- 832
5
votes
Accepted
trilinear hex elements
You are correct: In general, the faces of hex cells are not planar. In fact, the set of cells you could generate with only planar faces is relatively small and not enough to create useful 3d meshes.
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- 56.2k
4
votes
FEM for vector valued problems: reference request
We can show how it works on the example of linear elasticity. In classical finite elements formulations, on every node, we will have a scalar shape (base) function to which we have associated number ...
- 906
2
votes
Calculate strains based on X,Y Deformation gradient with time
If you have $x$,$y$,$z$-coordinates and displacements $u$,$v$,$w$ for a set of points, then you could approximate the displacement gradient by finite differences (or possibly other interpolations). So ...
- 86
1
vote
Accepted
Building blocks for solving a vector valued problem
Your assembly procedure seems correct to me. I made some edits in your post to correct some possible typos. Feel free to raise objections. Looking at the graphs and their legends, I see the rate of ...
- 832
1
vote
deal.ii - ParaView "warp by scalar" of my output is not continuous
It seems like you are using deal-ii for your simulations. Its a well established fem solver and there is a very less chance that the mistake is with the FEM solver. However, Please check the BC that ...
- 369
1
vote
Accepted
Displacement field not correct?
As mentioned by @Wolfgang Bangerth , the value may be at the interior points. However, to visualise that better in paraview, You can use a filter called "plot over line" which plots the data ...
- 369
1
vote
Confusion about bilinear form for elasticity equation in deal.ii tutorial
Its not the summation that is wrong, but the lack of indices inside it. Below this expression on their site they define:
$$\epsilon(\mathbf{u})=\frac{1}{2}([\nabla\mathbf{u}]+[\nabla\mathbf{u}]^{\...
- 1,023
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