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"periodic" boundary condition in structural mechanics
Posted Feb 4, 2019, 7:02 a.m. EST Structural & Acoustics 4 Replies
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Hello, I am wondering how one can prescribe the correct boundary conditions to a periodic mechanical structure. For illustration purposes let's have a simple system as shown in the attached picture. The full system is an infinite series of this unit cell, shifted along the horizontal axis. Blue is a hard, red is a soft material, and we apply a high pressure inside the white void.
Since the full system is periodic, the first idea is to prescribe a periodic BC on the left and right sides. However, this constrains the displacements on the two boundaries to be equal: u<sub>dst</sub> = u<sub>src</sub>.
Since the structure is vertically symmetric, it will not bend when the pressure is applied, however, the left/right boundaries of the symmetry cell will not remain flat. The cell will expand due to the internal pressure.
After all, what would be needed is something like this, u,v,w meaning the displacements along the 3 directions, index 1 or 2 means left or right boundary. z is the horizontal axis in the picture.
u2 = u1 v2 = v1 w2 = w1 + C
where C is a constant. What is the best way to achieve this?
Thank you Daniel
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Hi Daniel,
This seems like a perfect fit for the Cell Periodicity feature, which was introduced in version 5.4.
Regards,
Henrik
Henrik Sönnerlind
COMSOL
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Hello Henrik, Thank you for your answer. Unfortunately the highest version I have access to is 5.3a. I would be grateful for any smart workaround. Best regards Daniel
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Hi Daniel,
There are some diffent approaches you could use, but the quickest is probably to edit the constraint expressions for the periodic boundary condition in Equation View.
Add 'C' as an extra DOF using a Global Equations node (without equation).
Then modify the constraint and constraint force expressions in the periodicity condition to something like
if(solid.incontact_pc1,u+C-solid.src2dst_pc1(u),0)
Regards,
Henrik
Henrik Sönnerlind
COMSOL
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Hi Henrik, Thanks a lot for your suggestion and help, it works. Daniel