Boundary condition to apply plane of symmetry?

[zolck511]

Hi,

I have a simple linear-elastic model I'm trying to run. It has a plane of symmetry, so I decided to put that plane on rollers. I first did this by constraining all nodes on that plane to have zero displacement in the z-direction, and let it free in the x- and y- directions. This failed.

I realized that I didn't constrain it enough. It's been a while since I learned the fundamentals, but I do remember having to constrain one node on that plane in all directions, and another node in two directions. I just don't remember where the second node needs to be in respect to the first node (fixed in x- y- and z-), and in which directions I need to constrain the second node to achieve a plane of symmetry BC.

Can someone explain/refresh me on this? Thanks

 

[ukbridge]

Qualitatively, think about the deflected shape of what it is you're trying to analyse. Is there any net deflection or rotation at your point of symmetry? That is the key to making these symmetrical half models.

For instance take a simply supported beam of length L subjected to a UDL along its length. The beam can be modelled as a an equivalent beam of Length L with a rotational restraint at midspan to mimic this effect. This because there is maximum moment and no rotation.

As another example take a portal frame fixed at its base subjected to a horizontal point load at the top corner. At the midspan of the beam there is no overall net vertical deflection, therefore apply a roller support.

 

[zolck511]

I reduced my model to a three point bending problem of a beam to get my head straight.

Initially, I take a 10 x 10 x 30 beam and fix it at both z=0 and z=30. I apply a 10N force at z=15. The reaction forces at z=0 and z=30 are 5N each. This is my baseline reference to check my symmetry BC in the next model.

Then, I take a 10 x 10 x 15 beam and fix it at z=0. At z=15, I constrain all nodes such that they cannot displace in the z-direction, but otherwise leave them free to move around in the x-y plane. I then apply a 5N force at z=15. The result I get from my code (reaction forces at z=0) is all 0N, when I'm expecting 5N. This makes me think I'm not constraining it enough.

 

[ukbridge]

Zolck,

Post a sketch of the model you've got it you would so I can have a look.

I did a quick LUSAS run to make sure I didn't give you erroneous advice for your 3-point bending problem, for both the full model and symmetrical half model. I think you might be going wrong with working with a 3D rather than a 2D problem and have a mechanism of some means. Note I overlooked applying only half the load only!

For the first model, why did you put a roller on it? What was it thata you're trying to model, a portal frame subjected to a lateral load?

 

[Denial]

As a general rule for a three-dimensional structure that is symmetric about an XY plane (and whose applied loadings are also symmetric about the same plane) you can model only half provided you fully constrain all nodes on the symmetry plane against Z displacement, XX rotation and YY rotation.[ ] Similarly, mutatis mutandis, if the plane of symmetry is YZ or ZX.[ ] If you have multiple orthogonal planes of symmetry, these constraints are additive for nodes on the line of intersection of the two symmetry planes.[ ] Point loads applied on the plane of symmetry must be applied as halved (and obviously they can only be IN the plane of symmetry or they would not be symmetrical with respect to the full model).

 

[inline6]

you fix the normal translational direction of the plane (i.e. DZ=0) and then other two DX and DY are free. for rotations its the opposite so RX=RY=0 and RZ is free.

translations: -,-,0
rotations: 0,0,-

where
'-' = free
'0' = fixed