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# Simply Supported Boundary Conditions

## Simply Supported Boundary Conditions

(OP)
I am attempting to model the buckling of a plate subject to the following loading conditions

See attached image (shows Biaxial-Shear Case)

(http://files.engineering.com/getfile.aspx?folder=43404653-f139-4c73-ab50-d08328d86d57&file=plate.png)

NOTE plate is not symmetric

unit load at A (distributed to all nodes along A)

SPC's (applied to all nodes along boundary)
A - 13
B - 3
C - 3
D - 123

What about the other cases? I am including my best guesses below

unit load at A and B

SPC's
A - 3
B - 3
C - 23
D - 13

unit along A towards D

SPC's
A - 23
B - 3
C - 123
D - 3

unit load at and along A

SPC's
A - 3
B - 3
C - 123
D - 3

unit load at A, B and along A

SPC's
A - 3
B - 3
C - 123
D - 3

Replies continue below

### RE: Simply Supported Boundary Conditions

(OP)
CORRECTION

unit load at A (distributed to all nodes along A)

SPC's (applied to all nodes along boundary)
A - 13
B - 3
C - 123
D - 3

### RE: Simply Supported Boundary Conditions

Another method I have successfully used is via "soft springs". Connect a handful of "soft springs" to prevent rigid body motion in all DOF. I typically connect 1 or 2 near each corner of the plate. You can imagine this as a plate in space, connected by bungee cords.

You then just apply a balanced set of loads to the part, without worrying about how to restrain the edges. If the loads are balanced, then the soft spring should carry a trivial amount of load (just enough to prevent rigid body motion due to mathematical roundoff, discretization, etc.)

I have correlated countless number of models to classical solutions via this approach. It is very robust and takes any guess work out of the boundary condition constraints. It is also easier to justify your results to others (i.e. the model is physically more obvious).

### RE: Simply Supported Boundary Conditions

(OP)
Brian,

When you say "soft springs" what do you exactly mean by soft? I have tried them as you suggested, but do not understand how they are changing my buckling eigenvalues. (running implicit global buckling in ls-dyna)

For example, I am using lbf/in for units and applying unit loads to a 10x10in flat plate. I would assume that any value of K<100 would give about the same answer since the springs would likely not exert a force on the nodes due to a displacement. However, I noticed that too small a value of K also didnt work. Could you explain or provide a link so i can understand this concept a bit better and understand how it works.

Thanks

### RE: Simply Supported Boundary Conditions

The objective of the springs is to prevent significant rigid body motion. They also should not pick up a significant amount of force. Therefore, you have a a range of values that work and do not work. But in the end, it works over a large majority of k values. The correct k will be depend on your model, but I would make it about 1% of the stiffness of the part.

Try this. If k is too low you will get rigid body motion. Increase it until you get a result. You may see you get some rigid body motion, along with your buckled shape. You should also see that the reaction force on the spring is very low.

Then increase the k to a very high value (very high). You will see that some of your applied force is reacted by the springs (which is not what you want).

Anything in between these two scenarios is sufficient. All you really have to do is ensure that you get a result and that the springs to not pick up more load than you find acceptable. With some experience, it is pretty easy to choose a suitable k value. The acceptable range is quite broad.

### RE: Simply Supported Boundary Conditions

In Nastran buckling you can specify two sets boundary conditions - one for perturbation (loading) and another for the buckling mode shape. This makes life a lot easier for the more complex cases.

### RE: Simply Supported Boundary Conditions

I use MSC Nastran 2012, I can take a quick look at your .bdf or .dat file and help out.

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