## 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

Uniaxial loading

Biaxial loading

Shear loading

Uniaxial-Shear loading

Biaxial-Shear loading

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

My BC's for uniaxial loading is:

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

Biaxial loading

unit load at A and B

SPC's

A - 3

B - 3

C - 23

D - 13

Shear loading (AD)

unit along A towards D

SPC's

A - 23

B - 3

C - 123

D - 3

Uniaxial-Shear loading

unit load at and along A

SPC's

A - 3

B - 3

C - 123

D - 3

Biaxial-Shear loading

unit load at A, B and along A

SPC's

A - 3

B - 3

C - 123

D - 3

Uniaxial loading

Biaxial loading

Shear loading

Uniaxial-Shear loading

Biaxial-Shear loading

See attached image (shows Biaxial-Shear Case)

(http

NOTE plate is not symmetric

My BC's for uniaxial loading is:

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

Biaxial loading

unit load at A and B

SPC's

A - 3

B - 3

C - 23

D - 13

Shear loading (AD)

unit along A towards D

SPC's

A - 23

B - 3

C - 123

D - 3

Uniaxial-Shear loading

unit load at and along A

SPC's

A - 3

B - 3

C - 123

D - 3

Biaxial-Shear loading

unit load at A, B and along A

SPC's

A - 3

B - 3

C - 123

D - 3

## RE: Simply Supported Boundary Conditions

My BC's for uniaxial loading is:

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

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).

Brian

www.espcomposites.com

## RE: Simply Supported Boundary Conditions

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

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.

Brian

www.espcomposites.com

## RE: Simply Supported Boundary Conditions

## RE: Simply Supported Boundary Conditions