Panel Deflections 3

[Stezza]

Hi,
I have a panel 10 inches long 4 inches wide subjected to an out of plane pressure. The panel is pinned along the 4 inch sides and free on the long edges. When the panel deforms it takes up a curved shape and because of this curvature the projected length view from above of the panel should reduce a bit - say to 9.8 inches.
I wanted to know this length reduction. As it turns out a linear analysis shows no length reduction (only out of plane deformation) and you need to do a non linear analysis to get results for the length reduction.
Can somebody help me understand the reasons why the linear analysis does not show the inplane deformations due to the out of plane load as I had not expected this before the analysis?
Just in case it's relevant I am using Nastran.
Thanks

 

[johnhors]

Can somebody help me understand the reasons why the linear analysis does not show the inplane deformations due to the out of plane load as I had not expected this before the analysis?

A lack of coupling terms in the element matrices. Only when the panel deflects can it begin to resist the normal pressure load. Think of a taut string, initially when you push on the centre of the string there is no resistance, only when the string deflects will you feel a resisting force.

http://www.Roshaz.com

 

[corus]

A linear analysis assumes small deflection theory. As there's no force along the length, there's no apparent deflection.

corus

 

[GBor]

The panel can't be "pinned", but still shorten. Say your panel is in the X-Y plane with the 4" sides along the X-axis. To see the length reduction that you are looking for, you will need to only limit translation in the Z- and X-axis directions. With it "pinned", it CAN'T move at the 4" ends, so it won't "shorten".

The non-linear point is probably also valid, and johnhors knows too much about the inner workings of FEA for me to always understand his analogies

 

[johnhors]

I assumed the OP meant that one of the pinned ends was sitting on "rollers"! (fixed only in out of plane direction)

http://www.Roshaz.com

 

[kellnerp]

If the ends are pinned/fixed the plate will get longer and the projected length will stay the same.

If the ends are simply supported the plate will stay the same length and the projected length will shorten.

If there is an inplane or geometric stiffening switch in your code you should pick this up in a linear analysis.

TOP
CSWP, BSSE

http://www.engtran.com

http://www.niswug.org

"Node news is good news."

 

[paddingtongreen]

Forgive me for being a grumpy old-timer but I am astounded that you put this into an analysis program.

You say pinned at both ends, as stated before, one end has to be supported but not pinned. Typically shown as a roller on diagrams.

From here it depends on the required accuracy, first the least accurate but probably close enough, given that material properties are part guesswork.

The deflection at the center of a uniformly loaded beam is:

y=5Wl*3/384EI, where; W is the total load, l is the 10" span, E is the elastic modulus of the material and I is the Moment of Inertia of the panel.

Calculate the length of an arc passing between and through supports, and through the deflected center, subtract the original 10" and the difference is approximately the distance moved.

If you want it more accurately, the formula for deflection at any point is:

y=Wx(l-x)(l*2+x(l-x))/24EIl

Where x is the distance from the left end

Put that into a spreadsheet cutting the beam into small lengths and add up the lengths of the resulting straight elements to find the length of the curve. Then proceed as above.

Timing has a lot to do with the outcome of a rain dance.

 

[kellnerp]

There is additional stiffness in a panel because of Poisson related bending.

If he says pinned on both ends I would take him literally. But Roark has a formula for that too.

TOP
CSWP, BSSE

http://www.engtran.com

http://www.niswug.org

"Node news is good news."

 

[paddingtongreen]

kellnerp, pinned ends don't move but the OP expects one end to move horizontally.

Timing has a lot to do with the outcome of a rain dance.

 

[GBor]

The purpose for performing an analysis of this simplicity would be to validate your use of the software, build to an analysis that isn't so easily calculated by hand. The deflection that the OP was looking for and apparently not getting is either a result from his/her application of the software, or misunderstanding of the problem. My response was trying to resolve that issue...

Agreed that this can be hand-calc'd with ease, so I'm assuming the issue is with making sure that the model is comparable to the formula to which the OP is comparing.

 

[Stezza]

Thank you for the good answers to the question.
The FEM was pinned at one end and on rollers at the other.
The problem I tried to describe was my test FEM I made when I noticed the much more complicated actual part not behaving as I thought it should.