FEA deflection calc. of vacuum chamber

[BoomerSooner7]

I am using CosmosWorks 2008 for an FEA analysis of a vacuum chamber of dimensions 49" x 49" x 38", with floor and wall thicknesses of 3/4" and top plate thickness of 1.25". My main question has to do with the pressure (vacuum) loading of the interior surfaces @ 29.9 inHg. Would I input +14.7 psig in the direction towards the inside of the box (putting tension on the inside walls)? And also a +14.7 psig on the outside of the walls in the same direction to account for atmospheric pressure outside of the box. Please help, I am not an FEA expert.

 

[corus]

If you apply a pressure on the inside and the same pressure outside then there is no effect. Pressure is normally given as gauge pressure, ie. a pressure above atmos. It's this pressure you apply to the outer surface.

corus

 

[JStephen]

Don't apply any force on the interior; apply 14.7 psi on the exterior.

Cylinders subject to vacuum can fail by buckling. Flat plates with pressure applied to them can develop membrane stresses due to large deflection. If your FEA doesn't account for these effects, it won't necessarily be useful in modeling the chamber.

 

[hacksaw]

if you work in psig then 0 on the outside and -14.7 on the inside.

if you work in psia, then 14.7 psia outside and 0 inside.

if you work in mmHg(g), the 0 mmHg(g) outside and -29mmHg(g) inside.

etc., etc....

 

[BoomerSooner7]

The pressure I initially applied on the interior was in the direction as to cause tension (pull) away from the walls towards the center. I believe the pressure input in this FEA software is in psig not psia, so entering a value of 0 (14.7 psia)will not have any effect on the structure. It sounds like I need to just account for the vacuum pressure inside the box and neglect the atmospheric pressure. Does this sound accurate?

thanks for the replies.

 

[BoomerSooner7]

Yes, Hacksaw what you're saying makes sense.

thanks.

 

[JStephen]

It depends. If you assume zero thickness, then applying an inward-acting pressure on either the inside face or the outside face will be the same thing. If you treat it as having a finite thickness (IE, multiple elements), the pressure should be on the outside. A vacuum doesn't "suck" on the inside, you simply have external atmospheric pressure on the outside, and a lack of balancing pressure on the inside.

 

[BoomerSooner7]

Thanks JStephen, that makes sense. I will set this up as a solid mesh with a pressure applied to the outside and re-run it with a shell mesh and see what the % variance is. I would also like to confirm the FEA analyses of the maximum deflection with a hand-calculation. Does anyone know of a good online source of plate deflection formulas?

thanks.

 

[JStephen]

Refer to Roark's Formulas for Stress and Strain. You should be able to combine the circular plate load case with edge moment with the cylinder solutions with end moment to get a complete elastic analysis. You can also check the large deflection formulas for the end plate, but I don't think there are adequate load cases to combine with the cylinder formulas.

 

[BoomerSooner7]

I found the following equation online to perform a hand calculation of the plate deflection at center under a load:

Y=K(W*R^4)/(E*T^3)

Where
E= elastic modulus
R= long dimension
W= pressure
T= thickness

From what I read, K is dependent on the end supports and the aspect ratio and poisson's ratio. I could not find any table values for K for mild steel with the edges supported.

Please help!!

 

[Duker37]

I too use CosmosWorks 2008 to run FEA on flat plates. Make sure after you choose your "Study Type" either fatigue, drop test, static, ect... that you "right click" on your Study Type Name and click on properties. Then, in this window make sure the tab called "Options" is showing and notice a check box called "Large displacement" I have this check box checked so that the large displacement theory is used in my FEA. Then I would start picking the outside surfaces of the tank and adding a pressure in the direction inward to the tank to what ever the limit is on the vacuum pump. Please note that a vacuum pump will draw out the air that is inside your chamber and you must be careful that your tank material will not be affected at whatever pressure the vacuum pump is rated at. The vacuum pump is capable of pulling out the gases in your material used to make your vacuum chamber so be careful. I hope this is helpful to you. As far as some good references for flat plate analysis I use (1) Design of Welded Structures by Omer W. Blodgett Section 6.4 How To Stiffen a Panel and (2) Tubular Steel Structures Theory and Design by M.S. Troitskey Section 7.5.5.2 Large Deflection Theory pg 7-27. Also note that the "end-condition" are very important in your analysis by hand. The end conditions I use are simply support because I use corner to corner welds when welding my panels. These joints are really "Hinged" connections but I can't find any good procedure to perform hand calc's on hinged connections. Please note that CosmosWorks FEA has an option called "Hinge" when adding restraints to your vacuum box.

 

[BoomerSooner7]

Thanks Duker37. I will re-run the FEA with the large deflection checked and see if the results are the same. I did find a formula for fixed end connections from the Machinery's Handbook and the results were 14% different than what the FEA analysis results were (acceptable tolerance in this application). So we'll see what the new analysis yields.

Thanks everybody for replying to this, you have all been great help!