FRP plate design

[mohanbabu2013]

Hello group,
I am trying to calculate the thickness of FRP plate (11"x11" - fixed all four sides) to sustain an impact with 2" metal ball hitting at 75 feet/sec. Any help pointing in the right direction is greatly appreciated. Any source/text book/web site to look for the formula or any equation to calculate the deformation and stresses in the plate.. will help.

(I know the tensile modulus of the material)

Thanks in advance.
Mohan

 

[drawoh]

mohanbabu2013,

There is a lot of flat plate stuff in Roark's Forumulas for Stress and Strain. I assume you need the stiffness (spring rate) and the stress. Strain energy calculations should tell you what you want to know.

--
JHG

 

[pperlich]

Once you have the spring rate of the plate, set up your mass-spring system. Then find the maximum deflection of the plate and see if it would cause the plate to be permanently deformed.

 

[hendersdc]

From Roark's 7th addition section 16.4:

For Vertical Impact:

di/d = Sigmai/Sigma = 1 + sqrt(1 + 2*h/d)

For Horizontal Impact:

di/d = Sigmai/Sigma = sqrt(v^2/(g*d))

Where:

di = deformation due to impact
d = deformation due to static load
Sigmai = stress due to impact
Sigma = stress due to static load
h = drop height
v = velocity at impact
g = acceleration due to gravity

These formulas basically give you a way to relate the results of a static load case to the force and deformation that may be seen during impact. I have applied these formulas in the past to model impact of a round object on a spherical plastic lens for a small handheld device and found them to be fairly accurate if not a little conservative though I wasn't working with velocities as high as yours. As drawoh said, you can find plenty of flat plat static load formulas in Roark's as well to get your input for these equations. In my case I did a static FEA of the impactor sitting on the lens with the only force being its own weight. Using the deformation and stresses found from the FEA I applied the formulas using the test drop height and found the deformation and stresses due to impact. The lens was protecting an LCD. During testing the impactor was dropped from increasing heights until failure which is where my opinion of the formulas being a little conservative comes from though I can't remember exact values.

Doug

 

[mohanbabu2013]

Thank you very much drawoh and pperlich for showing me some direction. Can I use Roark's for plastics also? I always used it for metals before (this is my first time working with plastics).

 

[mohanbabu2013]

I tried energy conservation equation as suggested by pperlich and tried Roark's as suggested by drawoh & hendersdc. There is big difference in answers. Plese see attached. I don't know where I am going wrong.... any help????

 

[hendersdc]

One thing I can see is that you are using the wrong loading force for the Roark's equations. You should use only the weight of the ball sitting on the plate. The di/d equation is the part that adds the effect of impact to the results so you don't need to guess the stopping time.

 

[mohanbabu2013]

Thank you hendersdc... once I change the weight of the body the deflections match. Now I can confirm the theoretical deflection of the plate for the given youngs modulus....

Thanks to you all guys....
mohan