Plate with hole under uniaxial tension

[FC2008]

Hi, I've been finding maximum stress in a plate with holes using Ansys and it's worked out good so far.
The thing is, I don't know how to do this by hand since it is as I understand quite complicated.

Could you guys point me in the right direction, be it resources or hints so that I can do this thing by hand?

I know there are some equations floating about to do this, but I would like to get dirty and do all the math.

thanks

 

[CoryPad]

The maximum stress at the edge of a circular hole in an infinite body that has tension applied to it is 3 times the global stress. This is based on stress concentration of elliptically-shaped flaws. The general equation is:

[σ]_max = [σ]_a [·] [1 + 2(a/b)]

Regards,

Cory

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

 

[GregLocock]

Aye, but where's the derivation? Does the famous Irish stress analyst Tim O'Shenko know?

Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[btrueblood]

I'll pop down to yon Roark's pub and ask him.



<snort>

 

[CoryPad]

Have to go back almost 100 years to get this one:

C.E. Inglis, Proceedings, Institute of Naval Architects 55, 219 (1913).

Regards,

Cory

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

 

[prost]

Ah, the Inglis paper--the bane of my existence. I searched for years to find this paper. Many people referenced it, but didn't have the actual paper in their library (sounds almost unethical to reference a source you don't actually possess, but I guess that's just me). This Inst. of Naval Arch. journal was very hard to find. Finally, I located a marvelous reference published by SPIE--a compilation of several historically significant fracture mechanics papers. This particular compendium has the Inglis paper--my torment continues,as othere are other important references that I cannot get.

The SPIE book is MS137 "Selected Papers on the Foundations of Linear Elastic Fracture Mechanics"

http://www.wam.umd.edcu/~sanford/ms137.html

There is also an MS138, "Selected Papers on Crack Tip Stress Fields"

http://www.wam.umd.edcu/~sanford/ms138.html

These are both very good, and recommended if you work with cracks and other places where the stress concentrates.

The equation CoryPad gave is the stress concentration at the hole edge. The full equation for the circular hole in an infinite plate is from Timothy Michael O'Shenko's book, Theory of Elasticity. Let S be the far field stress, in the y direction. Let Syy be the normal stress in the y-direction. Then
Syy=(S/2)*(2+(a/r)^2+3*(a/r)^4), where 'a' is the radius of the hole, and 'r' is the distance from the center of the hole. Naturally, r<a makes no sense.


Note that this is for a centered, open hole in an infinite plate. Your FE solution naturally has a finite plate. Now what? You can just keep extending those boundaries of the plate until the ratio of the maximum stress Syy at the edge of the hole, divided by "S" is near 3.0 (say to within 5%, or to within 1% if you are ambitious). This raises the larger question, I believe, is how do you decide your solution is good if you don't have the exact solution. This is a much larger discussion, so I'll not start it here.

Anyway, hope the equation above helps. Good hunting.

 

[FC2008]

That equation might to the trick prost.
I've done some searching and have found out that I lack any knowledge of continuum mechanics etc.
I only have a bs in mechanical engineer.

I'll go and find some decent books on the topic and go trough them. Anyone know of some good resources on the subject?

Thanks

 

[Tmoose]

Once I got close to Roark's with my model, I started playing, adjusting for hole finish and residual stresses left by drilling with a dull Solid Carbide 130° 3 Flute drill bit.

 

[CoryPad]

FC2008,

There are joking references in this thread about an Irish author. In reality, they are referring to Stephen Timoshenko. He has written multiple books that would be educational for you. Just type his name at Google Books or Amazon and select the ones you want/need/can afford/etc.


Regards,

Cory

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

 

[prost]

Yes, the two by Timoshenko, Theory of Elasticity, and Theory of Plates and Shells, are excellent.

Personally, I prefer the text from my undergrad class, by Bauld--not that I think it is superior to others, but because I like to use references with familiar notation. I know where stuff is in this book, so I don't have to spend hours looking for it.

For a true continuum mechanics book (not just linear elasticity, but full large displacement/large strain treatments), I use Malvern. Others use the book by Eringen. Continuum mechanics is an odd subject--it's difficult, because you need to spend a lot of time learning tensor notation and learning new stress and strain quantities you have no idea existed--Lagrange strains, 1st Piola Kirchhoff stress. Unnecessarily complicating matters is the complete lack of standardization in the notation from author to author.

 

[FC2008]

I've done some reading during the weekend, and it truly is an odd subject although very interesting. This will make for a long study I think. Thanks!

 

[rb1957]

that same equation is derived in a NACA TN, which includes more generalised stress states ... only i don't have the number on my laptop ... 1273 rings a bell.

 

[prost]

rb1957
Are you referring to NACA TN 2073? Stress and Strain Concentration at a Circular Hole in an Infinite Plate, by Elbridge Stowell? Published in 1950.

 

[rb1957]

that'd be the one ! ... i guess i scored two bulls and one cow ??