Plate with hole under uniaxial tension
Plate with hole under uniaxial tension
(OP)
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
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





RE: Plate with hole under uniaxial tension
σmax = σa · [1 + 2(a/b)]
Regards,
Cory
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RE: Plate with hole under uniaxial tension
Cheers
Greg Locock
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RE: Plate with hole under uniaxial tension
<snort>
RE: Plate with hole under uniaxial tension
C.E. Inglis, Proceedings, Institute of Naval Architects 55, 219 (1913).
Regards,
Cory
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RE: Plate with hole under uniaxial tension
The SPIE book is MS137 "Selected Papers on the Foundations of Linear Elastic Fracture Mechanics"
www.wam.umd.edcu/~sanford/ms137.html
There is also an MS138, "Selected Papers on Crack Tip Stress Fields"
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.
RE: Plate with hole under uniaxial tension
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
RE: Plate with hole under uniaxial tension
RE: Plate with hole under uniaxial tension
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: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips Fora.
RE: Plate with hole under uniaxial tension
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.
RE: Plate with hole under uniaxial tension
RE: Plate with hole under uniaxial tension
RE: Plate with hole under uniaxial tension
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.
RE: Plate with hole under uniaxial tension