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2D or 3D analysis
Hello:
First of all, I am really excited to see this forum, this is a great way to interact and learn. Thank you so much to all who are involved in making it happen.
I have a very fundamental question about a FEA analysis. Let’s say I have a one inch by one inch by 6 inch long specimen with a small singularity in it (like a crack or flaw or foreign material). Let’s assume for now that the flaw is through the thickness so that all longitudinal sections are same. Now if I were to do an FEA analysis of this specimen I have there choices, (i) 2D plain strain (as specimen is relatively thick) (ii) 3D analysis but only 1 element in thickness direction or (iii) 3D analysis with more number of element in thickness direction.
In your opinion what difference in results I should expect. I know I can run the analysis fairly easily and see but let’s just think fundamentally.
Please feel free to point me to any article or book where this problem has been captures in detail
Thanks
Rahul
Re: 2D or 3D analysis
Assuming you apply the correct, w=0 boundary conditions at z=0 and z=h, the 3D analyses (i and ii) will give results identical to the plane strain analysis. Any correctly-formulated 3D element can reproduce the constant stress state in the thickness direction. Of course, it goes without saying that the 3D analyses will be more computationally costly than the 2D one.
3D effect
I agree with Bill. But, if you leave the surfaces at z = 0 and h to be traction free (without specifying the constraint on displacement), you will see the 3D effect, as I mentioned in another comment before.
If you only look at the in-plane stresses, it may not matter. If you compare the shapes of the hole after deformation, I believe you will see differences among 2D plane-strain, 2D plane-stress, and 3D models (with more than one elements in thickness direction). The 2D plane-stress model will give a larger diameter after deformation than the 2D plane-strain, while the diameter will vary along the thickness direction in the 3D model (relatively small variation, maybe). Sounds like you can do all these models easily. Why don't you tell us what you get? I don't know if anybody else have done the same analysis. The result may be presented in a simple plot of the average diameter along the thickness direction from the 3D model as a funciton of the plate thickness, which should approach the two 2D limits for thick and thin specimen.
Some consequences of this 3D effect may be further investigated, including some mentioned in this previous discussion.
RH