Hello everybody,
I have a very simple doubt in 3D model simplification. I believe plane stress and plane strain conditions are the two extreme states to simplify a 3D model to 2D case.
- I took a simple example of a square plate. I fixed the bottom edge and applied a force (say 1000 N) on the top edge. Analysing it as simple 2D cases of plane stress and plane strain, I have some results for von Mises stress in the plate.
- Now extending the same to 3D, I applied same force (1000 N) on the top face and fixed the bottom face. I expected a result between the two extremes of negligible thickness (P.stress) and very high thickness (P.strain), but my result of 3D was an order of magnitude less.
What I think is, I should scale the applied force (in 2D) proportional to the area (Area*(Force/unit area)) in which it is being applied, to get result between the two extremes. Is that the right way?
Please correct me if I am wrong.
Thanks for your time.
Regards,
Shree
UPDATE : Clarified. Question can be deemed closed.
I think that thickness is the key to your problem. You need to make sure, obviously, that each of your models is loaded with the same pressure and not the same load if you want to compare models with different thicknesses. You might also need to rethink your understanding of plane strain. It is not that the thickness is very large but more that the two planes are constrained from displacement.
You might find the following document of interest:
http://www.ramsay-maunder.co.uk/downloads/NBR03.pdf
Dear Dr. Ramsay,
First of all, thank you for your answer. I am going through the 'pdf'.
- By plane strain I understand that the displacement (U_z) and the displacement gradient (dou/dou_z) along third direction is zero. This means strain along 'z' is zero assuming dimension of 'z' is larger compared to other two dimensions. Please correct me if I am wrong.
- Also, can you please brief on why I can only compare models loaded with same pressure and not same force?
Regards
Shree
Dear Shree,
Plane strain models, by definition, have zero strain in the z direction. A 3D model could mimic this if you constrain the z displacements on the two z=constant planes. If you do not constrain these planes in this manner then you will find at the end planes the solution is like that achieved with a plane stress model whereas at the centre of the model the solution might tend towards the plane strain solution although this is strongly load and geometry dependent as I have tried to show in the document you are examining.
All I was saying about pressure rather than total force was that if your models have different thickness in the z direction then it is the pressure that needs to be the same for the models if your want to compare like with like. If you used the same force applied over a different area then, obviously, the pressure would be different.
Hope this helps.
Regards,
Angus.
Dear Angus,
Thanks a lot for the explanation. It took a while but I understand it now. Thanks for your help and insight into the concept.
Regards,
Shree
You're welcome Shree. Do add some likes to my comments if you felt it was useful to you.
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