Deformation Analysis: When to Use Plane Strain vs 3D?

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Discussion Overview

The discussion revolves around the conditions under which plane strain analysis is preferred over three-dimensional analysis in deformation analysis, particularly in the context of materials with non-zero Poisson's ratio. Participants explore specific examples and clarify concepts related to plane strain and plane stress.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Hassan questions when it is justified to use plane strain analysis instead of three-dimensional analysis, suggesting that thin sheets may be one case.
  • Another participant points out the distinction between plane stress and plane strain, emphasizing that they are used in different circumstances.
  • Hassan clarifies that he meant "plane strain" and presents a scenario involving a hollow cylinder, questioning the validity of using plane strain given the dimensions of the cylinder.
  • A participant provides an example of a roller bearing under compression, explaining how it can be approximated as undergoing plane strain due to confinement.
  • Hassan acknowledges the example and relates it to his own case of vibration analysis in an electric motor, noting its complexity compared to the provided example.

Areas of Agreement / Disagreement

Participants generally agree on the importance of understanding the differences between plane strain and plane stress, but there remains uncertainty regarding specific applications and the validity of using plane strain in certain scenarios.

Contextual Notes

Participants discuss the applicability of plane strain analysis based on geometric considerations, such as the dimensions of the hollow cylinder and the effects of confinement in examples like roller bearings. There is mention of the need for additional parameters, such as wall thickness, to determine the appropriate analysis method.

Who May Find This Useful

Individuals interested in deformation analysis, mechanical engineering, and the application of different modeling techniques in engineering problems may find this discussion relevant.

Hassan2
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Hi all,

I have a question regarding deformation analysis.

For materials with non-zero Poisson's ration, when is it justified to use plane strain analysis rather than three-dimensional? Perhaps one case is when we are going to analyze a thin sheet. Are there other cases too?

Thanks,

Hassan
 
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Well did you mean plane stress (the thread title) or plane strain (in the question)?

They are different and for different circumstances. Do you understand the difference?

The short answer to when do we use one or the other is 'Whenever we can', since either simplifies the analysis.
 
Last edited:
Thanks. I didn't know the difference but after your emphasis , I searched and learned a little bit about them. In fact I meant "Plane Strain".

Suppose we have a hollow cylinder with a radios of 10 cm and the a height of 15 cm. the force distribution on the inner wall is normal to the surface and independent of the coordinate along the axis and I thought maybe I can use plane strain. However the height is not large enough compared with the radius, so it doesn't seem to be a case of plane strain. I have seem some papers doing the analysis in two dimensions, and I wonder if their result is valid .

Thanks.
 
OK plane strain it is.

Since you are studying mech eng here is a mech example.

Consider a roller bearing - that is a solid roller (cylinder) confined between two loading plates.

So the bearing is loaded in compression transversally to the cylindrical axis.

Consider any thin slice or section of the cylinder, except at the extreme ends.

This disk suffers two diametrically opposed point compression loads, in the plane of the disk.

However the disk is unable to expand normal to its own plane because of the confining effect of the material (other disks) on each side.
So to a very good approximation the disk undergoes plain strain radially.
The resulting stresses and deflections are known as Hertzian.

Does this help?

BTW You need two radii to define a hollow cylinder!

Stress analysis of such a cylinder will depend upon wall thickness as to whether we can use a membrane or hoop stresses or whether we have a thick walled pipe.
 
It helped a lot. Thanks.

My case is the vibration analysis of and electric motor which is more complicated than your example but essentially the same.
 
:wink:

Post again if you need more.
 

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