Plane Strain

[corus]

In FE software it is common for generalized plane strain elements and plane strain elements to be specified. I know that the generalized plane strain element represents a constant out-of-plane strain, and thus represents an infinitley thick 2D section, whilst ordinary plane strain represents zero out-of-plane strain. Would it be incorrect to use ordinary plane strain elements which assume zero out-of-plane strain across the section?

corus

 

[JWB46]

Hi Corus,
I'm a little bit rusty on this but I think plane strain conditions infer zero out-of-plane strain, plane stress conditions infer zero out-of-plane stress.

I will check up later today and come back eating humble pie if I've got it wrong.
Hope it helps anyway.
Cheers.

 

[JWB46]

Corus,
I was right what I said in my last thread, but I now realize I misread your question! Sorry.
Are you looking at a linearly elastic problem ?

 

[corus]

JWB46,
It is linear elastic, however, the point I was trying to make was that there are different kinds of plane strain and it is whether a zero out-of-plane strain is correct or should the more generlaised plane strain (constant strain not necessarily zero) be used.

Many thanks


corus

 

[EdR]

corus:

Maybe I'm also misreading your question, but:

Plane strain always refers to the condition of epsz = 0 which is an infinitely thick 2-D section...(i.e. the third strain regardless of what it is called)

The more generalized problem of epsz = constant is not properly referred to as a plane strain problem....While I'm not sure I would doubt that there are many codes provide elements that allow this condition to be specified....Indeed this problem is lies somewhere between a plane stress and a plane strain solution...i.e. a 3-D problem

Ed.R.

 

[Drej]

Corus-

Generalised plane strain is a condition known as two-and-a-half-D (or 2.5D), since it allows the user to specify a finite out-of-plane thickness. In true plane strain, of course, this thickness is considered to be infinite, hence the problem is 2D planar only. With a generalised plane strain condition, the out-of-plane (Z) thickness is supposed to give more practical results where the Z in the physical system is considered too short for plane strain, and too long for plane stress. Hence the problem is now one of 2.5D.

Hope this helps

-- drej --

 

[corus]

No out of plane thickness is required for plane strain. The generalised plane strain element has 3 additional degrees of freedom, one for the out of plane displacement, and two others for the out of plane rotations. It can be imagined in 3D as the 2D section being bounded out of plane by two rigid planes. If the out of plane displacement and rotations are set to zero then this is equivalent to the plane strain element where the out of plane strain is zero. If the rotational degrees of freedom are restrained then the imaginary rigid planes remain parallel and the out of plane strain will be a constant value, but not zero. For an analysis where a thermal load was applied, the out of plane strain would not be zero but some constant value, regardless of thickness. In general then is it incorrect to use plane strain, with zero out of plane strain?

corus

 

[EdR]

corus:

Agree with everything in your last post....with the exceptions below..

Yes it is incorrect to use "plane strain" to refer to any condition where the out-of-plane strain in non-zero...i.e. the correct use of "plane strain" implies that the out-of-plane strain is zero...

Note that your thermal loading case referenced above does not necessarily have to generate a non-zero strain out of plane...The total strain could still be kept at zero ("plane strain&quot and the inplane strains/stresses adjusted accordingly....i.e. eps=eps(sigma)+eps(thermal) (Hookes Law) I really depends on the way the actual structure behaves.

Ed.R.

 

[Drej]

Within ANSYS you are able to specify a thickness when using generalised plane strain conditions. I realise that no out-of-plane thickness is required, hence why I stated that in true plane strain the thickness is considered to be infinite. As EdR says above, plane strain conditions requires that the out-of-plane strain is zero, whereas the stresses will be non-zero.

 

[brad]

Corus--
You said: "For an analysis where a thermal load was applied, the out of plane strain would not be zero but some constant value, regardless of thickness. In general then is it incorrect to use plane strain, with zero out of plane strain? "

I do not agree with this statement for all cases. If your two bounding planes are fixed, for generalized plane strain the out-of-plane strain would be zero. In plane strain, the strain is definitively zero (since by formulation there are no "bounding planes" as exist in generalized plane strain).

I'm speaking "on the fly" here, but I think I'm right: generalized plane strain with both bounding planes parallel and fixed devolves into a "pure" plane strain problem.

For such a case (using generalized plane strain), an applied thermal load will generate a zero total strain (hence e(thermal)= -e(mechanical) ). This is also true of plane strain.

Does this answer your question, or do I misunderstand your question (or am I even wrong)?
Regards,
Brad

One other thing--in a similar fashion, generalized plane can also be devolved into an axisymmetric problem by setting the bounding planes accordingly.

 

[corus]

I was wrong and Drej is quite correct in saying that a thickness is required for plane strain. It would appear that the thickness is irrelevant though except for where the mass is required, say in a dynamic analysis.

For a thermal load axisymmetric analysis where the top and bottom surfaces are parallel to the R direction, generalized plane strain can be simulated by fixing the bottom surface axially, say, and allowing the top surface to expand axially whilst remaining parallel to the R direction. In this case the strain would be constant in the axial direction and would represent an infinitely long shell. For plane (zero) strain both the top and bottom surfaces would be fixed axially, preventing expansion, and different results would obtained as the thermal stresses would be much higher.

For a 2D section, Abaqus has different elements, one plain strain, and one generalized plane strain. Do they both give the same result for thermal loads if the assumed bounding planes are only fixed rotationally and as such are restrained only to remain parallel as in the axisymmetric case?

Yours confused,

corus

 

[brad]

Corus-
Your last question--"Yes, presuming that the bounding planes are parallel." That was what I was trying to state above. Note though, that generalized plane strain does not require the bounding planes to be parallel (i.e.--the out-of-plane thickness can vary).

Brad