Setup of Plate elements for correct span

[tigerbob]

I'm working on a precast concrete box section and modeling it with Visual Analysis 4.0. I have limited experience with FEA, but understand the concepts of the loading, restraints, results, etc. for the limited work that I do. One question that I have is this:

If I have a box section that is 6'x6' (ID) with 6" walls, do I set my plate mesh to span 6'x6', or do I span them from the midspan of each wall. This would change my span to 6.5'x6.5'.

This issue is not as critical in this regard as it is wih product of larger spans and very heavy loads.

Any help is greatly appreciated.

 

[corus]

For plate/shell elements used to define box sections, it is common practice to use the mid plane of the sections for the element geometry as this will give you approximately the correct MOI (Ixx etc) for the section. Using the outer dimensions would give you a higher MOI and thus lower than expected stresses which could result in incorrect assessment of the structure. If you're not sure then run a test case of a box section as a cantilever, say, that can be compared with a hand calculation of exact stresses to be expected.

 

[pjhype]

When you use plate or shell elements and model to the mid-plane of the cross section, you inherently assume that the section is in a state of plane stress, where all out-of-plane strain components are equal to zero. This approach is entirely valid for the modeling of thin plates. A 6" thick section may not be in a state of plane stress. If you are interested in the stresses in the section, I would recommend that you use solid (brick) elements. If you are only interested in the "macroscopic" bending behavior of the box section, you should get acceptable results using the plates, however, you may get even more accurate results using bar elements.

pj

 

[brad]

pjhype--
Plane stress assumes that out-of-plane stress components are zero. Out-of-plane strains can be none-zero, and are due to Poisson effects.

Plane strain is the assumption which yields zero out-of-plane strain.

Shell formulation (pland stress) is commonly used to model such behavior consistent with the above problem. Shell theory can adequately describe such states of stress as tigerbob is describing (although thick shell formulation may often be necessary).

Corus's approach is appropriate and correct, IMHO.

Brad

 

[pjhype]

brad,

Please explain something for me... According to plate theory, the strain-displacement equations for a plate element (in the x-y plane) reduce to e=e0-zk0, where e is the strain, e0 is the strain at the neutral surface, z is the offset distance from the neutral surface, k0 is the curvature of the neutral surface. For a plate element, the resulting strain field is defined by only exx, eyy and exy, which are in-plane strains, all other strain components identically zero. Is plate theory wrong? How can such elements correctly model the out-of-plane stress if the strains must be a function of the neutral surface displacement field? Exactly what are the states of stress that tigerbob is describing that the shell element is valid? The states of stress that he is describing are not apparent to me when I read his post.

pj

 

[brad]

From Gere & Timoshenko (for those who need a source):

Strains for plane strain:

ex= 1/E (sigx -v*sigy)
ey= 1/E (sigy-v*sigx)
ez = -v/E (sigx + sigy)

(v = "nu"--Poissons ratio).

ez does not equal zero

Strain in z is entirely dependent on the in-plane strains, but it is not zero (in general).


Regarding the "state of stress"--there isn't enough information for me to unequivocally state that this approach is appropriate for his problem. His length-to-thickness ratio (12) is pretty good, but we don't have all the load details.

Brad

 

[pjhype]

brad,

For the time being, let us depart from the terminology and semantics (i.e. "plane stress" vs. "plane strain&quot. It is my understanding that the typical finite element plate is capable of producing a strain field that is valid for the neutral surface of the plate. Therefore, the displacement field includes only the in-plane strains (ex, ey and exy) and the curvatures (kx, ky and kxy). In order to calculate the strains that are not on the neutral surface, it is necessary to define those strains as a linear function of the z-offset from the neutral axis. Because of this, I have always assumed that the plate formulation is valid for only thin sections that are subject largely to extensional and bending loads. In your previous post, you seem to be implying that the plate element can be used to accurately predict the stress field for "thick" plates subjected to an arbitrary loading (tigerbob never defined the loading or the state of stress). While I agree there will be a very small out-of-plane strain component due to poisson's effect, I do not believe that it is safe to assume that this will be the largest out-of-plane strain component. This is especially true for thicker sections or for structures that have disimilar materials (such as re-bar for concrete structures). The safe way to proceed in such cases is to model a portion of the structure with brick elements and then determine whether it is reasonable to simplify the model by using plates.

pj

 

[brad]

pj,
I think "semantics" are important--plane stress has a physical meaning. My intent was not pick on you over semantics. I've respected your posts over the last several months, and I wanted to correct your statement such that an errant assumption is not propogated. I certainly don't mean anything negative in this.

Your basic assumptions of stresses being a function of plane strains and curvatures are correct, but this does not necessarily imply that this approach is then only valid for thin shells. There are several thick shell theories that are valid for problems such as has been described by tigerbob above. There are "thin shells" in the commercial FEA domain, along with "thick shells".

Another note--in nonlinear problems (most notably sheet metal forming problems), out-of-plane strain due to Poisson effects is VERY significant. For linear elastic FEM, this is admittedly not as critical; but it is still relevant.

Finally, there are actually theories being introduced for "solid" shells--shell theory which includes through-thickness as a primary variable which can, to some extent, couple with the classic shell formulational approach.

One last note--you are correct in that at some point the problem will still become too "thick" (or other limitations of shell theory will become significant)--in these cases often solid elements do need to be used.

Best regards,
Brad