Plate deflecTion FEM 1

[Atul Sharma]

I am trying modelling a simply supported plate model in with 10×10 mesh with density 25 Knm2 and E2510^6 and comparing it with results of other finite element applications and also with numerical matrix analysis by hand calculations. Both fem app and hand calculations results match but those of csi bridge and staad pro doesn't though they matched with each other.

I was sure of correct modelling and also checked for equilibrium each time, I tried models of other dimensions l b and h as well. Each time fem results and hand calculations matched perfectly.

For example I tried modeling 35×50 m plate with 2m depth. Hand and fem calculation results were 30 and 33 mm at centre resp. But csi bridge and staad pro for same parameters gives 300mm. For other models also the result are far too variable like this case only. Please I need urgent support. Any reference would be appreciated.



Also how come two csi fem applications give these absurd results for exact same parameters?

 

[JStephen]

Some discussion of assumed properties, cracked vs uncracked, etc. here:

https://www.eng-tips.com/viewthread.cfm?qid=498468

Make sure density Knm2/ Knm3/Kgm2/Kgm3 are not being confused in the different versions. Also E=25*10^6 vs 2.5*10^6.
Formulas in Roark may help for a sanity check as well.

 

[JoshPlumSE]

First off, I'll say that different programs use different element formulations and that can make a difference in the solution results. Heck, some of them are better suited towards thin plate or thick plate applications.

Another issues that can come into play is related to what results you're looking at. If you look at deflections and rotations that is the most basic result. Same thing with the nodal reactions (force and moment) at the places where there is a boundary condition / restraint. These are the results that are most likely to match up.

If you're looking at the stresses, forces and moments that are reported within the plate element results themselves that's not as easily comparable. That's somewhat dependent on the element formulation. Beyond that, if you're looking at plate element CONTOURS then this is dependent on the way in which the contouring is performed.

In RISA (for example) the plate element contours diverge from the theoretical close to supports. This is because RISA doesn't have a "correction" to the contouring algorithm related to the boundary conditions. This is just a weakness of the contouring algorithm.

Caveat:
I spent 16 years working in RISA tech support (ending in late 2017). I now work for CSI which writes the CSiBridge program you mentioned. I found out about the difference in the RISA / SAP2000 results some years ago when I still worked for RISA and a user asked me to explain the differences in contours between the two program for a simple model.

 

[stanleyshum1997]

Different finite element programs have different level of expertise. For example, Lisa-fret calculates according to mechanical equations from strength of material without the reduction factors to different materials and the safety factors to factored loads. But finite element programs like Sap2000 and Etabs work in construction codes. In hand calculation, people often neglect the allowable stress factor to different materials and the stress factor in factored loads which make a difference to the answer when the reduction factors to different material and the safety factors to factored loads are included.

Also, modeling is often a problem. The choice of a thin plate is different from a thick plate. A thin plate is a membrane or shell which folds without bending moment but a thick plate have bending moment.

 

[kostast88]

Plate deflection with density 25 kN/m3 means concrete. Did you check to account for creep? Creep has significant effect on plate deflections.

Link

If that's not the case, check your input. 30 -> 300 sounds like a units problem.

 

[centondollar]

stanleyshum1997 wrote:
"The choice of a thin plate is different from a thick plate. A thin plate is a membrane or shell which folds without bending moment but a thick plate have bending moment."
Yes, thin plates and thick plates are different, but not in the way you describe. The classical definitions are

- thin plate = Kirchoff plate (no transverse shear deformation, 2D version of Euler-Bernoulli beams)
- thick plate = Reissner-Mindlin plate (transverse shear deformation with constant shear angle, 2D version of Timoshenko beams)

Membrane elements do not bend and are thus neither "thick" nor "thin" plates, but rather "thin slab" or "plane deformation" elements which carry only axial forces.

Shell elements are a combination of membrane and thin or thick plate formulations, and if the stiffening (tension) or softening (compression) effect of axial load is taken into account by von Karmán type kinematics, the general shell problem becomes non-linear and superposition of in-plane (normal force components Nxx, Nyy and Nxy) and out-of-plane (shear, bending, twisting) effects cannot be done.

To the original poster: make sure you are using the same element (thin or thick, with or without axial-bending coupling), the correct units and the same stiffness modifiers (if the programs use such modifiers). If you use non-linear von Karmán kinematics with Kirchoff elements in one program and just Kirchoff elements (no axial-bending coupling) in the other program, you can expect the difference in results to be very large - once deflection is over half the plate thickness (roughly) and local rotations exceed 10-15 degrees, the plate will start to resist transverse loads by axial mode in addition to the bending mode. Because axial stiffness is orders of magnitude larger than bending stiffness, the result is self-evident: the "real plate" will be much stiffer than a "bending only"-plate element calculation shows.