OpenSees & PDelta: Difference to Drain2DX in PO with PDe

[Haraldinho]

I’ve got a question how OpenSees is handling PDelta effects. The manual only says that a (linear) geometric transformation of beam stiffness and resisting force from the basic to the global coordinate system is performed. Is that the same what Drain 2DX is doing? (As far as I know Drain 2DX is adding a geometric stiffness matrix to the tangent stiffness matrix.)

The reason why I am asking is the big difference between the push-over curves which I am obtaining for my 20-story SAC model from OpenSees and the curves from the literature. (They all use Drain 2DX.) Whereas the curves without PDelta effects are pretty similar, my strength plateau after yielding and before decreasing again is 3 times larger with OpenSees. If of interest, I am using BeamWithHinges with fiber sections for the columns and pre-defined moment-curvature relationship for the beams. PDelta is assigned as Geometric Transformation for the columns, linear for the beams. Assigning corotational for the columns does not make a real difference.

[pejman_opensees]

As far as I know there are 2 elements namely E15 and E16 in DRAIN2DX which are nonlinear beam column elements. E15 incorporates P-big delta matrix into the element stiffness matrix and E16 (Asgarian et al) adds p-small delta to the existing E15. for more information see the paper by asgarian et al 2005 inelastic postbuckling of tubular braces. Using Opensees (nonlinear beam column with corotational transformation), you handle the problem of geometric nonlinearity more precisely as stiffness matrix of basic system transforms via updatable transformation matrix in every instance and large displacement effects are accounted for accurately. in this case equilibrium equations are solved in deformed shape and P-big delta effect is handled intrinsically given the fact that P-big delta effect is a special case of equilibrium of forces in deformed configuration without consideration of some nonlinear terms.As for p-small delta effects, Filippou et al introduced CBDI method and used mixed formulation to account for the best realistic modeling of second order effects. For more info. you should really see the publication of professor Filippou and even his former student Dr. Remo de souza.
This nonlinear force beam column element is one major reason that excells opensees over other finite element programs which look at the structures globally.

[Haraldinho]

Thanks for the very informative answer. But still there is a question left:

"Using Opensees (nonlinear beam column with corotational transformation), you handle the problem of geometric nonlinearity more precisely..."

Well, is that really only true for the combination of the nonlinearBeamColumn element and the corotational transformation? I thought the PDelta transformation is doing almost the same thing (for sure a bit less precisely because the geometry is linearized, but with PDelta I don't have any problems converging during seismic analysis). And what's about the other elements (e.g. beamWithHinges - I'd like to use it for my semi-rigid column bases)? I thought the transformation method is independent of the chosen element. Btw, the push-over analysis is showing no significant differences with nonlinearBeamColumn elements and corotational transformation.

Thanks again,
-Harald

[pejman_opensees]

You are absolutely right about independence of transformation. Actually this is the main advantage of corotational formulation because it just tranlates and rotates the stiffness matrix of basic system of any element to undeformed configuration which containes more columns and rows from stiffness matrix point of view!.
If you ask me to highlight you about pdelta drawback, I suggest you to model a snap-through element and apply a static cyclic loading on one end as I did in a post ( you can find it in useful script room). then test different transformations and follow the behavior of the element. you will see for yourself the superiority of corotational transformation. As for beam with hinges which uses lumped plasticity instead of distributed plasticity, normally we should not encounter any problem as it does not matter whatever the material nonlinearity is, transformation handles the problem of geometric nonlineaity independently.