Rayleigh Damping Implementation

[Brent]

My question is in regards to how Rayleigh damping is implemented, particularly with regard to the stiffness coefficient, betaK (all types). When the PDelta geometric transformation is used, is betaK multiplied with the element stiffness only or with the element + geometric stiffness? Also, we have had problems with significant numerical damping when the corotational geometric transformation is used and betaKinit is specified. It appears to be that while the corotational geometric transformation updates the current element orientation and stiffness, the initial element stiffnesses that are used with betaKinit to calculate the damping matrix are not updated in the current orientation. Are there any plans to address this issue?
Thanks for your help in answering these questions.

[esi_opensees]

If Kinit then it is clear that the stiffness will not be updated If Ktangent then the stiffness will be updated (there is a choice which stiffness to use).

[vesna]

betaKcomm is the one that corresponds to Ktangent.

[Brent]

I am a bit confused now. My understanding is that betaKinit uses the stiffness from the beginning of the analysis to formulate the damping matrix and that the damping matrix will not change throughout the analysis, betaK uses the current tangent stiffness to formulate the damping matrix at each iteration, and betaKcomm uses the tangent stiffness from the previous iteration to reformulate the damping matrix. Is this correct? The point that I was getting at in my first post is that if I want to use betaKinit so that my damping matrix does not change during the analysis but I am also using the corotational geometric transformation then I can get significant numerical damping. This occurs because elements, such as a lean-on column, rotate during an analysis and introduce velocities (i.e. vertical velocities) that would not be there if the PDelta transformation was used. The numerical damping happens because the damping matrix is not rotated to account for the current orientation of the element. Using betaK will somewhat address this problem because it uses the tangent stiffness to reformulate the damping matrix. However, betaK not what I am looking for because material nonlinearities will change the tangent stiffness and thus the stiffness portion of the damping matrix. My preference is to have the initial stiffness (from the beginning of the analysis) rotated at each iteration to account for element rotation then multiplied by betaKinit to form the stiffness portion of the damping matrix at each iteration.

[vesna]

betaKinit, betaK, and betaKcomm, are based on structure stiffness that includes both, nonlinear geometry and nonlinear material. As of now there is no OpenSees command for what you want to do.

[IsmBaha]

Even though long time ago that was posted, I came across this N wanted to fix Brent's one sentence:
"betaKcomm uses the tangent stiffness from the previous STEP to reformulate the damping matrix."
not ITERATION.