Geometric stiffness in link element

[maksins]

Many elements in OpenSees which are based on link elements(2 Node, 12 DOF) have geometric stiffness inbuilt in them. Does anybody know the theoretical formulation of these geometric stiffness matrix? I know the formulation of simple truss(2-D) and beam elements but can't figure how to formulate geometric stiffness of link element.
Geometric stiffness from elastomeric bearing in local co-ordinates is as below:
// add geometric stiffness to local stiffness
double kGeo1 = 0.5*qb(0);
kl(5,1) -= kGeo1;
kl(5,7) += kGeo1;
kl(11,1) -= kGeo1;
kl(11,7) += kGeo1;
kl(4,2) += kGeo1;
kl(4,8) -= kGeo1;
kl(10,2) += kGeo1;
kl(10,8) -= kGeo1;
double kGeo2 = kGeo1*shearDistI*L;
kl(5,5) += kGeo2;
kl(11,5) -= kGeo2;
kl(4,4) += kGeo2;
kl(10,4) -= kGeo2;
double kGeo3 = kGeo1*(1.0 - shearDistI)*L;
kl(5,11) -= kGeo3;
kl(11,11) += kGeo3;
kl(4,10) -= kGeo3;
kl(10,10) += kGeo3;

[vesna]

All formulas are given in the source code:
http://opensees.berkeley.edu/WebSVN/lis ... ddc5e1def1

[maksins]

Thanks Vesna,
I understand the formulation for two node link element. But the above geometric stiffness matrix I presented is for Elastomeric bearing element, and it's different from usual two node link elements. If you look carefully in the source code of elastomeric bearing, the geometric stiffness terms are in rotational direction, which seem unusual to me.
If you compare the geometric stiffness in the source codes of the two-node link element for the case D3N12 (3D, 12 DOF) to the elastomeric bearing element, they are different, although I think they are supposed to be the same?
I searched a lot, but couldn't come to the same answer as in elastomeric bearing. So I was wondering if it is correct in elastomeric bearing, and if it is, is there a place or related reference where I can find the theoretical derivation of that?

[AryanRZRD]

Dear maksins
did you work with ElastomericBearing element in 2D ?
or any other Base Isolation material such as KIKUCHI ?
did you compared the results such as Hysteresis Curves of OpenSees and Other Programs such as SAP2000 ?

[aafshari]

Dear Vesna
We have two new parameters in "element elastomericBearing ... "
$alpha 2 and $mu.
(elastomericBearing $eleTag $i $j $kInit $fy $alpha1 [[[ $alpha2 ]]] [[[ $mu ]]] -P $matTag -Mz $matTag <-orient $x1 $x2 $x3 $y1 $y2 $y3> <-shearDist $sDratio> <-doRayleigh> <-mass $m>)

please explain these two parameters.
I can guess both of them. but I'm not sure .