| Matrix or Vector | Shape Functions | Integration Points |
|---|---|---|
| Stiffness and Damping Matrices | None | None |
| Stress Stiffening Matrix | None | None |
The following sections describe the different matrices used by the COMBI214 element:
If KEYOPT(2) = 0, the element lies in the (XY) plane and the stiffness, damping and stress-stiffness matrices in nodal coordinates are:
 | (13–317) |
 | (13–318) |
 | (13–319) |
where:
| K11, K12, K21, K22 = stiffness coefficients (input as K11, etc. on the R command) |
| C11, C12, C21, C22 = damping coefficients (input as C11, etc. on R command) |
|
| L1 = distance between the two nodes I and J |
| L2 = distance between the two nodes K and J |
The matrices for KEYOPT(2) equals 1 or 2 are developed analogously.
Stiffness and/or damping matrices may depend upon the rotational velocity (input through OMEGA or CMOMEGA) if real constants are defined as table parameters.
The mass matrix is:
 | (13–320) |
where:
| M11, M12, M21, M22 = mass coefficients (input as M11, etc. on the R command) |
| s1, s2 = coefficients based on the KEYOPT(6) setting: |
| KEYOPT(6) | s1 | s2 |
| 1 | 1 | 0 |
| 2 | 0.5 | 0.5 |
| 3 | 0 | 1 |
In a rotating reference frame analysis (CORIOLIS,ON,,,OFF), additional terms are included if the bearing is stationary. The equation of the element forces in the stationary reference frame is:
 | (13–321) |
where:
| {Fe} = element forces in the stationary reference frame |
| {r} = displacement vector in the stationary reference frame |
Following the discussion in Rotating Damping Matrix, the element forces in the rotating reference frame can be expressed as:
 | (13–322) |
where:
| {Fe'} = element forces in the rotating reference frame |
| {r'} = displacement vector in the rotating reference frame |
In a linear analysis, if the rotating damping effect is activated
(RotDamp = ON on the CORIOLIS command) and
C11 = C22 with C12 =
C21 = 0, the second term is included and will modify the apparent
stiffness of the element.
In the general case, the element forces are periodic at twice the rotational velocity and are only included in a transient analysis with NROPT,FULL.
For information on equations used for Reynolds equation integration, see Finite Length Formulation for 2D Elements.
The following sections describe the output quantities from the COMBI214 element:
The stretch is computed as:
 | (13–323) |
 | (13–324) |
where:
| u', v', w' = displacements in nodal Cartesian coordinates (UX, UY, UZ) |
The static forces are computed as:
 | (13–325) |
 | (13–326) |
Finally, if a nonlinear transient dynamic (ANTYPE,TRANS, with TIMINT,ON) analysis is performed, a damping force is computed:
The damping forces are computed as:
 | (13–327) |
 | (13–328) |
where:
| v1, v2 = relative velocities |
Relative velocities are computed using Equation 13–323 and Equation 13–324, where the nodal displacements u', v', and w' are replaced with the nodal Newmark velocities.
The pressure forces are calculated by integration of the pressure on the bearing surface. For more information, see Finite Length Formulation for 2D Elements.