13.40. COMBIN40 - Combination

Matrix or VectorShape Functions Integration Points
Stiffness, Mass, and Damping MatricesNone (nodes may be coincident)None
 

13.40.1. Characteristics of the Element

The force-deflection relationship for the combination element under initial loading is as shown below (for no damping).

Figure 13.10: Force-Deflection Relationship

Force-Deflection Relationship

where:

F1 = force in spring 1 (output as F1)
F2 = force in spring 2 (output as F2)
K1 = stiffness of spring 1 (input as K1 on R command)
K2 = stiffness of spring 2 (input as K2 on R command)
ugap = initial gap size (input as GAP on R command) (if zero, gap capability removed)
uI = displacement at node I
uJ = displacement at node J
FS = force required in spring 1 to cause sliding (input as FSLIDE on R command)

 

13.40.2. Element Matrices for Structural Applications

The element mass matrix is:

(13–72)

(13–73)

(13–74)

where:

M = element mass (input as M on R command)

If the gap is open during the previous iteration, all other matrices and load vectors are null vectors. Otherwise, the element damping matrix is:

(13–75)

where:

c = damping constant (input as C on R command)

The element stiffness matrix is:

(13–76)

where:

and the element Newton-Raphson load vector is:

(13–77)

F1 and F2 are the current forces in the element.

 

13.40.3. Determination of F1 and F2 for Structural Applications

  1. If the gap is open,

    (13–78)

    If no sliding has taken place, F1 = F2 = 0.0. However, if sliding has taken place during unidirectional motion,

    (13–79)

    and thus

    (13–80)

    where:

    us = amount of sliding (output as SLIDE)

  2. If the gap is closed and the slider is sliding,

    (13–81)

    and

    (13–82)

    where:

    u2 = uJ - uI + ugap = output as STR2

  3. If the gap is closed and the slider is not sliding, but had slid before,

    (13–83)

    where:

    u1 = u2 - us = output as STR1

    and

    (13–84)

 

13.40.4. Thermal Analysis

The above description refers to structural analysis only. When this element is used in a thermal analysis, the conductivity matrix is [Ke], the specific heat matrix is [Ce] and the Newton-Raphson load vector is , where F1 and F2 represent heat flow. The mass matrix [M] is not used. The gap size ugap is the temperature difference. Sliding, Fslide, is the element heat flow limit for conductor K1.