| Matrix or Vector | Shape Function | Integration Points | |
|---|---|---|---|
| Stiffness Matrix | W = C1 + C2x + C3x2 | None | |
The CONTA176 description is the same as for CONTA174 - 3-D 8-Node Surface-to-Surface Contact except that it is a 3-D line contact element.
Three different scenarios can be modeled by CONTA176:
Internal contact where one beam (or pipe) slides inside another hollow beam (or pipe) (see Figure 13.31: Beam Sliding Inside a Hollow Beam).
External contact between two beams that lie next to each other and are roughly parallel (see Figure 13.32: Parallel Beams in Contact).
External contact between two beams that cross (see Figure 13.33: Crossing Beams in Contact).
Use KEYOPT(3) = 0 for the first two scenarios (internal contact and parallel beams). In both cases, the contact condition is only checked at contact nodes.
Use KEYOPT(3) = 1 for the third scenario (beams that cross). In this case, the contact condition is checked along the entire length of the beams. The beams with circular cross-sections are assumed to come in contact in a point-wise manner.
Contact is detected when two circular beams touch or overlap each other. The non-penetration condition for beams with a circular cross-section can be defined as follows.
For internal contact:
 | (13–331) |
and for external contact:
 | (13–332) |
where:
| g = gap distance |
| rc and rt = radii of the cross-sections of the beam on the contact and target sides, respectively. |
| d = minimal distance between the two beam centerlines (also determines the contact normal direction). |
Contact occurs for negative values of g.
The contact model can be either contact force- based (KEYOPT(3) = 0 or 1) or contact traction-based (KEYOPT(3) = 2 or 3). For the contact traction-based model, the program determines the area (based on the underlying beam element length and the contact radius, R2) associated with the contact node.
In order to satisfy contact compatibility, forces are developed in a direction normal (n-direction) to the target that will tend to reduce the penetration to an acceptable numerical level. In addition to normal contact forces, friction forces are developed in directions that are tangent to the target plane.
 | (13–333) |
where:
| Fn = normal contact force |
| Kn = contact normal stiffness (input as FKN on R command) |
| un = contact gap size |
 | (13–334) |
where:
| FT = tangential contact force |
| KT = tangential contact stiffness (input as FKT on R command) |
| uT = contact slip distance |
|
For orthotropic friction, μeq is computed using the expression:
 | (13–335) |
where:
| μeq = equivalent coefficient of friction for orthotropic friction |
μ1, μ2 = coefficients of friction in first and second principal directions
(input as MU1 and MU2 using TB command with Lab = FRIC) |