Product: ABAQUS/Standard
The purpose of this example is to verify the performance of a gap element in a simple case. Three parallel cantilever beams are initially separate but have possible contact points in five locations, as shown in Figure 1.1.1–1. A pair of pinching loads is applied, as shown. Only small displacements are considered, so each beam responds in pure bending. The problem is entirely linear, except for the switching contact conditions.
The sequence of events is readily imagined:
The top and bottom beams bend as the pinching forces are applied, and the first contact occurs when the tip of the top beam hits the tip of the middle beam (gap 3 closes). Up to this point the problem is symmetric about the middle beam, but it now loses that symmetry.
Subsequent to this initial contact, the top and middle beams bend down and the bottom beam continues to bend up until contact occurs at gap 5.
As the load continues to increase, gap 2 closes.
Next, gap 3 opens as the support provided to the top beam by gap 2 causes the outboard part of the top beam to reverse its direction of rotation. At this point (when gap 3 opens), the solution becomes symmetric about the middle beam once again.
Finally, as the pinching loads increase further, gaps 1 and 4 also close. From this point on the contact conditions do not switch, no matter how much more load is applied.
Each cantilever is modeled using five cubic beam elements of type B23. Initially all gaps are open, with an initial gap clearance of 0.01. The pinching loads are increased monotonically from 0 to 200. The beam lengths, modulus, and cross-section are shown in Figure 1.1.1–1. (The units of dimension and force are consistent but not physical.)
The loads are applied in 10 equal increments, with the increment size given directly by using the DIRECT parameter on the *STATIC option.
Table 1.1.1–1 Beam/gap example: solution summary.
| Increment | Pinching | Force in gap | ||||
|---|---|---|---|---|---|---|
| force, P | 1 | 2 | 3 | 4 | 5 | |
| 1 | 20 | Open | 6.5 | 0.732 | Open | 7.97 |
| 2 | 40 | Open | 18.3 | Open | Open | 18.3 |
| 3 | 60 | Open | 28.7 | Open | Open | 28.7 |
| 4 | 80 | Open | 39.1 | Open | Open | 39.1 |
| 5 | 100 | Open | 49.5 | Open | Open | 49.5 |
| 6 | 120 | Open | 59.8 | Open | Open | 59.8 |
| 7 | 140 | 10.7 | 68.6 | Open | 10.7 | 68.6 |
| 8 | 160 | 31.6 | 75.9 | Open | 31.6 | 75.9 |
| 9 | 180 | 52.5 | 83.2 | Open | 52.5 | 83.2 |
| 10 | 200 | 73.4 | 90.4 | Open | 73.4 | 90.4 |
