Cylindrical to Cylindrical Formulation
This formulation is used to model contact between two cylindrical bodies. Similar to the spherical-to-spherical formulation, the gap between the source and the destination boundaries is computed. If the gap is less than zero, a penalty force is applied to prevent penetration.
There are two possible ways in which two cylinders can come into contact with each other. The first one is the parallel arrangement of the cylinders; that is the contacting cylinder axes in parallel alignment. In this case, all the points on the source boundary have the same distance to the destination boundary. This is not true for the second case, when the cylinder axes are not parallel. In this case, there will be a unique contact point on the source and destination boundaries.
The gap distance computation depends on the location of the source with respect to the destination. When the source is outside of the destination, the gap is defined as
Here, d is the shortest distance between the source and destination axes, rs and rd are the radii of the source and destination cylinders.
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Figure 3-31: Rigid body contact between two cylindrical bodies showing the gap distance.
If the source and destination are parallel and the source is inside the destination, the gap is defined as
For the parallel arrangement of source and destination axes, the shortest distance between the axes (d) is calculated as
Here, Xsrc and Xdst are the undeformed location of the source and destination centers, usrc and udst are the corresponding displacements, and es is the direction vector of the source axis.
The direction vector from the contact point on the source to the contact point on the destination (ec) is defined as
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When the source and destination axes are not parallel, the shortest distance between the axes (d) is calculated as
Here, Xsrc and Xdst are the undeformed location of the source and destination centers, usrc and udst are the corresponding displacements, and es and ed are the direction vectors of the source and destination axes.
The direction vector from the contact point on the source to the contact point on the destination (ec) is defined as
The contact force for the penalty and the penalty dynamic methods are the same as in the Spherical to Spherical Formulation.
Figure 3-32: Rigid body contact between two cylindrical bodies showing the gap distance. Here, the source is located inside destination.
The contact force for the penalty and the penalty dynamic methods are same as in the Spherical to Spherical Formulation.