Spherical to Cylindrical Formulation
This formulation is used to model contact between a spherical source and a cylindrical destination. Similar to the spherical-to-spherical formulation, the gap between the source and destination boundaries is computed. If the gap is less than zero, a penalty force is applied to prevent penetration.
When a sphere comes in contact with a cylinder, it can touch either the curved surface or the planar ends of the cylinder. Depending on the size of the destination cylinder, two types of formulations are used to compute the gap. In the first case, the destination cylinder is assumed to be of infinite length, whereas in the second case, the destination cylinder is of finite length. The infinite length assumption is useful, when the length of the cylinder is very large compared to the size of the contacting sphere and the point of contact on destination is always on the curved boundaries of the cylinder. Use the finite length formulation for the gap computation, when the length of the cylinder is comparable to the radius of the contacting sphere, and if there is a chance that the sphere can go beyond the ends of the cylinder.
When the infinite length assumption is used, the destination cylinder is represented by a line representing the axis of the cylinder having finite radius. In this case, the gap distance is computed from the spatial positions of the source center, destination axis, and the radii of the source sphere and destination cylinder.
Similar to the spherical-to-spherical formulation, the gap distance computation depends on the location of the source with respect to the destination. When the source is outside the destination, the gap is defined as
Here, d is the shortest distance between source center and destination axis, rs is the radius of the source sphere, and rd is the radius of the destination cylinder.
Figure 3-27: Rigid body contact between a spherical source and a cylindrical destination. The source is located outside the destination.
If the source is inside the destination sphere, the gap is defined as
The shortest distance between the source center and destination axis (d) is calculated as
Here, Xsrc and Xdst are the undeformed locations of the source and destination centers, and usrc and udst are the corresponding displacements. ed is the direction vector of the destination axis.
A direction vector from source center to the contact point on destination cylinder (ec) is defined as
Figure 3-28: Rigid body contact between a spherical source and cylindrical destination showing the gap distance. Here, the source is located inside the destination.
In case of a finite length destination, the contact force between the source and destination is calculated only if the source is within the destination’s extents. If the source is outside the ends of destination cylinder, the gap is assumed as infinite and the contact force is taken as zero. In the other case, when the source is within the destination limits, the gap computation is similar to the infinite length destination case.
The contact force for the penalty and the penalty dynamic methods are the same as in the Spherical to Spherical Formulation.