Cylindrical to Planar Formulation

This formulation is used to model contact between a cylindrical source and a planar surface of a rigid body. The cylindrical source is assumed to be of finite length having an axis with two end points. The planar surface is considered to be infinitely long, defined by a point on the surface and surface normal.

When the cylinder axis is parallel to the plane, all points on the cylinder are equidistant from the plane. For an inclined cylinder, either the cylinder’s top or the bottom end would be closest to the plane. The shortest distance between the cylinder (axis) and the plane is given by whichever end point is closer to the plane. If the gap is less than zero, a penalty force is applied to prevent penetration. The gap is defined as

Here, d is the shortest distance between the source end and the destination plane, rs is the radius of the source cylinder, ec is the direction vector from source end to the contact point on destination plane and es is the direction vector of the source axis.

Figure 3-33: Rigid body contact between a cylindrical source and a planar destination showing the gap distance.

The shortest distance between the source and the planar destination (d) is the projection of the distance between source end point and a point on the plane in the surface normal direction. It is calculated as

Here, Xse and Xdst are the undeformed locations of the source end and a point on the destination plane, and use and udst are the corresponding displacements. nd is the surface normal of the destination plane.

The direction vector from source end to the contact point on destination plane (ec) is defined as

The contact force for the penalty and the penalty dynamic methods are defined as for the Spherical to Spherical Formulation.