Spherical to Arbitrary Formulation
Using Rigid Body Contact, it is also possible to model the structural contact between a spherical source and arbitrary shaped boundaries of rigid or elastic bodies. In the case of irregular shaped boundaries, contact is detected only at the point closest to the source body. In case of multiple points of destination having the same distance from the source center, only a single point is chosen for contact.
From the source center, the closest point on the outer boundary of the destination is determined using a General Extrusion operator. The gap distance is defined as the distance between the outer boundary of the source and the closest point on the destination boundary. This method uses a penalty-based formulation, where the contact force is applied if the gap between the source and destination becomes negative. The input penalty factor determines the stiffness of the spring preventing penetration.
Figure 3-27: Rigid body contact between a spherical source and an arbitrary shaped destination, showing the gap distance.
The gap between source and destination is defined as
Here, rs is the radius of source sphere.
The distance between source center and the contact point on the destination boundaries (d) is calculated as
Here Xsrc is the undeformed location of the source center, xdst is the spatial position vector of the closest point on the destination boundaries, and usrc is the displacement of the source center.
The direction vector from the source center to the contact point on the destination (ec) is defined as
The contact force for the penalty and the penalty dynamic methods are same as in the Spherical to Spherical Formulation.