Rigid Motion Suppression
The Rigid Motion Suppression feature is a convenient way to automatically create a set of constraints which are sufficient to inhibit rigid body modes. The constraints are selected so that no reaction forces are introduced as long as the external loads are in equilibrium.
Consider that the undeformed and deformed positions of a body are measured in the same coordinate system, see Lagrangian Formulation for details. These are related by the displacement vector as
where x is the spatial coordinate, X is the material coordinate, and u is the displacement.
An average displacement of the body can be obtained by a volume average, which requires a domain integration. However, a computationally leaner operation is to only consider the domain boundaries or geometrical points when averaging the displacement. When defining the rigid motion constraints, it is sufficient to only consider the geometric points of the body.
Constraining the average displacement to zero is equivalent to having the same average position (barycenter or centroid) in the undeformed and deformed body. Since the average displacement can be written as
The constraint
is imposed, so the average centroid is the same for the deformed and undeformed body. This is enforced by adding three displacement constraints in 3D or two constraints in 2D.
The averaging is done by considering all the geometrical points in the domain, but it is also possible to consider a subset of points.
Three additional constraints in 3D, or one additional constraint in 2D are required to constrain the rotation with respect to the average centroid position