Rigid body motion
In most cases, a structure must have a set of constraints which is sufficient to suppress any rigid body motions. A stationary problems is solvable only if the structure is sufficiently constrained. There must not be any possible rigid body modes; thus no stress-free deformation states are allowed. In a dynamic analysis, rigid body motions are admissible. The inertial forces will then balance the external forces.
The number of possible rigid body modes for different geometrical dimensions is shown in the table below.
Table 2-3: Number of possible rigid body modes
Dimension
Number of rigid body modes
3D
6 (3 translations + 3 rotations)
2D axisymmetric
1 (Z-direction translation)
2D (solid, beam, truss)
3 (2 translations + 1 rotation)
2D (plate)
3 (1 translation + 2 rotations)
If the model is underconstrained, you may encounter the following problems:
•
The solver reports that the stiffness matrix is singular.
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The solver reports that the stiffness matrix is ill-conditioned. Theoretically, the matrix is singular for a structure with rigid body modes, but because of the round-off errors during the solution this is not exactly determined.
•
A nonlinear analysis fails to converge.
•
An iterative linear equation solver fails to converge.
•
You get a solution with an extremely large displacement, orders of magnitude larger than what is expected.
For a single body, it is seldom difficult to see whether it is fully constrained or not, but for a more complex assembly, including several physics interfaces, or advanced couplings and boundary conditions, it may not be trivial. If you suspect that rigid body modes is a problem in your model, you can run an eigenfrequency analysis, and check for modes with zero eigenfrequency as described in Eigenfrequency Analysis.
If there are no constraints which are dictated by the physical boundary conditions of the structure, you can use the Rigid Motion Suppression boundary condition to automatically remove the rigid body motions. When you do this, the assumption is that the external loads are in equilibrium. If not, reaction forces and stress concentrations will appear at seemingly arbitrary points where the automatic constraints were placed.
As an alternative to applying constraints, you can also add elastic supports through a Spring Foundation node to suppress rigid body motion.
Rigid Motion Suppression Boundary Condition in the Structural Mechanics Theory chapter.