Detecting Underconstrained Bodies

You can use the Underconstrained Bodies tool to detect any rigid (or free) body modes of bodies that are not adequately supported by fixtures, connectors, or bonded interaction conditions.

To detect underconstrained bodies, do one of the following:

  • From a static study tree, right-click Connections and click Underconstrained Bodies .
  • From the CommandManager, select Diagnostic Tools, and click Underconstrained Bodies .
  • From the System Options > General dialog box, select Automatically detect underconstrained bodies.

As a best practice, before you run the Underconstrained Bodies tool, define realistic materials, loads, and boundary conditions for your model. The study properties should reflect, as accurately as possible, the operating loads and boundary conditions of the model you are trying to analyze.

For each part of an assembly, the algorithm checks for free translations and rotations in the global X, Y, and Z direction and also in oblique directions. It is also able to detect instability issues in assemblies with chain (or hinge) mechanisms between parts. In cases where free body modes are detected, the Underconstrained Bodies tool animates them accordingly.

The detection of underconstrained bodies is based on the transformation of the stiffness matrix associated with a finite element model to a reduced-size stiffness matrix (typically with three translational and three rotational degrees of freedom per body). The underconstrained modes of the reduced system are equivalent to the original system of equations.

The transformation of the global stiffness matrix to a reduced-size stiffness matrix is completed by:
  • Introducing a single representative node (reference point) with six degrees of freedom for each body that represent the translational and rotational motion of each body
  • Transforming the element stiffness matrices by replacing the original degrees of freedom with the degrees of freedom of the representative nodes
  • Assembling the transformed element stiffness matrices to determine the reduced-size stiffness matrix

Advantages

The solution is much faster. The performance improvement is based on the adoption of the Singular Value Decomposition (SVD) technique that is performed over the reduced stiffness matrix. The reduced stiffnesses are calculated from the interface surface interaction between bodies originating from boundary conditions, bonded and contact interactions, or connectors.

The following is an example of a reduced stiffness matrix:

Each body reduces to one reference point in the stiffness matrix. The global stiffness matrix reduces from hundreds of thousands of degrees of freedom to only 18 (3 bodies x 6 degrees of freedom). The method considers stiffnesses that originate from the interactions between bodies. Bodies 1 and 2 come into contact, so the method considers the effect of their stiffnesses between their reference points. The method considers stiffnesses that originate from boundary conditions as well, for example, the stiffness between Body 1 and the ground.

The SVD technique decomposes the reduced stiffness matrix to three matrices.



The U and V vectors are orthonormal to each other and describe the shape of the displacement field. The middle matrix is a diagonal matrix. The diagonal terms represent the relative stiffnesses of the links between the bodies or between a body and the ground. If any of the diagonal terms is zero or close to zero, then this is an indication of a rigid body mode.

When detecting rigid body modes, the method considers all features you apply in a static study, including contact interactions and connectors. For example, the car suspension assembly below includes several pin connectors between parts. The advanced underconstrained bodies method considers the stiffnesses of these connectors when it calculates the reduced stiffness matrix of the assembly. The analysis detects two rigid body modes, one translational and one rotational because of the mechanism.


Arrows point to the location of pin connectors in the car suspension assembly


Translational rigid body mode in the Z direction


Rotational body mode about the Z direction because of the mechanism

You can view animations of the unconstrained displacements of the whole assembly.

You can view animated translations or rotations in oblique directions.

Stabilize any underconstrained bodies with the appropriate translational or rotational restraints, before you proceed with the analysis. See also SOLIDWORKS Simulation Help: Use Soft Spring to Stabilize Model and Preventing Rigid Body Motion.