# Advanced Detection of Underconstrained Bodies

The advanced underconstrained bodies method computes and displays a model’s rigid (or free) modes because of instability during simulation.

Available in SOLIDWORKS Simulation Professional and SOLIDWORKS Simulation Premium.

The advanced detection of underconstrained bodies method transforms 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). It then evaluates the underconstrained modes of the reduced system, which 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 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

The solution is much faster. For a model that takes hours to run in SOLIDWORKS Simulation Standard, the detection of rigid body modes takes only seconds. 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 advanced 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.

SOLIDWORKS Simulation Standard bases the analysis on the Lower-Upper (LU) decomposition technique that it performs on the large original stiffness matrix. The analysis takes much more time.
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. In SOLIDWORKS Simulation Standard, you can only view free motions in the global directions.