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
Advantages
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.
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.