Detail Removal
Introduction
In finite element analysis, the geoemtry of CAD models is often too complex
to analyse in a reasonable timescale, meaning an idealised model must be
constructed, often from scratch. The research presented here invistiages
the use of the medial axis to automatically suppress details on 2D models,
and using topological operations to manually merge, collapse, and kill
to suppress details on 3D models. Eventually the medial surface may be
to automate these topological operations on 3D models.
Loop and Edge Aspect Ratios on 2D objects
Holes and inner loops of material in a 2D region can be identified from
their aspect ratio using the medial axis. In these figures the outline
of a 2D region is shown in blue while the medial axis is shown in red.
The loop aspect ratios shown here are the length of the medial axis around
the loop divided by the average radius of the inscribed disks centred on
the medial axis. The smallest aspect ratios indicate those holes which
could be removed with least effect on the stress distribution.
The figure below shows the edge aspect ratio of all the edges in the
model. Here aspect ratio is defined as the length of the object edge divided
by the average radius of the inscribed disks touching it. Note how the
small fillet radii are identified.
These edge ratios can be used to select holes and edges to suppress.
As shown below, the fillet radius has been removed, the hole reduced to
a node, and the slot dimensionally reduced to a crack.
Moreover, as shown in the figure below, other simple features such as
notches and protrusions could be identified, and then classified using
measures similar to those outlined above. A notch aspect ratio would be
the length of the medial axis touching the notch boundary, divided by the
average radius of the inscribed disc centred on that portion of medial
axis. Protrusions could be classified by the amount of taper in the associated
medial axis. Eventually these details could be suppressed as illustrated
in the diagram below.
After meshing using TR6 elements, although the simplified model required
significantly fewer elements, the deflection results are within 7% of the
fully detailed analysis, as shown below:
Topological Merging and Collapsing Operations
To suppress details in 3D solid models, several euler operators have been
implemented using the ACIS solid modeller. These permit a user to interactively
perform operations such as merge_faces, merge_edges, kill_void, kill_hole,
collapse_face_to_edge, collapse_face_to_vertex. The resulting model can
then be cut into convex primitives and hex meshed using mid-point sub-division.
The pictures below illustrate how a support bracket, and a housing were
simplified and meshed, using an interactive version of the chopper.
These models took approximately twenty minutes to simplify and mesh, and
required considerably less elements than the original fully detailed models.
Error Estimation
After details have been removed, it is important to know the accuracy of
the results from the FE analysis. One method being investigated for this
is using submodelling. In submodelling deflection results from a coarse
global model are applied to the boundary of a submodel of the detail. If
the stiffness of the detail is similar to the stiffness of the equilivant
region in the simple coarse, then stress values around the boundary of
the submodel should be similar to those in corresponding positions of the
simple coarse model. Summing up these stress jumps between coarse model
and submodel around the boundary of the submodel, should provide an estimate
of the accuracy of the simplification. If these errors are hiigh the detail
should be reinstated and a futher analysis performed. Below is shown a
plate with a small semi-circular notch. The coarse model ignores the notch
completely and uses only six elements. Four submodels of radii 0.5, 1.0,
2.0 and 3.0 were then analysised as submodels of this coarse model. The
stress jump energy for the 0.5 notch is small relative to the total strain
energy in the global model, whilst the 3.0 notch is over a tenth of the
total strain energy.
Further work
Research is currently being focused on using the medial surface to automatically
select faces and edges to suppress, and on performing estimates of the
errors resulting from these simplifications
