OS-E: 3025 Optimization of the Modal Frequencies of a Disc using Constrained Beading
Patterns
Finding a good reinforcement pattern for a single modal frequency is difficult when
dealing with beaded plates since adding stiffness in one direction often reduces stiffness
in another direction.
The problem posed by finding a good reinforcement pattern for four modal frequencies
simultaneously is more than four times more difficult. Add to that the difficulty
constraints on the variety of reinforcement patterns, and the problem becomes a
formidable task.
Model Files
Before you begin, copy the file(s) used in this example to
your working directory.
By implementing topography optimization and pattern grouping, the task is greatly
simplified and good quality results are quickly generated. All optimization set up
is done using the Optimization panel and its subpanels in
HyperMesh.
The first four modal frequencies of a thin metal disc are to be optimized using bead
reinforcement patterns. A variety of different manufacturing methods are being
considered which place limitations on the bead reinforcement patterns allowed. The
metal disc has a hole in the center where it is constrained (Figure 1).Figure 1. Constraints on the Disc Model
The objective for the model is to increase the sum of the frequencies of the first
four normal modes of the disc. This is achieved by using the
WFREQ response type. The WFREQ response is
the sum of the inverse eigenvalues of the chosen frequencies. This is done in order
to assign higher weight to the earlier modes than the latter ones.
The first manufacturing method to be considered is turning the disc on a lathe. This
restricts the bead reinforcements to being circular. A circular pattern grouping
type is define. The DTPG card for this configuration is:
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
DTPG
1
PSHELL
1
+
5.0
60.0
YES
2.5
NORM
SPC
+
PATRN
2
0.0
0.0
0.0
0.0
0.0
1.0
The anchor node is set at the center of the disc and the first vector points in the z
direction. The nodes in the center ring are removed from the design region by
choosing Spc in the Boundary skip
option in the topography subpanel. No other additions to the finite element model
were required.
The solution for the circular reinforcement pattern method is shown in Figure 2. OptiStruct generated a single wide circular bead
running from the inner ring to about three-quarters of the way to the outer edge of
the disc. The bead is gently sloped throughout its width. This reinforcement pattern
more than doubled the frequencies of the first three modes and increased the fourth
and fifth modes by over 75%.Figure 2. Solution for the Circular Bead Pattern Method
The second manufacturing method to be considered is stamping with radial beads only.
The topography set up for this approach is almost identical to that of the one for
the circular approach with the only change being the radial pattern grouping type.
The DTPG card for this configuration is:
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
DTPG
1
PSHELL
1
+
5.0
60.0
YES
2.5
NORM
SPC
+
PATRN
4
0.0
0.0
0.0
0.0
0.0
1.0
The solution for the radial reinforcement pattern is shown in Figure 3. OptiStruct generated a series of eight evenly spaced
wide radial beads. Note that the beads are not drawn to their full height. This
demonstrates that full height beads are not necessarily optimal. This reinforcement
pattern also doubled the frequencies of the first three modes and increased the
fourth and fifth frequencies by more than 70%, but was not quite as efficient as the
circular pattern.Figure 3. Solution for the Radial Bead Pattern Method
The third manufacturing method to be considered was stamping with no constraints on
the bead shapes. No pattern grouping was defined for this approach. The
DTPG card for this set up is:
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
DTPG
1
PSHELL
1
+
5.0
60.0
YES
2.5
NORM
SPC
The solution for this setting is shown in Figure 4. OptiStruct generated a reinforcement pattern that
appears to be a combination of the circular and radial reinforcement patterns. The
inside of the disc has a series of radial beads while the outside has a roughly
circular reinforcement. This reinforcement pattern had the best increases in the
modal frequencies for all of the patterns compared.Figure 4. Solution for the Default Pattern Method
Since the default reinforcement pattern is almost symmetric, a cyclically symmetric
pattern can be used to clean up the solution. Choosing four wedges for cyclical
symmetry appears to be very close to the pattern created with the default settings.
The cyclical symmetry pattern grouping type is applied. The DTPG
card for the cyclical symmetry method is:
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
DTPG
1
PSHELL
1
+
5.0
60.0
YES
2.5
NORM
SPC
+
PATRN
41
0.0
0.0
0.0
0.0
1.0
0.0
+
PATRN2
4
1.0
0.0
0.0
For cyclical symmetry, both the first vector (fields 12, 13, and 14) and second
vector are defined in the same plane as the disc. The anchor node is located at the
center of the disc. This cyclical pattern is set up to have four symmetric wedges
with each wedge being symmetric about itself.Figure 5. Cyclical Symmetry Pattern for 4 Symmetric Wedges
The solution for the cyclical pattern grouping option is shown in Figure 6. OptiStruct generated a reinforcement pattern very
similar to the default pattern grouping pattern but with fourfold symmetry. The
modal frequencies were slightly less than those for the default pattern.Figure 6. Solution for the Cyclical Pattern Method with 4 Symmetric Wedges
Results
The frequency results (in Hz) for the first six normal modes for the baseline model
and four reinforcement patterns are:
