The design space consists of a cantilever beam loaded at the mid-section of the free
end.
Subcase Section
The objective
function (compliance) is a subcase dependent response, therefore the response
reference is part of the subcase definition. The constraint (volume fraction) is
a global response, therefore the reference is outside the
subcase.
The responses and
constraints are defined in the Bulk Data section. Two responses are defined
here: the compliance, which is referenced by the objective function, and the
volume fraction, which is referenced by the constraint statement to put up an
upper bound of 0.25 (25% of the design space volume). The constraint statement
is then referenced as a global constraint in the subcase
section.
BEGIN BULK
$
DRESP1,1,comp,COMP
DRESP1,2,volfrac,VOLFRAC
DCONSTR,2,2,,0.2
The volume fraction constraint is set to 25%
of the total design material. In the beam.fem file, the
following PSOLID entry is used:
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
PSOLID
1
1
1
The "1" in the 9th field denotes that the component is designated
as design material. The example is run for 20 iterations.
By running the
file, beam.HM.comp.cmf, as a command file in HyperMesh, the elements are grouped into sets according
to their final material density values. The set labeled "0.0 - 0.1" contains all
of the elements in which densities range from 0% to 10%. The set labeled "0.1 -
0.2" contains all of the sets in which densities range from 10% to 20%. The
elements in the sets that have material densities less then 30% are masked so
that the solution is easier to visualize. The material densities of the
remaining elements are plotted. Figure 1. Finite Element Model of a Cantilever Beam
This example is analyzed in the one-file setup with the file,
beam.fem. The OptiStruct batch
job is submitted using the command shell script, % optistruct
beam.
Results
The optimization runs for 20 iterations. The results are requested in HyperMesh binary format and written to the file,
beam.res. The shape of the solution at the final iteration
is visualized by creating an assign plot of the density results at the 20th
iteration in the HyperMeshContour panel. By removing components labeled "0.1 - 0.2", "0.2
- 0.3", "0.3 - 0.4", and "0.4 - 0.5" from the display, a concept of the optimized
beam can be visualized. Figure 2. OptiStruct Results Thresholds at 25%
