The DRESP
DENSITY_MEASURE
is defined
in the following way:
|
where
is the relative density
in each element of the given user-defined element group and
is the number of elements in the defined element group, respectively.
Analysis-Independent Design Response
For the density measure the following table shows the allowed combinations
between the strategy and the items OBJ_FUNC
and CONSTRAINT
with C for controller and S for sensitivity-based optimization.
|
TOPO |
SHAPE |
BEAD |
SIZING |
OBJ_FUNC |
S |
|
|
|
CONSTRAINT |
S |
|
|
|
The DRESP
named DENSITY_MEASURE
can be applied for measuring the amount of intermediate densities. The
DENSITY_MEASURE
can be used in the OBJ_FUNC
or CONSTRAINT
for minimizing and surpassing the number
of elements containing intermediate densities. This design response can
be used for additional penalization of intermediate elements and thereby,
obtain more clearly defined solid/void conceptual designs.
DENSITY_MEASURE
is aimed at advanced dynamic applications
like modal eigenfrequency analysis and frequency response analysis.
intermediate density of all elements |
value of DENSITY_MEASURE |
0.5 |
1.0 |
1.0 |
0.0 |
|
|
DRESP
DENSITY_MEASURE
yields the
value 1.0 for the intermediate density 0.5 of all elements.
DRESP
DENSITY_MEASURE
yields the
value 0.0 for the intermediate density 1.0 of all elements.
DRESP
DENSITY_MEASURE
yields the
value
for the intermediate minimum density
of all elements.
The following figure shows the DRESP
DENSITY_MEASURE
depending on element density with all elements having the same intermediate
density.
Command in Parameter File
The DRESP
DENSITY_MEASURE
is defined
in the following way:
DRESP
ID_NAME = DRESP_DENSITY_MEASURE
DEF_TYPE = SYSTEM
TYPE = DENSITY_MEASURE
EL_GROUP = ………
GROUP_OPER = SUM
END_
The DRESP
DENSITY_MEASURE
can then
be applied in the objective function or in the constraint in the following
way:
OBJ_FUNC>
ID_NAME = DENSITY_MEASURE_ONJ
DRESP = ....
DRESP = DRESP_DENSITY_MEASURE, <weighting_factor>
TARGET = MIN
END_
Or
CONSTRAINT
ID_NAME = DENSITY_MEASURE_constraint
DRESP = DRESP_DENSITY_MEASURE
MAGNITUDE = ABS
LE_VALUE = 0.05
END_
The design response DENSITY_MEASURE
drives the optimization towards a local minimum and therefore needs to be used with care.