OS-E: 0925 Solve an Optimization Problem Not Defined by a Finite Element Model
This example involves the optimization of a box defined entirely by equations (there is no finite element model in the solution).
Model Files
Before you begin, copy the file(s) used in this example to
your working directory.
Model Description
The optimization problem is defined as:
- Objective
- Maximize the volume of a cube AxBxC
- Constraint
- The surface of the cube should be between 2.0 and 3.0
- Design Variables
- A, B, C
The volume and surface are defined as equations using
DRESP2 and
DEQATN:
$
$ VOLUME
$
DEQATN 1 VOL(W,L,H)=W*L*H
$
$ SURFACE
$
DEQATN 2 AREA(W,L,H)=2.0*(W*H+L*H+W*L)
$
DRESP2 1 VOLUME 1
DESVAR 1 2 3
DRESP2 2 SURFACE 2
DESVAR 1 2 3
$
DESVAR 1 W 1.1 0.1 10.0
DESVAR 2 L 0.9 0.1 10.0
DESVAR 3 H 2.0 0.1 10.0
$
Then, in the optimization problem, the objective and constraint are global responses (for example, DESOBJ and DESGLB are used outside of a SUBCASE).
To trick OptiStruct into solving this problem, a dummy finite element model must be provided. Here, a single shell element with some load is used.
Results
As expected, the solution yields a cube with even sides of about 0.707, a surface of 3.0, and a volume of 3.53.