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 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.

Model Files

The model files used in this example include:

<install_directory>/hwsolvers/demos/optistruct/examples/box.fem