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.

box.fem

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.