# 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

Refer to Access the Model Files to download the required model file(s).

The model file used in this example includes:

box.fem

## Model Description

- 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

```
$
$ 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.