# OS-E: 0915 Cantilever Beam using Equations

Demonstrates how to use the equation utility to define cross-sectional properties in a size (parameter) optimization.

## Model Files

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

The model file used in this example includes:

bar.fem

## Model Description

```
$AREA
DEQATN,111,A(D)=PI(1)*D**2/4
$MOMENT OF INERTIA
DEQATN,122,I(D)=PI(1)*D**4/64
$TORSIONAL CONSTANT
DEQATN,133,J(D)=PI(1)*D**4/32
```

```
DESVAR,1,Diam1,10,1,20,0.5
DVPREL2,11,PBAR,1,4,,,111
+,DESVAR,1
```

The optimization problem to be solved is the minimization of the tip displacement with a volume constraint of 4000. Convergence was achieved after four iterations.

## Results

Diameter 1 | Diameter 2 | Diameter 3 | Diameter 4 | Diameter 5 | Tip-Displ | |
---|---|---|---|---|---|---|

Initial | 10.00 | 10.00 | 10.00 | 10.00 | 10.00 | 40.42 |

Final | 12.48 | 11.49 | 10.28 | 8.70 | 6.29 | 26.51 |