10-bar Truss Sizing
The 10-bar truss model was developed for:
Venkayya, V. B. (1971). "Design of Optimum Structures," Computers & Structures, 1(1), 265-309.
The design problems for this page are described in:
Haftka, Raphael T. Elements of Structural Optimization. Springer, 1992. Pages 238, 244.
Cofe example files are located here:
NASTRAN_CoFE/examples/1001_ten_bar_truss_optimization/
Details
- Young's modulus: 10^7 psi
- Specific mass: 0.1 lbm/in^3
- Minimum area: 0.1 in^2
- Allowable stress: +/- 25000 psi
- The ten design variables are the areas of the ten members.
Design Problem 1
Design for minimum weight with stress constraints.
| Design Variable | Design from CoFE + SQP | Design in Haftka |
|---|---|---|
| $x_1$ | 7.94 | 7.94 |
| $x_2$ | 0.1 | 0.1 |
| $x_3$ | 8.06 | 8.06 |
| $x_4$ | 3.94 | 3.94 |
| $x_5$ | 0.1 | 0.1 |
| $x_6$ | 0.1 | 0.1 |
| $x_7$ | 5.74 | 5.74 |
| $x_8$ | 5.57 | 5.57 |
| $x_9$ | 5.57 | 5.57 |
| $x_{10}$ | 0.1 | 0.1 |
| Objective Function | Design from CoFE + SQP | Design in Haftka |
|---|---|---|
| Weight | 1593.2 lb | 1593.2 lb |
Design Problem 2
Design for minimum weight with previous stress constraints and additional displacement constraints:
| Nodes | Direction | Upper Limit | Lower Limit |
|---|---|---|---|
| 1-4 | Vertical | 2 | -2 |
| Design Variable | Design from CoFE + SQP | Design in Haftka |
|---|---|---|
| $x_1$ | 30.52 | 30.52 |
| $x_2$ | 0.1 | 0.1 |
| $x_3$ | 23.20 | 23.20 |
| $x_4$ | 15.22 | 15.22 |
| $x_5$ | 0.1 | 0.1 |
| $x_6$ | 0.55 | 0.55 |
| $x_7$ | 7.46 | 7.46 |
| $x_8$ | 21.04 | 21.04 |
| $x_9$ | 21.53 | 21.53 |
| $x_{10}$ | 0.1 | 0.1 |
| Objective Function | Design from CoFE + SQP | Design in Haftka |
|---|---|---|
| Weight | 5060.85 lb | 5060.85 lb |