72-bar Truss Optimization
The 72-bar truss model was developed for:
Fox, Richard L., and Lucien A. Schmit, JR. "Advances in the Integrated Approach to Structural Synthesis." Journal of Spacecraft and Rockets 3.6 (1966): 858-866.
The design problem for this page are described in:
Haftka, Raphael T. Elements of Structural Optimization. Vol. 11. Springer, 1992. Pages 238, 244.
There are typos in Haftka's problem description that are detrimental to the benchmark results. The problem is described without typos in:
Sedaghati, R. "Benchmark Case Studies in Structural Design Optimization Using the Force Method." International Journal of Solids and Structures 42.21 (2005): 5848-5871.
Cofe example files are located here:
NASTRAN_CoFE/examples/1004_72_bar_truss_optimization/
Design Problem
Design for minimum weight subject to stress and displacement constraints.
72-two bar truss image from Sedaghati.
- Young's modulus: 10^7 psi
- Specific mass: 0.1 lbm/in^3
- Minimum area: 0.1 in^2
- Allowable stress: +/- 25000 ps
- Allowable displacement nodes 1-4: ±0.25 in in X and Y
| LOAD CASE | NODE | Force X | Force Y | Force Z |
|---|---|---|---|---|
| 1 | 1 | 5000 | 5000 | -5000 |
| 2 | 1 | 0 | 0 | -5000 |
| 2 | 2 | 0 | 0 | -5000 |
| 2 | 3 | 0 | 0 | -5000 |
| 2 | 4 | 0 | 0 | -5000 |
Design Variables
| DESIGN VARIABLES | AREA OF MEMBERS |
|---|---|
| 1 | 1-4 |
| 2 | 5-12 |
| 3 | 13-16 |
| 4 | 17-18 |
| 5 | 19-22 |
| 6 | 23-30 |
| 7 | 31-34 |
| 8 | 35-36 |
| 9 | 37-40 |
| 10 | 41-48 |
| 11 | 49-52 |
| 12 | 53-54 |
| 13 | 55-58 |
| 14 | 59-66 |
| 15 | 67-70 |
| 16 | 71-72 |
Result
| DESIGN VARIABLE # | Design from CoFE + SQP | Design from Sedaghati |
|---|---|---|
| 1 | 0.1565 | 0.1565 |
| 2 | 0.5456 | 0.5456 |
| 3 | 0.4104 | 0.4104 |
| 4 | 0.5697 | 0.5697 |
| 5 | 0.5237 | 0.5237 |
| 6 | 0.5171 | 0.5171 |
| 7 | 0.1 | 0.1 |
| 8 | 0.1 | 0.1 |
| 9 | 1.268 | 1.268 |
| 10 | 0.5117 | 0.5117 |
| 11 | 0.1 | 0.1 |
| 12 | 0.1 | 0.1 |
| 13 | 1.886 | 1.886 |
| 14 | 0.5123 | 0.5123 |
| 15 | 0.1 | 0.1 |
| 16 | 0.1 | 0.1 |