1. V. Optimization Procedure
2. The GHC approximations i n Cases B, C and 0 are more conservative than that i n Case A. Effects of constraint conservatism are revealed by the optimization results displayed i n Figure 7. It can be seen that the structural weight trajectory during early stages of the optimization process i s more stable for cases i n which the GHC approximation i s more conservative. While the designs i n Cases B and C were driven into the infeasible region at the third analysis, the more conservative GHC i n Case D kept the design i n the feasible region after two normal modes analyses were conducted. The final structural weight obtained i n these three cases i s approximately 111 Ibs requiring 7-9 normal modes analyses.
3. The third example problem i s the design of a payload frame structure which can be used i n the Space Shuttle Orbiter t o carry payloads. The f i n i t e element model i s shown i n Figure 8. Element connectivities are listed i n Table 4. The dash lines i n Figure 8 represent circular tubes with hinged ends, and dimensions are given i n inches. Elements 1-4 and 9-22 have cross section shapes of rectangular boxes, and members 5-8 and 23-29 represent symmetric I beams. The frame i s supported i n the X and Z directions at nodes 1 and 5, i n the Z direction at nodes 12 and 16, i n the Y direction at the node 9. Material properties are identical t o those used i n the second example problem. The frame supports a total payload of 25,000 Ibs which are represented by the concetrated masses i n the f i n i t e element model. The concentrated masses with a constant value of 2000 Ibs are located at nodes 2, 4, 6, 8, 13, 15, 17 and 19, and those with a value of 1500 Ibs are located at nodes 3, 7, 10, 11, 14 and 18. Lower limits are placed on the f i r s t three natural frequencies, i.e., w1 >6Hz, 2 6 .5 Hz.andw 3?9Hz. No other constraints are imposed except for small minimum gagerestrictionst LO.OO1 i n and and A L0.01 i n .