The suitability of a simultaneous analysis and design (SAND) formulation for ground structure based sizing optimisation of geometrically non-linear structures

[摘要] ENGLISH ABSTRACT: Optimisation techniques have been applied to many practical engineering problems.The authors were particularly interested in its application to the optimisation of structures. Haftka [1985] motivated re-investigating the Simultaneous Analysis andDesign (SAND) formulation of structural optimisation because of the significant developmentin optimisers up to that point. Since then the MMA and SAOi optimisershave been developed. SAOi appeared to be ideally suited to the SAND formulation,so it was proposed that the motivation used by Haftka [1985] and Haftka and Kamat[1989] be followed. The feasibility of the SAND formulation for optimising bothlinear and non-linear structures with the SAOi optimiser was investigated.This work starts with a literature study on the topic to find the problems whichneeded special attention. Next a set of numerical experiments to find solutions tothese problems was done. In particular an effective method for scaling the problemwas proposed and appropriate approximations for use in the SAOi optimiser werechosen. The density of the matrices involved were derived, and it was found thatthey are sparse in the SAND formulation. Next the effect of using either force ordisplacement control for loading the structures was investigated and it was foundthat using the displacement control scheme was better than using the force controlscheme.Using the results of those experiments a collection of runs were done to comparethe performance of the Nested Analysis and Design (NAND) and SimultaneousAnalysis and Design (SAND) formulations. It was found that for linear structuresthe move from NAND to SAND is unfounded, while for non-linear structures therewas a strong motivation for the move. However, the move to SAND formulationwas found to be ineffective. The SAND formulation was not competitive with theNAND formulation because the problem became much more difficult in the SANDformulation. It was concluded that there were two main reasons for this. The primaryreason was that the optimum lay at a point where the equilibrium equationswere nearly singular. In the NAND formulation the solver could cope with thisbut in the SAND formulation this was inhibitory. The other reason for the SANDformulation's disappointing performance was due to the fact that an interior pointsolver was used. While this was the state of the art solver, its solution techniqueundermines one of the primary advantages of the SAND formulation. Namely thecapacity to traverse the infeasible region. Finally a number of avenues for furtherresearch in this area were proposed.

[发布机构] Stellenbosch University