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

McDougall, Duncan John (2015-12)

Thesis (MEng)--Stellenbosch University, 2015.

Thesis

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 and Design (SAND) formulation of structural optimisation because of the significant development in optimisers up to that point. Since then the MMA and SAOi optimisers have 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 both linear and non-linear structures with the SAOi optimiser was investigated. This work starts with a literature study on the topic to find the problems which needed special attention. Next a set of numerical experiments to find solutions to these problems was done. In particular an effective method for scaling the problem was proposed and appropriate approximations for use in the SAOi optimiser were chosen. The density of the matrices involved were derived, and it was found that they are sparse in the SAND formulation. Next the effect of using either force or displacement control for loading the structures was investigated and it was found that using the displacement control scheme was better than using the force control scheme. Using the results of those experiments a collection of runs were done to compare the performance of the Nested Analysis and Design (NAND) and Simultaneous Analysis and Design (SAND) formulations. It was found that for linear structures the move from NAND to SAND is unfounded, while for non-linear structures there was a strong motivation for the move. However, the move to SAND formulation was found to be ineffective. The SAND formulation was not competitive with the NAND formulation because the problem became much more difficult in the SAND formulation. It was concluded that there were two main reasons for this. The primary reason was that the optimum lay at a point where the equilibrium equations were nearly singular. In the NAND formulation the solver could cope with this but in the SAND formulation this was inhibitory. The other reason for the SAND formulation’s disappointing performance was due to the fact that an interior point solver was used. While this was the state of the art solver, its solution technique undermines one of the primary advantages of the SAND formulation. Namely the capacity to traverse the infeasible region. Finally a number of avenues for further research in this area were proposed.

AFRIKAANSE OPSOMMING: Optimeringstegnieke is in die verlede toegepas op verskeie ingenieurs-probleme. Baie outeurs het spesifiek belang gestel in die toepassing van optimering op strukture. Haftka [1985] het verdere ondersoek na die gelyktydige analise en ontwerp (GAO) formulering vir strukturele optimering voorgestel as gevolg van noemenswaardige ontwikkelings in optimerings algoritmes op daardie stadium. Sedertdien is die MMA en SAOi algoritmes ontwikkel. Nadere ondersoek het aangedui dat SAOi geskik is vir GAO, en daar was dus besluit om die motiverings van Haftka [1985] and Haftka and Kamat [1989] opgevolg sal word. Die toepaslikheid van die SAOi algoritme om beide lineêre en nie-lineêre strukture op te los is dus ondersoek. Hierdie studie begin met ’n literatuurstudie om probleme te identifiseer wat spesiale aandag benodig. Daarna is numeriese eksperimente uitgevoer in ’n poging om oplossings vir hierdie probleme te vind. In die besonder is ’n effektiewe manier vir skalering van die toepaslike benaderings in die SAOi algoritme voorgestel. Die digtheid van die matrikse in die GAO formulering is ondersoek, en dit is bevind dat die matrikse yl is. Verder is die effek van krag-en verplasings-beheer ondersoek, en dit is bevind dat verplasings-beheer beter as krag-beheer is. Met behulp van hierdie eksperimente is n reeks lopies gedoen om die effektiwiteit van geneste analise en ontwerp (NAO) en GAO te bepaal. Dit is bevind dat die skuif vir lineêre strukture van NAO na GAO nie die moeite werd is nie, terwyl daar n sterk motivering is vir die skuif vir nie-lineêre strukture. Die GAO metode is egter oneffektief. Die GAO formulering was nie kompeterend met die NAO metode nie, omdat die probleem baie moeiliker in GAO is. Die gevolgtrekking is gemaak dat daar twee hoof redes hiervoor is. Die primêre rede is dat die oplossing by n punt lê waar die ewewigsvergelykings byna singulier is. In die NAO formulering was die oplosser in staat om hierdie komplikasie te oorkom, maar in die GAO formulering was dit nie moontlik nie. ’n Verdere rede waarom GAO teleurstellend presteer het, was dat ’n ingeslote punt oplosser gebruik is. Alhoewel dit die voorpunt van die tegnologie verteenwoordig, ondermyn die algoritme een van die primêre voordele van GAO, naamlik die moontlikheid om buite die toelaatbare gebied te beweeg. Laastens is ’n aantal onderwerpe vir verdere ondersoek uitgelig.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/97927
This item appears in the following collections: