Structural optimisation via genetic algorithms

Appelo, Sophia Aletta (2012-12)

Thesis (MScEng)--Stellenbosch University, 2012.


ENGLISH ABSTRACT: The design of steel structures needs to incorporate some optimisation procedure that evolves the initial design into a more economic nal design, where this nal design must still satisfy all the initial design criteria. A candidate optimisation technique suggested by this research is the genetic algorithm. The genetic algorithm (GA) is an optimisation technique that was inspired by evolutionary principles, such as the survival of the ttest (also known as natural selection). The GA operates by generating a population of individuals which 'compete' with one another in order to survive, or di erently stated, in order to make it into the next generation. Each individual presents a solution to the problem. Surviving solutions which propagate through to the next generation are typically 'better' or ' tter' than the ones that had died o , hence suggesting a process of optimisation. This process continues until a de ned convergence criteria is met (e.g. speci ed maximum number of generations is reached), where after the best individual in the population serves as the ultimate solution to the problem. This study thoroughly investigates the inner workings that drive the algorithm, after which an algorithm is presented to face the challenges of structural optimisation. This algorithm will be concerned only with sizing optimisation; geometry, topology and shape optimisation is outside the scope of this research. The objective of this optimising problem will be to minimise the weight of the structure, it is assumed that the weight is inversely propotional to the cost of the structure. The motive behind using a genetic algorithm in this study is largely due to its ability to handle discrete search spaces; classical search methods are typically limited to some form of gradient search technique for which the search space must be continuous. The algorithm is also preferred due to its ability to e ciently search through vast search spaces, which is typically the case for a structural optimisation problem. The genetic algorithm's performance will be examined through the use of bench-marking problems. Benchmarking is done for both planar and space trusses; the 10 - and 25 bar truss problems. Such problems are typically analysed with stress and displacement constraints. After the performance of the algorithm is validated, the study commences towards solving real life practical problems. The rst step towards solving such problems would be to investigate the 160 bar truss benchmarking problem. This problem will be slightly adapted by applying South African design standards to the design, SANS (2005). This approach is more realistic, when compared to simply specifying stress and displacement constraints due to the fact that an element cannot simply be assigned the same stress constraint for tension and compression; slenderness and buckling e ects need to be taken into account. For this case, the search space will no longer simply be some sample search space, but will consist of real sections taken from the Southern African Steel Construction Handbook, SAISC (2008). Finally, the research will investigate what is needed to optimise a proper real life structure, the Eskom Self-Supporting Suspension 518H Tower. It will address a wide variety of topics, such as modelling the structure as realistically as possible, to investigating key aspects that might make the problem di erent from standard benchmarking problems and what kind of steps can be taken to over-come possible issues and errors. The algorithm runs in parallel with a nite element method program, provided by Dr G.C. van Rooyen, which analyses the solutions obtained from the algorithm and ensures structural feasibility.

AFRIKAANSE OPSOMMING: Die ontwerp van staal strukture moet 'n sekere optimalisasie proses in sluit wat die aanvanklike ontwerp ontwikkel na 'n meer ekonomiese nale ontwerp, terwyl die nuwe ontwerp nog steeds aan al die aanvanklike ontwerp kriteria voldoen. 'n Kandidaat optimeringstegniek wat voorgestel word deur hierdie navorsing is die genetiese algoritme. Die genetiese algoritme (GA) is 'n optimaliserings tegniek wat ge- ïnspireer was deur evolusionêre beginsels soos die oorlewing van die sterkste (ook bekend as natuurlike seleksie). Dit werk deur die skep van 'n bevolking van individue wat 'kompeteer' met mekaar om dit te maak na die volgende generasie. Elke individu bied 'n oplossing vir die probleem. Oorlewende oplossings wat voortplant deur middel van die volgende generasie is tipies 'beter' of ' kser' as die individue wat uitgesterf het, dus word 'n proses van optimalisering word saamgestel. Hierdie proses gaan voort totdat 'n bepaalde konvergensie kriteria voldoen is (bv. 'n gespesi seerde aantal generasies), waar na die beste individu in die bevolking dien as die uiteindelike oplossing vir die probleem. Hierdie studie ondersoek die genetiese algoritme, waarna 'n algoritme aangebied word om die uitdagings van strukturele optimalisering aan te spreek. Hierdie algoritme het alleenlik te doen met snit optimalisering; meetkunde, topologie en vorm optimalisering is buite die bestek van hierdie navorsing. Die motief agter die gebruik van 'n genetiese algoritme in hierdie studie is grootliks te danke aan sy vermoë om diskrete soek ruimtes te hanteer; klassieke soek metodes word gewoonlik beperk tot 'n vorm van 'n helling tegniek waarvoor die soektog ruimte deurlopende moet wees. Die algoritme is ook gekies as gevolg van sy vermoë om doeltre end deur groot soektog ruimtes te soek, wat gewoonlik die geval vir 'n strukturele probleem met optimering is. Die genetiese algoritme se prestasie sal ondersoek word deur die gebruik van standaarde toetse. Standarde toetse word gedoen vir beide vlak en ruimte kappe, die 10 - en 25 element vakwerk. Sulke probleme word tipies met spanning en verplasing beperkings ontleed. Na a oop van die bekragtiging van die algoritme, word praktiese probleme hanteer. Die eerste stap in die rigting sou wees om die 160 element vakwerk toets probleem te ondersoek. Hierdie probleem sal e ens aangepas word deur die toepassing van die Suid-Afrikaanse ontwerp standaarde, SANS (2005) aan die ontwerp. Dit is 'n meer realistiese benadering in vergelyking met net gespesi seerde spanning en verplasing beperkings as gevolg van die feit dat 'n element nie net eenvoudig dieselfde spanning beperking vir spanning en druk toegeken kan word nie; slankheid en knik e ekte moet ook in ag geneem word. In hierdie geval sal die soek ruimte nie meer net meer eenvoudig 'n sekere teoretiese soek ruimte wees nie, maar sal bestaan uit ware snitte wat uit die Suid Afrikaanse Konstruksie Handboek kom, SAISC (2008). Ten slotte sal die navorsing ondersoek instel na 'n standaard Eskom Transmissie toring en dit sal 'n wye verskeidenheid van onderwerpe aanspreek, soos om die modellering van die struktuur so realisties as moontlik te maak, tot die ondersoek van sleutelaspekte wat die probleem verskillend van standaard toets probleme maak en ook watter soort stappe geneem kan word om moontlike probleme te oor-kom. Die algoritme werk in parallel met 'n eindige element metode program, wat deur Dr GC van Rooyen verskaf is, wat die oplossings ontleed van die algoritme en verseker dat die struktuur lewensvatbaar is.

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