Marmaras, Konstantinos

Denne afhandling omhandler diskret multimateriel dimensionering af laminerede kompositkonstruktioner, herunder lokale svigt kriterier og fremstillingsbegrænsninger. Vores modeller læner sig sæt op af en umiddelbar generalisering af "Discrete Material Optimization", der tillader samtidig bestemmelse af hensigtsmæssige laminat tykkelser og materialevalg i strukturen. De optimale design problemer der opstår formuleres med ikke–konveks blandet heltalsprogrammering. Vi anvender forskellige omformuleringsteknikker til at angive optimeringsproblemerne som enten lineære, eller konvekse ikke–lineære blandede heltals 0–1 programmeringsproblemer. Fremstillingsbegrænsningerne er blevet håndteret ved at udvikle eksplicitte modeller med gunstige egenskaber.I denne afhandling har vi udviklet og implementeret specialiserede metoder til global optimering, og heuristiske teknikker til at løse denne klasse af problemer. Den kontinuerte relaksering af de blandede heltalsprogrammerings problemer bliver løst med en implementering af en primal–dual indrepunkts metode til ikke–lineær programmering, der opdaterer barriere parameteret adaptivt. Metoden er valgt for sine fremragende konvergensegenskaber og metodens evne til at reagere hurtigt på store ændringer i problemet. I modsætning til den oprindelige "Discrete Material Optimization" metode, opnår vi diskrete brugbare løsninger på de anskuede blandede 0–1 konvekse problemer ved anvendelse af avancerede heuristiske teknikker. Disse heuristikker baserer sig på at løse en endelig sekvens af velformede optimeringsproblemer. Det giver os enten en diskret brugbar løsning eller beviser at løsningsrummet et tomt. Vores mål er at løse de anskuede problemer til beviselig global optimalitet. Vi foreslår en kombination af konvergerende ydre approksimeringer (Outer Approximation) og lokale forgreningsalgoritmer (Local Branching) til at udføre den globale optimering. Effektiviteten af de foreslåede modeller undersøges på et sæt velkendte diskrete multimaterielle dimensioneringsproblemer med oprindelse i litteraturen. Inddragelsen af fremstillingsbegrænsninger sammen med strukturelle overvejelser i den tidlige design fase, resulterer i konstruktioner med bedre strukturel ydeevne, og reducerer behovet for manuel efterbehandling af de fundne designs.This thesis considers discrete multi material and thickness optimization of laminated composite structures including local failure criteria and manufacturing constraints. Our models closely follow an immediate extension of the Discrete Material Optimization scheme, which allows simultaneous determination of the appropriate laminate thickness and the material choice in the structure. The optimal design problems that arise are stated as nonconvex mixed integer programming problems. We resort to different reformulation techniques to state the optimization problems as either linear or nonlinear convex mixed integer 0–1 programming problems. The manufacturing constraints have been treated by developing explicit models with favorable properties.In this thesis we have developed and implemented special purpose global optimization methods and heuristic techniques for solving this class of problems. The continuous relaxation of the mixed integer programming problems is being solved by an implementation of a primal–dual interior point method for nonlinear programming that updates the barrier parameter adaptively. The method is chosen for its excellent convergence properties and the ability of the method to react swiftly to changes of scale in the problem. As opposed to the original Discrete Material Optimization methodology, we obtain discrete feasible solutions to the stated mixed 0–1 convex problems by the application of advanced heuristic techniques. Our heuristics are based on solving a finite sequence of well–posed optimization problems. They provide us with a discrete feasible solution or correctly determine problem infeasibility. Our aim is to solve the considered problems to proven global optimality. We propose a combination of the convergent Outer Approximation and Local Branching algorithms to perform the global optimization. The efficiency of the proposed models is examined on a set of well–defined discrete multi material and thickness optimization problems originating from the literature. The inclusion of manufacturing limitations along with structural considerations in the early design phase results in structures with better structural performance reducing the need of manually post–processing the found designs

Online Research Database In Technology

Optimal Design of Composite Structures Under Manufacturing Constraints

http://orbit.dtu.dk/ws/files/103645086/Thesis_KM_2014_282_29..PDF

Optimal Design of Composite Structures Under Manufacturing Constraints

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Online Research Database In Technology