Modular-Topology Optimization of Truss Structures Composed of Wang Tiles

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F17%3A00312934" target="_blank" >RIV/68407700:21110/17:00312934 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Modular-Topology Optimization of Truss Structures Composed of Wang Tiles

Popis výsledku v původním jazyce

Despite vivid interest of researchers, fueled further by recent advances in additive manufacturing, efficient handling of structural modularity remains an unresolved topic in topology optimization. This master thesis presents a unifying bilevel optimization framework that allows for simultaneous optimization of modules topology and their distribution within a structure. The approach combines topology optimization of truss structures, which identifies the optimal distribution of a material within a predefined ground structure, and the formalism of vertex-based Wang tiles, which naturally introduces jigsaw-like compatibility of individual modules and allows for straightforward generation of a compatible assembly plan. The topology optimization, suitably modified to account for modularity constraints, determines the globally optimal design of the modules for a given assembly plan, while either simulated annealing or the genetic algorithm is used to arrive at the optimal assembly plan. The approach thus couples mathematical programming, namely Second-Order Cone Programming or Semidefinite Programming, with meta-heuristics. The developed methodology is applied to an illustrative problem of compliance minimization of a simply supported beam and the influence of module size is discussed. The optimal design of modular truss structures can be also seen, in a broader perspective, as a preliminary step to optimal design of non-periodic microstructures, approximated by truss members.

Název v anglickém jazyce

Modular-Topology Optimization of Truss Structures Composed of Wang Tiles

Popis výsledku anglicky

Despite vivid interest of researchers, fueled further by recent advances in additive manufacturing, efficient handling of structural modularity remains an unresolved topic in topology optimization. This master thesis presents a unifying bilevel optimization framework that allows for simultaneous optimization of modules topology and their distribution within a structure. The approach combines topology optimization of truss structures, which identifies the optimal distribution of a material within a predefined ground structure, and the formalism of vertex-based Wang tiles, which naturally introduces jigsaw-like compatibility of individual modules and allows for straightforward generation of a compatible assembly plan. The topology optimization, suitably modified to account for modularity constraints, determines the globally optimal design of the modules for a given assembly plan, while either simulated annealing or the genetic algorithm is used to arrive at the optimal assembly plan. The approach thus couples mathematical programming, namely Second-Order Cone Programming or Semidefinite Programming, with meta-heuristics. The developed methodology is applied to an illustrative problem of compliance minimization of a simply supported beam and the influence of module size is discussed. The optimal design of modular truss structures can be also seen, in a broader perspective, as a preliminary step to optimal design of non-periodic microstructures, approximated by truss members.

Druh

O - Ostatní výsledky

CEP obor

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OECD FORD obor

20101 - Civil engineering

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů