The advent of rapid manufacturing has enabled the realization of countless products that have heretofore been infeasible. From customized clear braces to jet fighter ducts and one-off dental implants, rapid manufacturing allows for increased design complexity and decreased manufacturing costs. The manufacturing capabilities of this process have evolved to the point that they have surpassed current design capabilities. Meso-scale lattice structures can now be built that contain more lattice struts than it is reasonable to efficiently define. This work has attempted to create a method for designing such lattice structures that is efficient enough to allow for the design of large or complex problems. The main hindrance to the design of complex meso-scale lattice problems is essentially the need to define the strut diameters. While it is obvious that a large design would contain more struts than can be specified by hand, designs also quickly surpass the current capabilities of computational optimization routines. To overcome this problem, a design method has been developed that uses a unit-cell library correlated to finite element analysis of the bounding geometry to tailor the structure to the anticipated loading conditions. The unit-cell library is a collection of base lattice primitives, or unit-cells, that have been specialized for certain applications. In this case, primitives have been created that perform best under the types of stress analyzed by finite element analysis. The effectiveness of this process has been demonstrated through several example problems. In all cases, the unit-cell library approach was able to create structures in less time than current methods. The resulting structures had structural performance slightly lower than similar models created through optimization methods, although the extent of this degradation was slight. The method developed in this work performs extremely well, and is able to create designs for even the most complex lattice structures. There is room for future development, however, in the streamlining of the design process and consideration of higher-order affects within unit-cells.

Advances in additive manufacturing technologies have brought a new paradigm shift to both design and manufacturing. There is a much bigger design space in which designers can achieve a level of complexity and customizability, which are infeasible using traditional manufacturing processes. One application of this technology is for fabrication of meso-scale lattice structures (MSLS). These types of structures are designed to have material where it is needed for specific applications. They are suitable for any weight-critical applications, particularly in industries where both low weight and high strength are desired. MSLS can easily have hundreds to thousands of individual strut, where the diameter of each strut can be treated as a design variable. As a result, the design process poses a computational challenge. Since the computational complexity of the design problem often scales exponentially with the number of design variables, topological optimization that requires multi-variable optimization algorithm is infeasible for large-scale problems. In previous research, a new method was presented for efficiently optimizing MSLS by utilizing a heuristic that reduces the multivariable optimization problem to a problem of only two variables. The method is called the Size Matching and Scaling (SMS) method, which combines solid-body analysis and predefined unit-cell library to generate the topology of the structure. However, the method lacks a systematic methodology to generate the initial ground geometry for the design process, which limits the previous implementations of the SMS method to only simple, axis-aligned structures. In this research, an augmented SMS method is presented. The augmented method includes the integration of free-mesh approach in generating the initial ground geometry. The software that embodies that ground geometry generation process is integrated to commercial CAD system that allows designer to set lattice size parameters through graphical user interface. In this thesis, the augmented method and the unit-cell library are applied to various design examples. The augmented SMS method can be applied effectively in the design of conformal lattice structure with highly optimized stiffness and volume for complex surface. Conformal lattice structures are those conformed to the shape of a part's surface and that can used to stiffen or strengthen a complex and curved surface. This design approach removes the need for a rigorous topology optimization, which is a main bottleneck in designing MSLS.

Thesis (M.S.)--Auburn University, 2008. / Abstract. Vita. Includes bibliographical references (p. 70).

Orientador: José Antonio Matthiesen / Banca: Renato Bertolino Júnior / Banca: Carlito Calil Júnior / Resumo: No Brasil, é comum o uso de estruturas treliçadas de madeira na construção de coberturas nas edificações e, que, na maioria das vezes, são feitas de forma artesanal ou empírica. Para que haja uma otimização na produção dessas estruturas, através da industrialização, é conveniente o conhecimento e o domínio dos sistemas construtivos disponíveis. A utilização dos conectores metálicos, de chapa com dentes estampados (CDE) nas ligações dos elementos estruturais das treliças, é considerada, pela literatura, uma boa opção de sistema construtivo em escala industrial. Neste trabalho foram determinadas a resistência e a rigidez das ligações por conector CDE, em peças estruturais de madeira, para as classes de resistência: C20; C30 e C40, através dos modos básicos de ruptura das peças ligadas, que são: arrancamento dos dentes na peça de madeira; cisalhamento e tração da chapa. Também foi verificada a influência da variação na umidade das peças de madeira, ao serem prensadas pelo conector CDE, na resistência e rigidez da ligação, visando com isso, contribuir com a Revisão da Norma Brasileira (NBR-7190/97). / Abstract: The usage of wood trusses is common in the construction of roofs in Brazil, the most of the times are built in way craft or empiric. Obtaining an optimization in the production of these structures, through the industrialization, it is convenient the knowledge and the domain of the available constructive systems. The usage of the metallic connectors, as the metal connectors plates (MCP) in the connections of the structural elements of the truss is considered, for the literature, a nice option of constructive system in industrial scale. In this work, the resistance and the rigidity of the connections for connector MCP, in structural pieces of wood, for the resistance classes C20; C30 and C40, were certained through the basic manners of rupture of the linked pieces are: pull-out of the teeth in the wood piece; cut and traction of the connector. The influence of the variation in the humidity of the wood pieces as they are pressed by the connector MCP, in the resistance and the rigidity of the connections was verified as well, seeking with that, to contribute with Brazilian Code (NBR-7190/97) Revision. / Mestre

Otimização estrutural é uma área relativamente nova que vem sendo cada vez mais explorada. Existem muitos métodos clássicos, e outros mais recentes vem surgindo para disputar em eficiência, confiabilidade e rapidez na obtenção de um resultado ótimo. Os algoritmos são classificados em algoritmos determinísticos, que utilizam a informação do gradiente, ou seja, usam os valores das funções e suas derivadas, e os meta-heurísticos, algoritmos de otimização aleatórios que são métodos probabilísticos não baseados em gradiente, ou seja, usam somente a avaliação da função objetivo. São apresentados dois algoritmos meta-heurísticos relativamente recentes: o Harmony Search, baseado na improvisação musical em busca da harmonia perfeita, e o Firefly Algorithm, que é inspirado no comportamento da luz dos vagalumes. Vários exemplos clássicos de treliças 2-D e 3-D considerando otimização paramétrica e de forma, com restrições de tensão, deslocamento, flambagem e frequência natural, são apresentados para demonstrar a eficiência dos métodos. Os resultados são comparados aos de outros autores usando diferentes métodos encontrados na literatura. Os resultados indicam que os algoritmos de otimização estudados neste trabalho são melhores ou tão eficientes quanto os demais. Por fim, os métodos são aplicados à estrutura de um projeto de engenharia adaptado. / Structural optimization is a relatively new area that has been increasingly exploited. There are many classical methods, and newer are emerging to compete on efficiency, reliability and speed in obtaining an optimal result. The algorithms are classified into deterministic algorithms, which use the gradient information, i.e., use the values of the functions and their derivatives, and meta-heuristic algorithms, random optimization methods which are probabilistic methods not based on gradient, i.e., they use only objective function evaluation. Two relatively recent meta-heuristics algorithms are presented, Harmony Search, based on musical improvisation in search of the perfect harmony, and Firefly Algorithm, which is inspired by the behavior of the light of fireflies. Several benchmarks of 2-D and 3-D trusses considering size and shape optimization, with stress, displacement, buckling and natural frequency constraints, are presented to demonstrate the effectiveness of the methods. The results are compared to the others authors using different methods found in the literature. The results indicate that optimization algorithms studied in this work are better than or as efficient as others. Finally, the methods are applied to the structure of an adapted engineering design.

Este trabalho apresenta um estudo sobre o comportamento de treliças espaciais formadas por elementos tubulares de seção circular, com ênfase no desempenho das tipologias de ligação utilizadas no Brasil. Foram ensaiadas experimentalmente 9 treliças espaciais com vãos de 7,5 x 15,0m e uma de 7,5m x 7,5m com altura de 1,5m, variando-se o tipo de ligação entre barras, com o objetivo de caracterizar e comparar o comportamento dos sistemas de ligações mais comuns (nó típico – extremidade estampada, nó de aço e nó com chapa de ponteira).A análise teórica, via elementos finitos, tem como objetivo aferir a validade dos modelos numéricos normalmente utilizados e refiná-los incluindo as características do comportamento estrutural observadas em ensaio. A análise numérica segue duas abordagens: análise global da estrutura incluindo os efeitos não-lineares, excentricidade na ligação e variação de seção nas extremidades das barras; com isso o comportamento das treliças ensaiadas foi representado de forma satisfatória. A análise do comportamento do nó típico, modelado tridimensionalmente com elementos de casca, possibilitou analisar a interação entre as barras na região nodal por meio de elementos de contato. Com esta modelagem, apesar das simplificações, foi possível reproduzir o modo de colapso observado experimentalmente. / This paper presents a study of the behavior of tubular circular section space trusses with the main emphasis placed on the performance of the various truss typologies used in Brazil. Nine space trusses with plan dimensions of 7.5m x 15.0m and one with plan dimensions of 7.5mx7.5m and height of 1.5m were tested. The joint type was varied with the objective to characterize and compare the behavior of the more common types of connection systems (typical node – stamped end, steel node, and end plate node). The theoretical analysis employing finite elements was adopted mainly to ascertain the validity of various numerical models commonly employed and hence refining them by including the some basic characteristics of the observed structural behavior.The numerical analysis employed was based on two methodologies: a global structural analysis that takes into account the effects of non-linearity, eccentricities at connection, and the variation of the end bars cross section. In this manner the actual behavior of the tested trusses was well represented. The analysis of the behavior of a typical node, modeled using tri-dimensional finite shell elements made it possible to analyze the interaction between bars that converge at the nodal region by applying contact elements. Despite it simplicity, predicted results of the collapse mode obtained by using the proposed model, very well reproduce the experimental observation.

[pt] Os galpões industriais constituem um dos segmentos da construção em aço mais comuns no mercado brasileiro. As características na construção são rapidez de execução, menor volume de material e a esbeltez dos elementos. Nesta dissertação avalia-se o desempenho e a necessidade da consideração das imperfeições iniciais e dos efeitos de segunda ordem nas estruturas treliçadas usuais nos galpões. Através da modelagem de um conjunto de pórticos treliçados realiza-se um estudo paramétrico das diferentes tipologias e busca-se oferecer uma solução prática de pré-dimensionamento. Realiza-se a comparação entre as metodologias de análises de segunda ordem: o método simplificado MAES da ABNT NBR 8800:2008 e a análise avançada efetuada no programa Autodesk Robot Structural Analysis Professional. Os resultados obtidos mostraram a consistência entre as metodologias de análises de segunda ordem. A partir estudo comparativo entre a análise de primeira ordem e a análise de segunda ordem conclui-se sobre a pequena influência dos efeitos de segunda ordem neste tipo de sistemas treliçados. Comprova-se a pouca sensibilidade à incorporação das imperfeições geométricas iniciais. Obtêm-se os gráficos de consumo aproximado de aço e de deslocamentos máximos. Para as diferentes soluções estruturais observa-se a incidência das tipologias das treliças no desempenho estrutural em relação aos deslocamentos máximos. Apresenta-se um procedimento simplificado de pré-dimensionamento mediante tabelas e ábacos produzidos para as diversas treliças. / [en] The industrials buildings are one of the segments of construction in most common steel in Brazil. The features in construction are rapidity of execution, a smaller volume of material and slenderness of de elements. In this dissertation evaluates the performance and the need consideration of initial imperfections and second order effects in the usual trusses structures in the sheds. Through modeling a set of trusses frames is carried out a parametric study of various types and seeks to provide a practical solution of pre-design. It carried out a comparison between the methodologies of second-order analysis: The simplified method MAES of the ABNT NBR 8800:2008 and the advanced analysis made in Autodesk Robot Structural Analysis Professional program. The result showed consistency between the methodologies of and order analysis. From a comparative study of the analysis of 1st order and 2nd order analysis is concluded on the small influence of 2nd order effects in this type of trusses systems. Proves to little sensitivity to the incorporation of initial geometric imperfections. They obtain the graphs of estimated consumption of steel and maximum displacements. For different structural solutions observes the incidence of types of trusses in the structural performance of maximum displacement. It presents a simplified procedure for preliminary design through tables and abacuses produced for different trusses.

Otimização estrutural é uma área relativamente nova que vem sendo cada vez mais explorada. Existem muitos métodos clássicos, e outros mais recentes vem surgindo para disputar em eficiência, confiabilidade e rapidez na obtenção de um resultado ótimo. Os algoritmos são classificados em algoritmos determinísticos, que utilizam a informação do gradiente, ou seja, usam os valores das funções e suas derivadas, e os meta-heurísticos, algoritmos de otimização aleatórios que são métodos probabilísticos não baseados em gradiente, ou seja, usam somente a avaliação da função objetivo. São apresentados dois algoritmos meta-heurísticos relativamente recentes: o Harmony Search, baseado na improvisação musical em busca da harmonia perfeita, e o Firefly Algorithm, que é inspirado no comportamento da luz dos vagalumes. Vários exemplos clássicos de treliças 2-D e 3-D considerando otimização paramétrica e de forma, com restrições de tensão, deslocamento, flambagem e frequência natural, são apresentados para demonstrar a eficiência dos métodos. Os resultados são comparados aos de outros autores usando diferentes métodos encontrados na literatura. Os resultados indicam que os algoritmos de otimização estudados neste trabalho são melhores ou tão eficientes quanto os demais. Por fim, os métodos são aplicados à estrutura de um projeto de engenharia adaptado. / Structural optimization is a relatively new area that has been increasingly exploited. There are many classical methods, and newer are emerging to compete on efficiency, reliability and speed in obtaining an optimal result. The algorithms are classified into deterministic algorithms, which use the gradient information, i.e., use the values of the functions and their derivatives, and meta-heuristic algorithms, random optimization methods which are probabilistic methods not based on gradient, i.e., they use only objective function evaluation. Two relatively recent meta-heuristics algorithms are presented, Harmony Search, based on musical improvisation in search of the perfect harmony, and Firefly Algorithm, which is inspired by the behavior of the light of fireflies. Several benchmarks of 2-D and 3-D trusses considering size and shape optimization, with stress, displacement, buckling and natural frequency constraints, are presented to demonstrate the effectiveness of the methods. The results are compared to the others authors using different methods found in the literature. The results indicate that optimization algorithms studied in this work are better than or as efficient as others. Finally, the methods are applied to the structure of an adapted engineering design.

Cellular materials, often called lattice materials, are increasingly receiving attention for their ultralight structures with high specific strength, excellent impact absorption, acoustic insulation, heat dissipation media and compact heat exchangers. In alignment with emerging additive manufacturing (AM) technology, realization of the structural applications of the lattice materials appears to be becoming faster. Considering the direction dependent material properties of the products with AM, by directionally dependent printing resolution, effective moduli of lattice structures appear to be directionally dependent. In this paper, a constitutive model of a lattice structure, which is an octet-truss with a base material having an orthotropic material property considering AM is developed. In a case study, polyjet based 3D printing material having an orthotropic property with a 9% difference in the principal direction provides difference in the axial and shear moduli in the octet-truss by 2.3 and 4.6%. Experimental validation for the effective properties of a 3D printed octet-truss is done for uniaxial tension and compression test. The theoretical value based on the micro-buckling of truss member are used to estimate the failure strength. Modulus value appears a little overestimate compared with the experiment. Finite element (FE) simulations for uniaxial compression and tension of octet-truss lattice materials are conducted. New effective properties for the octet-truss lattice structure are developed considering the observed behavior of the octet-truss structure under macroscopic compression and tension trough simulations.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第22417号 / 工博第4678号 / 新制||工||1730(附属図書館) / 京都大学大学院工学研究科社会基盤工学専攻 / (主査)教授 高橋 良和, 教授 清野 純史, 教授 八木 知己 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM