The recent improvement of additive manufacturing has allowed designers to achieve a level of complexity and customizability that is difficult or impossible to accomplish using traditional manufacturing processes. As a result, much research has been conducted on developing new methods to utilize the larger design space brought by additive manufacturing. One such research area is in the design of mesoscale lattice structures. Mesoscale lattice structures are a type of cellular structure with support element sizes on the order of magnitude of centimeters. These types of structures are engineered for high performance and have applications in industries where both low weight and high strength are desired. However, due to the small size of their struts, these structures can easily have hundreds to thousands of individual struts. As a result, design poses a unique challenge. Current methods approach design of mesoscale lattice structures as a topological optimization problem, treating each strut diameter in the structure as a design variable. For structures with a fewer number struts, these optimization methods can converge, but will generally be very time-consuming. For structures with a large number of struts, the optimization problem becomes too large for current algorithms to solve. In previous research, a new, highly efficient design method for mesoscale lattice structures was presented that eliminates the need for global size or topological optimization. This method, termed the Size, Matching and Scaling method, used a unique combination of a solid-body finite element analysis and a library of pre-defined lattice configurations, termed the "unit-cell library," to generate lattice topologies. The results from this method were highly promising: design time was significantly reduced when compared to optimization methods. Furthermore, lattices designed using the SMS method had performance results that were either comparable or better than their optimized counterparts. However, the method developed was highly conceptual, lacking a true systematic methodology for generating topologies and suffering from some gaps in implementation. In this research, we present a modified Size Matching and Scaling (SMS) design method. Firstly, we introduce and outline the modified methodology. This methodology particularly includes an optimization step for determining strut diameters that replaces the manual search used in the original method. Secondly, we expand and explore the unit-cell library in an attempt to improve the performance of lattices generated using the SMS method. In particular, we optimize several unit-cell configurations and compare their performance in the context of the SMS method. Finally, we test the updated SMS methodology and unit-cell library using various design examples. Results from the various example problems indicate that optimization is not only a viable systematic method for determining diameter values, but is actually preferred to the manual, iterative process used in the original method. Furthermore, various optimization algorithms and approaches yield different results. Between the two optimization algorithms utilized in this method: constrained optimization and least-squares minimization, constrained minimization converges faster, but least-squares minimization yields slightly improved performance results. In addition to these algorithms, a one-variable approach using an untested, simplifying assumption, dubbed the "28% approach," was tested. Results indicate that this assumption was incorrect and cannot be utilized. Finally, results from the expanded unit-cell library indicate that the best unit-cell configuration is still the same original unit-cell configuration utilized in the first SMS method. The addition of more unit-cell does not improve the performance of structures generated using the SMS method. In fact, both performance and design time worsen when additional configurations are utilized.

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).

Thesis (M.S.)--Brigham Young University. Dept. of Civil and Environmental Engineering, 2005. / Includes bibliographical references (p. 101-102).

Thesis (M.S.)--Brigham Young University. Dept. of Civil and Environmental Engineering, 2006. / Includes bibliographical references (p. 121-122).

[pt] O presente trabalho apresenta uma generalização do teorema de Castigliano para a análise quase-estática de treliças inelásticas com dano (elasto-plásticas e elasto-viscoplásticas). É desenvolvida uma formulação abstrata geral para o problema considerando-se qualquer tipo de teoria constitutiva com variáveis internas. Uma técnica de aproximação numérica é apresentada, com base na decomposição aditiva do operador, e um algoritmo de solução é proposto. Finalmente a teoria proposta é testada simulando-se a ruptura de treliças metálicas submetidas a carregamentos monótonos e cíclicos (fadiga). / [en] The present work is concerned with an extension of the Castigliano s theorem to the case of inelastic damageable trusses (elasto-plastic and elasto-viscoplastic behavior). A general formulation that takes into account any kind of constitutive theory with internal variables is presented. A numerical technique, based on the operator splitting method, for approximating the resulting equations is proposed. Finally, the proposed theory is checked through examples concerning cyclic and monotone loadings in metallic trusses.

A presente dissertação apresenta o estudo de estruturas reticuladas planas, também chamadas de treliças. A grande demanda da construção civil, e projetos cada vez mais arrojados motivaram esta pesquisa. Foram realizados três modelos de treliças, com o intuito de comparar o problema estático em relação ao problema dinâmico e verificar qual a influência dos esforços nas juntas tipo K das treliças. As juntas das treliças foram utilizadas para analisar a região plastificada e a tensão (von-Mises). As rotinas de cálculo para obtenção dos resultados, foram implementadas no software Matlab®, para o problema estático e os resultados foram comparados entre o software FEM-Reticulado2D do Matlab e software comercial onde as diferenças ficaram em menos de um por cento. No problema dinâmico foi adicionado amortecimento, estando mais próximo de uma estrutura real. Para este caso foi utilizado o amortecimento de Rayleigh, que é encontrado por meio da frequência natural e o método utilizado para integração no tempo foi o método de Newmark. A frequência natural também foi obtida por meio de formulações implementadas no Matlab. A região de plasticidade e a tensão (von-Mises) nos nós foram obtidas com auxílio do software Ansys. Tendo em vista os resultados, pode-se concluir que o problema dinâmico por levar em consideração a influência das forças de inércia, resultou em esforços maiores em relação ao problema estático. Verificou-se que quanto mais esbelta for a estrutura, menor será a frequência natural da mesma, por isso, deve-se tomar cuidado para que estruturas esbeltas não venham a absorver energia de ações externas como o vento e entrarem no efeito de ressonância. A plasticidade e a tensão (von-Mises) dependem da intensidade das forças e das propriedades geométricas e físicas do perfil utilizado. / Submitted by Ana Guimarães Pereira (agpereir@ucs.br) on 2015-10-26T17:52:35Z No. of bitstreams: 1 Dissertacao Maicon Manuel Rancan.pdf: 2645025 bytes, checksum: cfbeb2a6f92934b51c95bbd2a648af6d (MD5) / Made available in DSpace on 2015-10-26T17:52:35Z (GMT). No. of bitstreams: 1 Dissertacao Maicon Manuel Rancan.pdf: 2645025 bytes, checksum: cfbeb2a6f92934b51c95bbd2a648af6d (MD5) / This thesis presents the study of plane frame structures, also called trusses. The great demand of construction, and projects increasingly bold motivated this research. Three models lattices were performed in order to compare the static problems concerning dynamic problem and check the influence of the joints efforts K type of truss. The joints of the truss were used to analyze the plasticized region and the stress (Von-Mises). The calculation routine for obtaining the results were implemented in Matlab software for the static problem and the results were compared with the FEM-Reticulado2D Matlab software and commercial software where the differences were less than one percent. In the dynamic damper problem was added, being closest to an actual structure. For this case we used the Rayleigh damping, which is found by means of the natural frequency and the method used for time integration method is the Newmark. The natural frequency was also obtained by formulations implemented in Matlab. The plasticity of the region and the tension (von Mises-) nodes were obtained with the help of Ansys software. Considering the results, it can be concluded that the dynamic problem by taking into account the influence of forces of inertia resulting in increased efforts in relation to the static problem. It was found that the more slender for the structure, the lower the natural frequency of the same, so one must be careful that slender structures will not absorb energy from external actions like wind and entering the resonance effect. The plasticity and the stress (Von-Mises) depend on the intensity of the forces and the geometrical and physical properties of the used profile.

No Brasil é comum a utilização de barras tubulares com extremidades estampadas na confecção das treliças metálicas espaciais, uma vez que representam uma significativa redução de custos, quando comparado a sistemas mais elaborados, devido a sua simplicidade de fabricação e montagem, entretanto trata-se aparentemente de um sistema precário do ponto de vista estrutural, merecendo estudos que estabeleçam critérios para uma utilização segura. Neste trabalho são apresentadas análises teóricas e experimentais destas estruturas, onde foi analisada a situação construtiva usual de treliça com nós típicos (extremidade das barras estampadas, sobrepostas e unidas por um único parafuso), e com nós de aço (sistema de conexão formado por uma peça com aletas de aço soldadas). Os resultados experimentais foram obtidos em ensaios de quatro protótipos que simulam um trecho de treliça espacial, constituídos por uma malha quadrada sobre quadrada, composta de nove módulos piramidais de 2,5 x 2,5 x 1,5 (m), totalizando uma estrutura com dimensões iguais a 7,5 x 7,5 x 1,5 (m), apoiada por colunas nos vértices, permitindo comparar a rigidez, o modo de falha e a resistência entre estes protótipos. A análise teórica dos protótipos foi feita admitindo-se os casos de linearidade e também de não linearidade física e geométrica, levando-se em consideração a variação de inércia das barras junto aos nós. / In Brazil the use of tubular bars with stamping extremities is common in space steel structures, as it means a significant reduction of cost, when caompared with more elaborete system, due to its simplicity of manufacture and assembly. However it is apparently an uncertain system from a structural point of view, which requires studies establishing safe utilization criteria. This paper presents theorical and experimental analysis of this structures. The usual constructive situation of space structure with \'nós típicos\' (bars with flattened ends, superposed and connected by a unique bolt), and \'nós de aço\' (connection system formed by a piece with steel fin welded) was studied. The experimental results were obtained in tests of four prototypes which simulated a section of space structure composed of a mesh squareon- square, with nine 2.5 x 2.5 x 1.5 (m) pyramidal modules, totaliing a structure with 7.5 x 7.5 x 1.5 (m) dimensions, supported by columns in their vertices, permiting to compare the stiffness, the failure manner and the resistance of this prototypes. The theorical analysis of prototypes was carried out by assuming the cases of linearity and physical and geometric non-linearity, taking into consideration the variation of stiffness of the bars next to the nodes.

Apresenta-se neste trabalho um processo de busca da solução de mínimo peso, para estruturas de aço treliçadas planas utilizando-se seções formadas por perfis comerciais comuns, dimensionadas segundo a norma brasileira para projeto e execução de estruturas de aço de edifícios. Como base do processo de otimização foi utilizado o método do gradiente inteiro, alterando-se alguns critérios, no sentido de melhorar o desempenho e levar em conta a relação não linear entre as características geométricas dos perfis. São abordados os conceitos matemáticos básicos envolvidos no processo de otimização, os de análise de estruturas treliçadas planas, bem como a formulação para o dimensionamento de barras sujeitas a tração ou compressão. São apresentadas ainda as listagens dos programas envolvidos no processo e também exemplos de aplicação para demonstrar a eficácia dos procedimentos utilizados. / This work presents a process to find a least weight solution for two-dimensional trusses composed of available steel sections, according to brazilian code for design and constructions or steel buildings structures. The optimization process is based on the method of integer gradient directions. Some modifications were introduced in order to improve the algorithm and take into account the non-linear relationship between geometric characteristics for steel cross-section. It is also presented the basic concepts of mathematics optimization to design two-dimensional trusses, as well as the formulation for designing members in tension or compression. The program listing used in this process is also presented, as well as some examples, to demostrate the efficacy of the process.