[pt] A união entre o conhecimento lógico acadêmico e a sabedoria popular espontânea vem resultando em uma série de objetos, nos quais a pesquisa destila informações para chegar cada vez mais próximo da popularização das arquiteturas leves baseadas nas superfícies mínimas. Procuram-se métodos de desenvolvimento de estruturas baseado na observação dos processos de crescimento contínuo das formações naturais. Para atingir esse objetivo alguns simples dispositivos são preparados para a geração de formas espontâneas, como as bolhas de sabão. Estas são controladas e manipuladas de modo a atingir parâmetros predeterminados de projeto, o que torna possível a visualização de potenciais geometrias que sirvam ao objeto almejado. Assim, essas formas são captura- das de modo a obter suas curvas da maneira mais clara possível. A combinação dessas capturas com os resultados dos cálculos no ambiente dos softwares torna possível a parametrização das formas o mais próximos possível das formas naturais. A obtenção e otimização dos cálculos numéricos que definem a geometria dos modelos em escala e de protótipos em escala de uso é fruto da interação de procedimentos artesanais e computacionais, que ampliam o escopo de entendimento do objeto. Esse método vem, atualmente, sendo experimentado e já resultou em alguns protótipos que foram colocados em uso de diversas maneiras. Tanto formas sinclásticas como anticlásticas foram obtidas. A preparação dos materiais e suas partes, assim como as montagens e desmontagens dos objetos, em escala real de uso, foram conduzidas pela equipe do laboratório, sem a necessidade de ferramentas especiais ou complexas. / [en] This union between logical academic knowledge and spontaneous popular knowledge has been resulting in a series of objects from which the research is gathering information to get as close as possible to an answer about the popularization of light- weight architecture. Methods for developing structures based on the observation of the natural formation s continuous growing process are being chased. Heading to this point, some simple devices are prepared to generate spontaneous shapes, such as soap bubbles and soap films. Those are controlled and manipulated to meet the predetermined project parameters and make possible the visualization of potential geometries for the intended object. Then, they are captured in order to obtain its curves. The combination between the captures and the results of software environment calculations make possible the parameterization of the shape as close as possible to the natural geometry. Interactions between artisanal procedures and computer work is found necessary to the obtainment and optimization of numerical calculation that define the geometry of scale models and prototypes, expanding the understanding of the object. This method is currently being experimented and the resulting objects were employed in a variety of ways. Both synclastic and anticlastic forms were obtained. The preparation of the material and their parts, as well as the assemble and disassemble of them, in use scale, were entirely con- ducted by the lab s staff, with no need of special or complex hardware.

Lightweight mechanical metamaterials with exception specific stiffness and strength are useful in many applications, such as transportation, aerospace, architectures and etc. These materials show great potential in mechanical tasks where weight of the material is restrained due to economy or energy reasons. To achieve both the lightweight and the high specific mechanical properties, the metamaterials are often in form of periodic cellular structures with well-designed unit cells. The strategies in designing and improving such cellular structures become the key in the studies of such mechanical metamaterials. In this work, we use both experimental and numerical approaches while probing three types of mechanical metamaterials: i) composite bending dominated hollow lattices (HLs); ii) triply periodic minimal surfaces (TPMSs) and extended TPMSs (eTPMSs); iii) corrugated TPMSs. We have demonstrated a few strategies in designing and improving the specific stiffness or strength via these examples of mechanical metamaterials. Using carbon/ceramic composite in the bending dominated HLs, we prove that using the composite layered material against the single layer ceramic is effective in improving the specific mechanical performances of the mechanical metamaterials. Next, while studying the nature of TPMS, we discover that under isotropic deformation TPMSs are stretch dominated with no stress concentrations within the shell structure. They also have an optimal specific bulk modulus approaching the H-S upper bound. Furthermore, we establish a strategy to smoothly connect the zero-mean-curvature surfaces in TPMSs with the extension of zero-Gaussion-curvature surfaces, forming new ‘eTPMSs”. These new shellular structures trade off its isotropy and have improved specific Young’s modulus along their stiffest orientation compared to their TPMS base structures. Lastly, we introduce corrugated sub-structures to existing TPMSs to improve their mechanical properties, such as Young’s modulus, yield strength and failure strength in compression. It is found that the corrugated sub-structure can effectively suppress the local bending behavior and redirect crack propagation while such structures were under uniaxial compression.

abstract: Additive manufacturing, also known as 3-dimensional (3-d) printing, is now a rapidly growing manufacturing technique. Innovative and complex designs in various aspects of engineering have called for more efficient manufacturing techniques and 3-d printing has been a perfect choice in that direction. This research investigates the use of additive manufacturing in fabricating polymer heat exchangers and estimate their effectiveness as a heat transfer device. Fused Deposition Modeling (FDM), Selective Laser Sintering (SLS) and Stereolithography (SLA) are the three 3-d printing techniques that are explored for their feasibility in manufacturing heat exchangers. The research also explores a triply periodic minimal structure–the gyroid, as a heat exchanger design. The performance of the gyroid heat exchanger was studied using experiments. The main parameters considered for the experiments were heat transfer rate, effectiveness and pressure drop. From the results obtained it can be inferred that using polymers in heat exchangers helps reducing corrosion and fouling problems, but it affects the effectiveness of the heat exchangers. For our design, the maximum effectiveness achieved was 0.1. The pressure drop for the heat exchanger was observed to decrease with an increase in flow rate and the maximum pressure drop measured was 0.88 psi for a flow rate of 5 LPM. / Dissertation/Thesis / Masters Thesis Mechanical Engineering 2019

The Lie symmetry groups of minimal surfaces by way of planar harmonic functions are determined. It is shown that a symmetry group acting on the minimal surfaces is isomorphic with H × H^2 — the analytic functions and the harmonic functions. A subgroup of this gives a generalization of the associated family which is examined.

In recent years, triply periodic minimal surfaces (TPMS) have drawn much attention in research mainly due to their smooth, highly symmetrical surfaces, non-self-intersecting features, and mathematically controllable topologies. TPMS can have pre-defined physical and mechanical properties. The advancement of additive manufacturing technology enables us to fabricate these intricate geometric structures which was not possible by traditional manufacturing methods. In this study, the vat photopolymerization technique was used to manufacture Primitive, Gyroid, and Diamond structures. Samples were cured under ultraviolet (UV) rays after printing. Uniaxial compression experiments were conducted to assess the compressive modulus and strength of these lightweight structures. The compressive behavior of TPMS structures was also predicted using finite element analysis (FEA). Dynamic mechanical analysis (DMA) was used to compare the behavior of these structures at different temperatures. UV-cured samples exhibited improved thermo-mechanical characteristics. The primitive structure had the highest compressive strength among other structures. FEA also revealed the stress concentration areas for each sandwich structure. The DMA findings indicate that TPMS sandwich structures demonstrate significantly reduced storage modulus compared to solid structures. A numerical investigation was performed to understand the heat exchanger application of TPMS structures. The velocity profile, temperature, and pressure distributions were observed for the Primitive heat exchanger. The results of this investigation provide valuable information regarding the enhanced structural and thermal characteristics of these structures manufactured using vat photopolymerization.

This research investigates the development and characterization of mechanical properties in two materials, employing triply periodic minimal surfaces (TPMS) at varying relative densities. The primary focus is on the design of TPMS structures to emulate the biomechanics of the heel pad, guided by equiaxed cells and Cartesian mapping. To achieve the desired densities and understand their influence on mechanical properties, solid-void boundary equations, volume preservation techniques, and cell wall ramping were utilized to create gradient models. Mechanical behavior was rigorously assessed through both uniaxial and cyclic compression testing, including responses under repetitive loading conditions. A key aspect of the study involved the examination of different TPMS cell shapes and their impact on mechanical properties. The results reveal that the 50A material within the specified density range effectively approximates the desired stiffness of the heel pad, albeit with some deviations from Ashby-Gibson model predictions. Among the TPMS structures, diamond configurations exhibited the highest stiffness and energy absorption, while Split-P, Lidinoid, and Gyroid structures demonstrated intermediate performance. Schwarz structures exhibited the lowest performance metrics. These findings underscore the potential of additively manufactured TPMS structures in diverse applications, including biomechanics, orthopedic prosthetics, energy absorption, protective equipment for impact mitigation, flexible soft robotics, and the creation of tailored materials with minimal waste. The research contributes to the field of engineering mechanics and properties of hyper-elastic TPMS designs, opening up avenues for innovative applications across various domains.

Most applications in computer vision suffer from two major difficulties. The first is they are notoriously ridden with sub-optimal local minima. The second is that they typically require high computational cost to be solved robustly. The reason for these two drawbacks is that most problems in computer vision, even when well-defined, typically require finding a solution in a very large high-dimensional space. It is for these two reasons that multiscale methods are particularly well-suited to problems in computer vision. Multiscale methods, by way of looking at the coarse scale nature of a problem before considering the fine scale nature, often have the ability to avoid sub-optimal local minima and obtain a more globally optimal solution. In addition, multiscale methods typically enjoy reduced computational cost. This thesis applies novel multiscale active contour methods to several problems in computer vision, especially in simultaneous segmentation and reconstruction of tomography images. In addition, novel multiscale methods are applied to contour registration using minimal surfaces and to the computation of non-linear rotationally invariant optical flow. Finally, a methodology for fast robust image segmentation is presented that relies on a lower dimensional image basis derived from an image scale space. The specific advantages of using multiscale methods in each of these problems is highlighted in the various simulations throughout the thesis, particularly their ability to avoid sub-optimal local minima and their ability to solve the problems at a lower overall computational cost.

O paradigma forma segue a função, originado na biologia, indica uma invariável dependência entre a origem anatômica de partes de plantas e animais com as funções desempenhadas por estas partes. Embora este paradigma, na biologia, tenha sido superado após Lamarck, a arquitetura e o design ainda se utilizam de analogias biológicas para justificar escolhas estéticas. Neste sentido, as formas mais belas seriam parametrizadas pela eficácia máxima de suas partes na distribuição de esforços. Esta analogia levou à adoção, na arquitetura de edifícios, de padrões geométricos demasiadamente homogêneos, sem vínculo com a complexidade ou linguagem das formas naturais, porém fortemente associados à lógica estrutural. Esta dissertação sugere um caminho alternativo em que a lógica estrutural de duas categorias de esforços (tração e compressão) não comprometa a linguagem presente ou a inspiração gerada pelas formas naturais. Para tal, fundamenta um processo de projeto de superfícies mínimas com base na identificação e parametrização de formas emergentes da natureza. O método proposto utiliza modelos de representação associando a evolução do projeto à aferição, sob o ponto de vista estrutural, da gramática da forma emergente. Os resultados obtidos confirmam as possibilidades de obtenção de eficácia estrutural originada em padrões naturais, sem que haja comprometimento da linguagem de inspiração. / The paradigm form follows function, originated in biology, shows an invariable connection between the anatomical origin of parts of plants and animals with the functions performed by these parts. Although this paradigm, in biology, has been overcome after Lamarck, architecture and design still apply biological analogies to justify aesthetic choices. In this sense, the most beautiful forms would be parameterized by their maximum efficiency at load distribution. This analogy led to the adoption, as a matter of building architecture, of geometric patterns too homogeneous, not linked with the complexity and language of natural forms, but strongly associated with its structural logic. This research suggests an alternative way, in which the structural logic of two load categories (tension and compression) does not change the language or inspiration taken from natural forms. Thus, it is proposed a design process of minimal surfaces, upon identification and parameterization of natural emergent shapes. The proposed method relies on representation by computer models, linking the design evolution to evaluation, under the structural point of view, of emergent shape grammar. The results confirm the possibilities of obtaining structural efficiency originated in natural patterns, without compromising its inspiring language.

Made available in DSpace on 2015-04-22T22:16:14Z (GMT). No. of bitstreams: 1 Ivana Soares Bandeira.pdf: 1022492 bytes, checksum: 3b38c680f7a59ceaf1675ecfe7f7fd0f (MD5) Previous issue date: 2012-05-14 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this work we are interested in replying the following question: a tridimensional stable minimal surface is a plane? For this, we need to understand three important facts: in R3 minimal graphics are planes (Bernstein s Theorem), next, minimal surfaces which are graphics of differentiable functions are stables (Theorem of J. L. Barbosa and M. Do Carmo), and finally, we have that the only tridimensional stable complete minimal surfaces are planes (Theorem of M. do Carmo and C. K. Peng) / Neste trabalho estamos interessados em responder a seguinte questão: Uma superfície tridimensional mínima, completa e estável é um plano? Para isso precisamos compreender três fatos importantes: os planos são as únicas superfícies mínimas que podem ser obtidas gráficos (Teorema de Bernstein), em seguida, superfícies mínimas que são gráficos de funções diferenciáveis são estáveis (Teorema de J. L. Barbosa e M. Do Carmo), e por fim, temos que as únicas superfícies tridimensionais, mínimas, completas, estáveis e orientáveis são os planos (Teorema de M. do Carmo e C. K. Peng)

Nesta dissertação, estudamos o problema de Björling para superfícies de tipo tempo nos espaços de métrica indefinida R^4_1 e R^4_2. Após apresentar uma versão paracomplexa do teorema de representação de Weierstrass para superfícies mínimas de tipo tempo, utilizamos esse teorema para obter uma fórmula de representação para as soluções desse problema de Björling, e através de extensões paraholomorfas dos dados iniciais do problema mostramos que a solução dada por essa fórmula é localmente única. Em seguida, apresentamos duas possíveis maneiras de se obter simetrias para soluções desse problema de Björling: através de uma versão paracomplexa do princípio de reflexão de Schwarz, e através de reflexões ao longo de k-planos que intersectam ortogonalmente a superfície. / In this dissertation, we study the Björling problem for timelike surfaces in the spaces of indefinite metric R^4_1 and R^4_2. After presenting a split-complex version of the Weierstrass representation theorem for minimal timelike surfaces, we use this theorem to obtain a representation formula for the solutions of this Björling problem, and through split-holomorphic extensions of the problems initial data we show that the solution given by this formula is locally unique. Following this, we present two possible methods through which symmetries for the solutions of this Björling problem may be obtained: through a split-complex version of the Schwarz reflection principle, and through reflections alongside k-planes that intersect the surface orthogonally.