Layout optimization for multi-bi-modulus materials system under multiple load cases

Financial support from the National Natural Science Foundation of China (Grant No. 51179164) and the Australian Research Council (Grant No. DP140103137) is acknowledged

Multi-Objective Topology Optimization for Curved Arm of Multifunctional Billet Tong Based on Characterization of Working Conditions

A windlass driven heavy duty multifunctional billet tong was designed for large-scale forging and casting to reduce the number of auxiliary material handling devices in manufacturing workshops. To improve its mechanical performance and safety, a novel multi-objective topology optimization method for its curved arm is proposed in this paper. Firstly, the influence of different open angles and working frequencies for the curved arm was simplified to a multi-objective optimization problem. A comprehensive evaluation function was constructed using the compromise programming method, and a mathematical model of multi-objective topology optimization was established. Meanwhile, a radar chart was employed to portray the comparative measures of working conditions, the weight coefficient for each working condition was determined based on the corresponding enclosed areas, combining the stress indices, the displacement indices and the frequency indices of all working conditions. The optimization results showed that the stiffness and strength of the curved arm can be improved while its weight can be reduced by 10.77%, which shows that it is feasible and promising to achieve a lightweight design of the curved arm of a billet tong. The proposed method can be extended to other equipment with complex working conditions

Dispersive Elastodynamics of 1D Banded Materials and Structures: Design

Within periodic materials and structures, wave scattering and dispersion occur across constituent material interfaces leading to a banded frequency response. In an earlier paper, the elastodynamics of one-dimensional periodic materials and finite structures comprising these materials were examined with an emphasis on their frequency-dependent characteristics. In this work, a novel design paradigm is presented whereby periodic unit cells are designed for desired frequency band properties, and with appropriate scaling, these cells are used as building blocks for forming fully periodic or partially periodic structures with related dynamical characteristics. Through this multiscale dispersive design methodology, which is hierarchical and integrated, structures can be devised for effective vibration or shock isolation without needing to employ dissipative damping mechanisms. The speed of energy propagation in a designed structure can also be dictated through synthesis of the unit cells. Case studies are presented to demonstrate the effectiveness of the methodology for several applications. Results are given from sensitivity analyses that indicate a high level of robustness to geometric variation.Comment: 33 text pages, 27 figure

Multi-Objective Topology Optimization for Curved Arm of Multifunctional Billet Tong Based on Characterization of Working Conditions

A windlass driven heavy duty multifunctional billet tong was designed for large-scale forging and casting to reduce the number of auxiliary material handling devices in manufacturing workshops. To improve its mechanical performance and safety, a novel multi-objective topology optimization method for its curved arm is proposed in this paper. Firstly, the influence of different open angles and working frequencies for the curved arm was simplified to a multi-objective optimization problem. A comprehensive evaluation function was constructed using the compromise programming method, and a mathematical model of multi-objective topology optimization was established. Meanwhile, a radar chart was employed to portray the comparative measures of working conditions, the weight coefficient for each working condition was determined based on the corresponding enclosed areas, combining the stress indices, the displacement indices and the frequency indices of all working conditions. The optimization results showed that the stiffness and strength of the curved arm can be improved while its weight can be reduced by 10.77%, which shows that it is feasible and promising to achieve a lightweight design of the curved arm of a billet tong. The proposed method can be extended to other equipment with complex working conditions

Multiscale optimization of non-conventional composite structures for improved mechanical response

Nowadays, due to governmental requirements to control climate change, there is a great inter- est on the part of the automotive and aerospace industry to design structures as light as possible, without jeopardize their performance, thus increasing their efficiency. Multi-material design is a way to achieve this goal, as will be shown in this work In this work, multi-material design is considered with the goal of improving the structure’s stiffness, strength, and non-linear behaviour when it yields. Firstly, a microstructural topology optimization is carried out seeking for multi-material microstructures with increased stiffness and strength compared to equivalent single-material microstructures. Afterwards, this study is further extended to perform multi-scale topology optimization, where a concurrent optimization of ma- terial and structure is done. Ultimately, the non-linear behaviour of hybrid fibre reinforced com- posites is optimized in order to introduce a so-called “pseudo-ductility”. Two different optimization problems are formulated and solved here. One compliance mini- mization with mass constraint problem and another stress-based problem where the maximal von Mises stress is locally minimized in the unit-cell. The multi-material design is investigated here using two different approaches. On one hand, the two solids coexist being bonded together across sharp interfaces. On the other hand, a functionally graded material is obtained as an extensive smooth variation of material properties on account of varying composition’s volume fractions of both solids throughout the design domain. The compliance-based optimization results show that multi-material microstructures can be stiffer compared to single-material ones for the same mass requirement. Regarding the stress-based problem, lower stress peaks are obtained in bi-material design solutions and, specially, in the case of graded material solutions. As regards multi-scale topology optimization, the results show that a multi-material structure can be stiffer than its single-material counterpart, which is in accordance with the microstructural study performed earlier. Hybrid composites can achieve the so-called “pseudo-ductile” behaviour mimicking the well- known elastic-plastic behaviour. To understand under what circumstances such behaviour is ob- tained, optimization problems are formulated and solved here. Two different types of optimiza- tion problems are considered. Firstly, one finds out the optimal properties of fibres to hybridize and get the pseudo-ductile behaviour. Once an optimal hybridization is found, another optimiza- tion problem is solved in order to understand the influence of the fibre dispersion on the composite response. The optimal results obtained show hybrid composites having a considerable pseudo- ductile behaviour.Atualmente, devido às imposições governamentais para controlar as alterações climáticas, existe um grande interesse por parte da indústria automóvel e aeroespacial para o projeto de es- truturas o mais leves possíveis, sem se comprometer o seu desempenho, aumentando assim a sua eficiência. O projeto multimaterial de estruturas é um dos caminhos para se alcançar este objetivo, conforme será mostrado neste trabalho. Neste trabalho, considera-se o projeto multimaterial de estruturas com o objetivo de se melho- rar a rigidez, resistência, e comportamento não linear após cedência. Primeiro, é feita uma otimi- zação de topologia ao nível da microestrutura procurando-se microestruturas multimateriais com maior rigidez e resistência quando comparadas com microestruturas de material único equivalen- tes. Depois, este estudo é explorado também no contexto de otimização topológica multi-escala, onde é realizada uma otimização concorrente do material e estrutura. Por fim, o comportamento não linear de compósitos híbridos reforçados por fibra é otimizado com vista à introdução de um efeito de “pseudo-ductilidade”. São formulados e resolvidos aqui dois problemas diferentes de otimização. Um problema de minimização de compliance (flexibilidade) sujeito a um constrangimento de massa e outro pro- blema baseado na tensão, onde a tensão máxima de von Mises é localmente minimizada na célula unitária. O projeto multi-material é investigado aqui utilizando duas diferentes abordagens. Numa das abordagens, os dois sólidos coexistem na sua forma discreta originando-se interfaces com uma variação abrupta de propriedades. Na outra abordagem, obtém-se um material de gradiente funcional onde existe uma suave variação das propriedades obtida variando pontualmente a fração volúmica dos sólidos ao longo de todo o domínio de projeto. Os resultados da otimização baseada na compliance mostraram que microestruturas multimateriais podem ser mais rígidas quando comparadas com as de material único para o mesmo requisito de massa. Relativamente ao pro- blema baseado na tensão, são obtidos picos de tensão mais baixos nas soluções constituídas por duas fases discretas de material e, sobretudo, nas soluções de material de gradiente funcional. No que que diz respeito à otimização topológica multi-escala, os resultados mostraram que uma estrutura multimaterial pode ser mais rígida que uma estrutura de material único equivalente, o que está de acordo com o estudo realizado anteriormente ao nível da microestrutura. Os compósitos híbridos conseguem alcançar um comportamento designado de “pseudo-dúc- til”, imitando o conhecido comportamento elasto-plástico. Para melhor se compreender sob que circunstâncias tal comportamento é obtido, são formulados e resolvidos problemas de otimização. São assim considerados dois tipos diferentes de problemas de otimização. Primeiramente, desco- brem-se quais as propriedades ótimas das fibras a hibridizar, obtendo-se o comportamento pseudo-dúctil. Assim que hibridização ótima tenha sido descoberta, outro problema de otimização é resolvido de modo a perceber-se a influência da dispersão das fibras na resposta do compósito. Os resultados ótimos obtidos mostram compósitos híbridos tendo um comportamento pseudo- dúctil considerável

A new computational approach to topology optimization in solid mechanics problems

Tesi en modalitat compendi de publicacionsThis doctoral thesis addresses topology optimization problems at a single scale. Based on this purpose, a new topology optimization approach is developed in order to improve existing and widespread techniques in the research community on the topic. The proposed technique presents several characteristics that overcome some of the well-known difficulties in topological optimization while maintaining a considerable degree of simplicity. In the first place, the formulation of the topological optimization technique is presented, as well as its algorithm. The method is based on 4 fundamental features: (1) the use of a 1-0 characteristic function, as well as the precise identification of the material boundaries from a discrimination function (0-level-set function), (2) the definition of a topological derivative consistent with the ersatz method (used in the state problem), as an approximation to the exact topological derivative, (3) the inclusion of a Laplacian regularization with minimum size control of the different components, and (4) the formulation of an analytical optimality condition aiming at the optimal topology solution. The approach is applied to different topology optimization problems, well-reported in the literature and used as numerical benchmarks (in structural and thermal problems), to examine their performance. In these fields, stiffness and conductivity maximization problems are considered for validation, respectively. In addition, different topological optimization problems of major engineering interest are tackled, including the design of compliant mechanisms within the structural field and thermal cloaking devices within the thermal field. Finally, a comparison of the formulation with other existing topology optimization techniques is performed, including (1) SIMP, (2) ESO/BESO, and (3) Level-set with Hamilton-Jacobi as the updating equation. The analysis of the results provides a comparison in terms of the quality of the topology of each method, the computational cost of the optimal solutions, as well as the simplicity of implementation. The resulting study reveals the potential of the developed methodology in these specific comparison terms. In an attempt to bring the method closer to other researchers and to promote its use, an educational version of the method (written in MATLAB) has been published in an online repository, together with documentation, facilitating its dissemination and subsequent use in other applications of interest.El objetivo de esta tesis doctoral es abordar el problema de optimización topológica a una única escala. En base a este propósito, se desarrolla una nueva técnica de optimización capaz de competir con técnicas ya existentes y extendidas entre la comunidad investigadora sobre el tema. Esta técnica presenta características que superan algunas de las dificultades bien conocidas en optimización topológica manteniendo un buen grado de simplicidad. En primer lugar, se presenta la formulación de la técnica de optimización topológica, así como su algoritmia. El método se fundamenta en 4 aspectos básicos: (1) la utilización de una función característica 1-0, así como la definición precisa de las fronteras materiales a partir de una función de discriminación (isonivel 0 de la función level-set), (2) la definición de una derivada topológica coherente con el método ersatz (utilizado en la ecuación de estado), como aproximación a la derivada topológica exacta, (3) la inclusión de una regularización Laplaciana con control de tamaño mínimo de los diferentes componentes, y (4) la definición de una condición de optimalidad analítica para la determinación de la solución óptima de la topología. La metodología se aplica a diferentes problemas de optimización topológica bien detallados en la literatura y utilizados como ensayos numéricos para examinar su respuesta frente a problemas estructurales y térmicos. En estos campos, se incluyen problemas de maximización de la rigidez y de la conductividad, respectivamente. Además, se resuelven diferentes problemas de optimización topológica con gran interés ingenieril en los campos estructurales con el diseño de mecanismos y térmicos con el diseño de dispositivos de camuflaje térmicos. Finalmente, se realiza una comparación de la formulación con otras técnicas ya existentes, por ejemplo: (1) SIMP, (2) ESO/BESO, y (3) Level-set con Hamilton-Jacobi como ecuación de evolución. El análisis de los resultados permite comparar la calidad de la topología de cada método, el coste computacional de las soluciones óptimas, así como la simplicidad de implementación, demostrando el potencial de la metodología desarrollada principalmente en estos términos de comparación. Con la finalidad de acercar el método a otros investigadores y de promover su utilización, se ha publicado una versión educativa del mismo (en MATLAB) en un repositorio online, junto a documentación, permitiendo así la divulgación del mismo y la posible utilización en otras aplicaciones de interés.Postprint (published version

Design of Thermal Structures using Topology Optimization

The design of structures subjected to elevated temperature environments has long been an important area of study in the aerospace industry. This is especially true in the modern day, where new problems related to embedded engine aircraft and high temperature exhaust-washed structures present new structural design challenges not found in past applications. In this work, the response of a class of thermal structures whose responses are characterized by significant amounts of restrained expansion, to which exhaust-washed structures belong, are studied. To address the complex design challenges that become evident in these investigations, structural topology optimization is applied due to its unique ability to identify optimal material layout. Since conventional methods for topology optimization fail to generate effective designs in the presence of thermoelastic effects, new formulations for thermoelastic topology optimization are demonstrated. These include techniques for addressing the amount of reaction loading generated by a structural concept and methods for incorporating stress-based design criteria in topology optimization problems with design-dependent thermal loading. When taken together, the developments in this work provide a design technique in which stresses can be directly treated in thermal structures by identifying the proper arrangement of structural components in a thermal environment

Optimal Design of Functionally Graded Parts

Several additive manufacturing processes are capable of fabricating three-dimensional parts with complex distribution of material composition to achieve desired local properties and functions. This unique advantage could be exploited by developing and implementing methodologies capable of optimizing the distribution of material composition for one-, two-, and three-dimensional parts. This paper is the first effort to review the research works on developing these methods. The underlying components (i.e., building blocks) in all of these methods include the homogenization approach, material representation technique, finite element analysis approach, and the choice of optimization algorithm. The overall performance of each method mainly depends on these components and how they work together. For instance, if a simple one-dimensional analytical equation is used to represent the material composition distribution, the finite element analysis and optimization would be straightforward, but it does not have the versatility of a method which uses an advanced representation technique. In this paper, evolution of these methods is followed; noteworthy homogenization approaches, representation techniques, finite element analysis approaches, and optimization algorithms used/developed in these studies are described; and most powerful design methods are identified, explained, and compared against each other. Also, manufacturing techniques, capable of producing functionally graded materials with complex material distribution, are reviewed; and future research directions are discussed