Thesis submitted in compliance with the requirements for the Master's Degree in Technology: Department of Mechanical Engineering, Durban University of Technology, 2008. / The development of an evolutionary optimisation method and its application to the design of an advanced composite structure is discussed in this study. Composite materials are increasingly being used in various fields, and so optimisation of such structures would be advantageous. From among the various methods available, one particular method, known as Evolutionary Structural Optimisation (ESO), is shown here. ESO is an empirical method, based on the concept of removing and adding material from a structure, in order to create an optimum shape. The objective of the research is to create an ESO method, utilising MSC.Patran/Nastran, to optimise composite structures. The creation of the ESO algorithm is shown, and the results of the development of the ESO algorithm are presented. A tailfin of an aircraft was used as an application example. The aim was to reduce weight and create an optimised design for manufacture. The criterion for the analyses undertaken was stress based. Two models of the tailfin are used to demonstrate the effectiveness of the developed ESO algorithm. The results of this research are presented in the study.

There are many challenges facing the aerospace industry that can be addressed with new concepts, technologies, and materials. However, current design methods make it difficult to include these new ideas early in the design of aircraft. This is especially true in the structures discipline, which often uses weight-based methods based upon statistical regressions of historical data. A way to address this is to use physics-based structural analysis and design to create more detailed structural data. Thus, the overall research objective of this dissertation is to develop a physics-based structural analysis method to incorporate new concepts, technologies, and materials into the conceptual design phase. The design space of physics-based structural design problem is characterized as highly multimodal with numerous discontinuities; thus, a large number of alternatives must be explored. Current physics-based structural design methods tend to use high fidelity modeling and analysis tools that are computationally expensive. This dissertation proposes a modeling & simulation environment based on classical structural analysis methods. Using classical structural analysis will enable increased exploration of the design space by reducing the overall run time necessary to evaluate one alternative. The use of physics-based structural optimization using classical structural analysis is tested through experimentation. First the underlying hypotheses are tested in a canonical example by comparing different optimization algorithms ability to locate a global optimum identified through design space exploration. Then the proposed method is compared to a method based on higher fidelity finite element analysis as well as a method based on weight-based empirical data to validate the overall research objective.

Additive manufacturing (AM) offers a way to manufacture highly complex designs with potentially enhanced performance as it is free from many of the constraints associated with traditional manufacturing. However, current design and optimisation tools, which were developed much earlier than AM, do not allow efficient exploration of AM's design space. Among these tools are a set of numerical methods/algorithms often used in the field of structural optimisation called topology optimisation (TO). These powerful techniques emerged in the 1980s and have since been used to achieve structural solutions with superior performance to those of other types of structural optimisation. However, such solutions are often constrained during optimisation to minimise structural complexities, thereby, ensuring that solutions can be manufactured via traditional manufacturing methods. With the advent of AM, it is necessary to restructure these techniques to maximise AM's capabilities. Such restructuring should involve identification and relaxation of the optimisation constraints within the TO algorithms that restrict design for AM. These constraints include the initial design, optimisation parameters and mesh characteristics of the optimisation problem being solved. A typical TO with certain mesh characteristics would involve the movement of an assumed initial design to another with improved structural performance. It was anticipated that the complexity and performance of a solution would be affected by the optimisation constraints. This work restructured a TO algorithm called the bidirectional evolutionary structural optimisation (BESO) for AM. MATLAB and MSC Nastran were coupled to study and investigate BESO for both two and three dimensional problems. It was observed that certain parametric values promote the realization of complex structures and this could be further enhanced by including an adaptive meshing strategy (AMS) in the TO. Such a strategy reduced the degrees of freedom initially required for this solution quality without the AMS.

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.

Desenvolvimento de uma rotina computacional para otimizar o pré-dimensionamento de edifícios em concreto armado, tratados simplificadamente como pórticos planos. Os softwares comerciais utilizados pelos escritórios de engenharia para o cálculo de estruturas partem do pré-dimensionamento, sendo esta etapa essencial ainda realizada geralmente a partir da experiência e intuição do projetista, por métodos de tentativa e erro. Apesar de que pequenos erros cometidos nesta fase serão corrigidos durante o dimensionamento, esse processo geralmente não leva à solução mais econômica, visto que podem existir diversas soluções de estruturas que atendam às condições de segurança exigidas pelas Normas e há pouco tempo para o engenheiro escolher, por meio de uma análise, a que lhe parecer ser a mais econômica. A otimização matemática é então utilizada como uma ferramenta de auxílio ao engenheiro para a determinação do projeto mais econômico, sendo que o prédimensionamento passa a ser feito utilizando técnicas matemáticas de avaliação das variáveis e restrições incluídas no projeto. A partir do posicionamento dos elementos e dos valores limites para as variáveis envolvidas, utilizando o método de programação quadrática sucessiva para resolver o problema geral de programação não-linear, aplica-se uma função de mínimo custo para a seção transversal das vigas e dos pilares, obtendo-se uma solução de mínimo custo para a estrutura estudada / A computational routine developed to optimize the first draft design of reinforced concrete buildings, approximated by plane frames. The commercial softwares used by the engineering offices for structural design is usually based in a first draft design, being this essential stage still accomplished by the engineer´s experience and intuition, using attempt and error methods. Although small mistakes made in this phase will be corrected during the design, that process doesn't guarantee the most economic solution, because there are several structural solutions that assists to Code’s safety conditions and there is little time for the engineer to choose, through an analysis, the one that seems to be the most economic. The mathematical optimization is used to assist the engineer to establish the cheapest structure, and the first draft design becomes made by mathematic techniques of evaluation of the project’s variables and restrictions. Based on the elements location and the set values for the involved variables, solving the general nonlinear programming problem using the successive quadratic programming algorithm and a user-supplied gradient, a function of minimum cost is applied for the beams and columns cross section, obtaining a solution of minimum cost for the structure under analysis

É cada vez mais curto o tempo que um engenheiro tem para desenvolver adequadamente os projetos. Com prazos cada vez menores para a concepção, o pré-dimensionamento das estruturas é, geralmente, definido com base em projetos desenvolvidos anteriormente e, essa estrutura assim concebida, é processada de modo a verificar o atendimento aos requisitos de segurança. Dessa forma, uma vez atendidos esses requisitos, dificilmente o grau de economia encontrado é verificado, uma vez que o projeto precisa ser entregue no prazo acordado. Os procedimentos automatizados de otimização de estruturas se inserem neste contexto para possibilitar uma agilidade no processo de se encontrar, entre as soluções possíveis, aquela que vai levar a uma estrutura mais econômica. Além de auxiliar na definição das dimensões dos elementos estruturais, o processo de otimização pode indicar ao projetista partes da estrutura que necessitam de uma maior atenção, de forma a se obter a economia desejada. Neste trabalho é apresentado um procedimento para otimizar o pré-dimensionamento de edifícios em concreto armado, tratados simplificadamente como pórticos planos. A partir do posicionamento dos elementos e dos valores limites para as variáveis envolvidas, utilizando um método de aproximações combinadas, é aplicada uma função de mínimo custo para a seção transversal das vigas e dos pilares, obtendo-se uma solução de mínimo custo para a estrutura estudada. / Engineers have nowadays considerably less time to adequately develop their projects than in the past. Because of increasingly shorter deadlines for project conception, the first draft design of the structures is usually defined based on previously developed projects, aiming evidently to assure all safety requisites. While the focus is on meeting the agreed deadlines and the aforementioned safety requisites, it is rare that we effectively address the issue of economic savings. In this context, we hereby present automated procedures for structures optimization in which the main goal is to yield tothe least-cost-solutions from a economical perspective, meeting short deadlines and all safety requisites. Besides helping in the definition of the dimensions of the structural elements, the optimization process allows the designer to have a clear vision of the critical structural parts, in order to obtain the desired economical savings/gains. We hereby present a procedure to optimize the first draft design of reinforced concrete buildings, approximated by plane frames. Based on the elements positioning and the set values for the involved variables, and by utilizing a method of combined approximations, it is applied a function for least cost beams and columns cross-section, obtaining the least cost solution for the structure under analysis.

Este trabalho aborda o desenvolvimento de uma metodologia para a da determinação de parâmetros de projeto de uma classe de robôs industriais hidráulicos com atuadores lineares diretamente acoplados aos elos. Um robô típico desta classe pode ser dividido em três partes: a base, o braço e o punho, sendo que, no presente trabalho, é abordado o desenvolvimento do braço. São propostos métodos sistemáticos para a determinação das dimensões dos elos, dos cursos angulares das juntas, dos pontos de acoplamento dos atuadores, da estrutura principal dos elos, e para a sistematização do procedimento de especificação dos atuadores e unidades de potência hidráulica. Estes métodos dependem da predefinição por um projetista das necessidades técnicas das tarefas que o robô deve realizar, a partir dos quais os métodos então buscam a determinação dos parâmetros ótimos do braço para estas tarefas. Também é apresentada a cinemática direta, inversa, e a matriz Jacobiana, e é feito o equacionamento da dinâmica do braço em forma matricial, considerando a influência da inércia e peso dos atuadores, de modo a permitir a análise dos carregamentos e facilitar o controle. As equações propostas são verificadas com comparações com softwares comerciais e resultados disponíveis na literatura. Um programa computacional que implementa a metodologia deste trabalho foi desenvolvido e aplicado para determinar os parâmetros de dois braços propostos como estudo de casos. A metodologia se mostrou capaz de rapidamente especificar o braço adequado para cada caso, calculando as características de desempenho que deverão possuir se construídos. Estes dados podem ser aplicados para a construção de um robô hidráulico, ou para assistir o projetista a determinar se um robô hidráulico é adequado ou não para realizar as tarefas predefinidas. / This work presents the development of a methodology for the determination of the design variables of a class of hydraulic industrial robots with linear actuators directly coupled to the links. A typical robot of this class can be divided in three parts: the base, the arm and the wrist, of which the development of the arm is tackled in this work. Systematic methods are proposed for the determination of the links’ dimensions, the joints’ angular strokes, the coupling points for the actuators, the main structure of the links, and for the systematization of the procedure used to specify the actuators and pumps. These methods depend on the technical specifications, predefined by the designer, that are required for the arm to be able to perform a given set of tasks, and then seek the optimum parameters for the arm. The direct and inverse kinematics are also presented, as well as the Jacobian matrix, and the dynamics of the arm are calculated in matrix form, taking into consideration the inertia and weight of the actuators, so as to allow the analysis of the structural loads and facilitate the control. The proposed equations are verified via comparisons with commercial software and results found in the literature. A computer program that implements the methodology of this work was developed and used to determine the parameters of two proposed arms as a case study. The program was able to quickly specify the configurations for the arm of each case, and also calculate the performance characteristics the arms should possess if built. This data can be used to build a hydraulic arm, or even to help the designer to determine if a hydraulic robot is ideal or not for the given set of tasks.

Submitted by Maria Cristina (library@lncc.br) on 2015-10-07T15:23:26Z No. of bitstreams: 1 TeseEduardoKrempserDaSilva.pdf: 3216403 bytes, checksum: 1c9a6669bd66c6ab34913d087cb25175 (MD5) / Approved for entry into archive by Maria Cristina (library@lncc.br) on 2015-10-07T15:23:44Z (GMT) No. of bitstreams: 1 TeseEduardoKrempserDaSilva.pdf: 3216403 bytes, checksum: 1c9a6669bd66c6ab34913d087cb25175 (MD5) / Made available in DSpace on 2015-10-07T15:23:55Z (GMT). No. of bitstreams: 1 TeseEduardoKrempserDaSilva.pdf: 3216403 bytes, checksum: 1c9a6669bd66c6ab34913d087cb25175 (MD5) Previous issue date: 2014-06-30 / Conselho Nacional de Desenvolvimento Científico e Tecnológico / In several situations, discontinuities and di_culties in the use of derivatives, as well as the presence of discrete or mixed design variables make the application of classic optimization methods less attractive. These dificulties suggest the application of population-based metaheuristics, and specially those with natural inspiration. Among them, we are interested in the so called Diferential Evolution (DE), which has obtained good results in the literature. Despite of the quality of solutions obtained by DE in several optimization problems, DE cannot be used when the solution evaluation involves a computational expensive simulation. Therefore, even considering the continuous improvement of computational power in recent decades with a cost reduction, the application of metaheuristics such as DE, is deficient in the mentioned cases due to the large number of evaluations/simulations required to obtain a solution. In this context, the application of metamodels, or surrogate models, together with metaheuristics has received a growing attention of researchers of several areas. The metamodels generate a computational model which is simpler to be used in parts of the optimization process, replacing the original model. Its construction is based in previously obtained simulation results during the current optimization process. This work presents a new application strategy of metamodels within DE, which allows for computational cost reduction, besides providing a mechanism to alleviate the user of the variant parameter definition, one of most important definitions in DE. The work presents also an evaluation of di_erent local approximation models used as metamodel in the proposed scheme. Finally, some improvements are proposed by means of Design of Experiments (DoE) techniques and the adaptive selection of metamodel parameters; the DoE are applied aiming for the best way to select the next points to be evaluation and, consequently, generating a better final solution with a lower cost. The other proposed use of Adaptive Operator Selection mechanism is to select the number of radial basis used in the Radial Basis Function Networks applied as metamodel. / Em várias situações de interesse, descontinuidades e dificuldades severas no uso de derivadas, bem como variáveis de projeto discretas ou mistas tornam a aplicação de métodos clássicos de otimização pouco atraentes. Essas dificuldades sugerem o emprego de meta-heurísticas populacionais, em especial as de inspiração natural. Dentre estas estamos interessados na chamada Evolução Diferencial (DE), que tem apresentado bons resultados na literatura. Apesar da qualidade das soluções obtidas pela aplicação da DE nos mais diversos problemas de otimização, seu uso mostra-se proibitivo quando a avaliacão de uma solução candidata envolve uma simulação computacionalmente cara. Portanto, mesmo considerando que se observa nas ultimas décadas um contínuo processo de evolução da capacidade de processamento e a redução de seu custo, a aplicação de meta-heurísticas, tais como a DE, ainda e deficiente para os casos de interesse devido ao grande número de avaliações/simulações necessárias para obtenção da solução. Nesse contexto, a aplicação de metamodelos em conjunto com meta-heurísticas tem recebido uma crescente atenção dos pesquisadores de diversas áreas. Os metamodelos fornecem um modelo computacionalmente mais simples a ser utilizado em parte do processo de otimização em substituição ao modelo original. Para sua construção vale-se dos resultados das simulações previamente realizadas durante o próprio processo de otimização. Este trabalho apresenta uma estratégia de aplicação de metamodelos na DE, o qual permite a redução do custo computacional envolvido, além de valer-se de um mecanismo capaz de evitar a seleção a priori, por parte do usuário, de um dos mais importantes parâmetros da DE, a variante a ser utilizada. O trabalho apresenta ainda uma avaliação do uso de diferentes modelos de aproximação local como metamodelos para o esquema proposto. Apresentam-se também aprimoramentos da proposta por meio da aplicação de técnicas de Desenho de Experimentos (DoE) e a seleção automática do parâmetro do metamodelo. O DoE é aplicado visando uma melhor seleção dos pontos a serem exatamente avaliados e, consequentemente, melhorando a solução final com um menor custo computacional. Uma outra proposta, que será apresentada no final do trabalho, utiliza um mecanismo de adaptação de operadores para a seleção do número de bases de função radial da Rede de Funções de Base Radial considerada como metamodelo ao final do trabalho.

O objetivo deste estudo consiste em obter um procedimento de dimensionamento estrutural otimizado de suportes metálicos utilizados em chassi de veículos comerciais, o qual apresenta, na maioria dos casos, restrições referentes ao projeto do produto e à manufatura. Realizou-se a revisão bibliográfica dos principais métodos de otimização estrutural, abrangendo problemas e soluções relacionadas ao seu uso, e também foram considerados os conceitos do projeto para fabricação e montagem. Foi proposto um procedimento de dimensionamento de suportes estruturais, utilizando a análise de elementos finitos e otimização paramétrica, de forma e topológica. A proposta verifica também itens como estabilidade estrutural, tipo de elemento utilizado e facilidade de fabricação e montagem. O procedimento foi aplicado no estudo de caso do desenvolvimento de um suporte de amortecedor, o qual apresentou falha em campo. Foi possível fazer a representação da falha no suporte com o modelo de elementos finitos e foram propostas estruturas otimizadas, que resolveram a falha e confirmaram a eficácia do procedimento proposto no estudo. Um benefício da aplicação da otimização topológica é a capacidade do método para a obtenção de novas estruturas com menor peso e com aumento da rigidez, considerando ainda as necessidades de fabricação e montagem. / The objective of this work is to achieve a procedure for structural design optimized metal brackets used in the chassis of commercial vehicles, which have in the most of the cases limitations related to product design and manufacturing. Was carried out a bibliographic review of structural optimization main methods, covering problems and solutions related to their use, were also considered the concepts of design for manufacture and assembly. It was proposed a procedure for structural brackets design, using the finite element analysis, parametric, shape and topology optimization. The proposal also notes items such as structural stability; type of element used and to improvement of fabrication and assembly. The procedure was applied in the case study to the development of a shock absorber, which has failed in the field. It was possible to represent the brackets failure of support with the finite element model and optimized structures have been proposed to resolve the failure and confirmed the effectiveness of the proposed procedure at work. One application benefit for topology optimization is the ability of the method to obtain new structures with lower weight and higher stiffness level, and considering manufacturing and assembly needs.

First of all, the PDE form of the classical level set function phi is parameterized with an analytical form of Radial Basis Function (RBF), which is real-valued and continuously differentiable. Such that the upwind scheme, extension velocity and reinitialization algorithms in solving the discrete Hamilton-Jacobi equation can be waived in the numerical process, the whole framework is transformed into a standard mathematical programming problem in which the linear objective function can be directly optimized by a gradient algorithm - shape sensitivity. The minimization of the mean compliance is studied and presented to demonstrate the advantages of the parametrical method. / Parametrization substantially reduces the complexity of the original discrete PDE level set method. However, the result shows that the high number of RBF knots leads to dense coefficient matrices. Thus, it induces numerical instabilities, slow convergence and less accuracy in the process. Consequently, we then study the distribution of knots density for faster computation. By updating the movement of the knot, the knot moves towards the position where the change is directly determined by the shape sensitivity. In such case, we may use lesser number of knots to describe the properties of the system while the smoothness of the implicit function is satisfied. The sensitivity study is evaluated carefully and discussed in detail. Results show a significant improvement in the computational speed and stability. / The study found significant improvement obtained in the structural optimization with the parametric level set method, both the stability and efficiency were given as the benefits of using the method of the parametrization. / Traditional structural optimization approaches can be referred to as sizing optimization, since their design variables are the proportions of the structure or material. A major restriction in the sizing problem is that the shape and the topology of the structure are fixed a priori. Undoubtedly, changes in shape (e.g., curved boundary) and topology (e.g., holes in a member) could produce more significant improvement in dynamic performance than modifications in size alone. A recent development of shape and topology optimization based on the implicit moving boundaries with the use of the renowned level set method is regarded as one of the most sophisticated methods in handling the change of the structural topology. In this thesis, we study the parametrization of the classical level set method for the structural optimization and the associated computational methodology. / Usually, a large-scale model will lead to bulk coefficient matrices in the RBF optimization and the linear function normally require O (N3) flops and O (N2) memory while processing. It is becoming impractical to solve as N goes over 10,000. In fact, the dense system equation matrix frequently leads to the numerical instabilities and the failure of the optimization. Finally, we introduce the method of Partition of Unity (POU) to deal with this problem. POU is often used in 3D reconstruction of implicit surfaces from scattered point sets. It breaks the global domain into smaller overlapping subdomains such that the implicit functions can be more efficiently interpolated. Meanwhile, the global solution is obtained by blending all the local solutions with a set of weighting functions. The algorithm of POU is presented here, and we analyze and discuss the numerical results accordingly. / Ho, Hon Shan. / Adviser: Michael Y. Wang. / Source: Dissertation Abstracts International, Volume: 73-03, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 106-119). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.