The advances in additive manufacturing removed most of the limitations that were once stopping designers when it comes to the manufacturability of the design. It allowed designers to produce parts with high geometric complexity such as cellular structures. These structures are known for their high strength relative to their low mass, good energy absorption, and high thermal and acoustic insulation compared to their relative solid counter-parts. Lattice structures, a type of cellular structures, have received considerable attention due to their properties when producing light-weight with high strength parts. The design of these structures can pose a challenge to designers due to the sheer number of variables that are present. Traditional optimization approaches become an infeasible approach for designing them, which motivated researchers to search for other alternative approaches. In this research, a new method is proposed by utilizing the material density information obtained from the topology optimization of continuum structures. The efficacy of the developed method will be compared to existing methods, such as the Size Matching and Scaling (SMS) method that combines solid-body analysis and a predefined unit-cell library. The proposed method shows good potential in structures that are subjected to multiple loading conditions compared to SMS, which would be advantageous in creating reliable structures. In order to demonstrate the applicability of the proposed method to practical engineering applications, the design problem of a commercial elevator sling will be considered.

A series of novel algorithms for performing aerostructural shape and topology optimization are introduced and applied to the design of aircraft wings. An isoparametric level set method is developed for performing topology optimization of wings and other non-rectangular structures that must be modeled using a non-uniform, body-fitted mesh. The shape sensitivities are mapped to computational space using the transformation defined by the Jacobian of the isoparametric finite elements. The mapped sensitivities are then passed to the Hamilton-Jacobi equation, which is solved on a uniform Cartesian grid. The method is derived for several objective functions including mass, compliance, and global von Mises stress. The results are compared with SIMP results for several two-dimensional benchmark problems. The method is also demonstrated on a three-dimensional wingbox structure subject to fixed loading. It is shown that the isoparametric level set method is competitive with the SIMP method in terms of the final objective value as well as computation time. In a separate problem, the SIMP formulation is used to optimize the structural topology of a wingbox as part of a larger MDO framework. Here, topology optimization is combined with aerodynamic shape optimization, using a monolithic MDO architecture that includes aerostructural coupling. The aerodynamic loads are modeled using a threedimensional panel method, and the structural analysis makes use of linear, isoparametric, hexahedral elements. The aerodynamic shape is parameterized via a set of twist variables representing the jig twist angle at equally spaced locations along the span of the wing. The sensitivities are determined analytically using a coupled adjoint method. The wing is optimized for minimum drag subject to a compliance constraint taken from a 2g maneuver condition. The results from the MDO algorithm are compared with those of a sequential optimization procedure in order to quantify the benefits of the MDO approach. While the sequentially optimized wing exhibits a nearly-elliptical lift distribution, the MDO design seeks to push a greater portion of the load toward the root, thus reducing the structural deflection, and allowing for a lighter structure. By exploiting this trade-off, the MDO design achieves a 42% lower drag than the sequential result.

A series of novel algorithms for performing aerostructural shape and topology optimization are introduced and applied to the design of aircraft wings. An isoparametric level set method is developed for performing topology optimization of wings and other non-rectangular structures that must be modeled using a non-uniform, body-fitted mesh. The shape sensitivities are mapped to computational space using the transformation defined by the Jacobian of the isoparametric finite elements. The mapped sensitivities are then passed to the Hamilton-Jacobi equation, which is solved on a uniform Cartesian grid. The method is derived for several objective functions including mass, compliance, and global von Mises stress. The results are compared with SIMP results for several two-dimensional benchmark problems. The method is also demonstrated on a three-dimensional wingbox structure subject to fixed loading. It is shown that the isoparametric level set method is competitive with the SIMP method in terms of the final objective value as well as computation time. In a separate problem, the SIMP formulation is used to optimize the structural topology of a wingbox as part of a larger MDO framework. Here, topology optimization is combined with aerodynamic shape optimization, using a monolithic MDO architecture that includes aerostructural coupling. The aerodynamic loads are modeled using a threedimensional panel method, and the structural analysis makes use of linear, isoparametric, hexahedral elements. The aerodynamic shape is parameterized via a set of twist variables representing the jig twist angle at equally spaced locations along the span of the wing. The sensitivities are determined analytically using a coupled adjoint method. The wing is optimized for minimum drag subject to a compliance constraint taken from a 2g maneuver condition. The results from the MDO algorithm are compared with those of a sequential optimization procedure in order to quantify the benefits of the MDO approach. While the sequentially optimized wing exhibits a nearly-elliptical lift distribution, the MDO design seeks to push a greater portion of the load toward the root, thus reducing the structural deflection, and allowing for a lighter structure. By exploiting this trade-off, the MDO design achieves a 42% lower drag than the sequential result.

Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第17511号 / 工博第3670号 / 新制||工||1558(附属図書館) / 30277 / 京都大学大学院工学研究科機械理工学専攻 / (主査)教授 西脇 眞二, 教授 田畑 修, 教授 蓮尾 昌裕 / 学位規則第4条第1項該当

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We consider the problem of structural optimization which has many important applications in the engineering sciences. The goal is to find an optimal distribution of the material within a certain volume that will minimize the mechanical and/or thermal compliance of the structure. The physical system is governed by the standard models of elasticity and heat transfer expressed in terms of boundary-value problems for elliptic systems of partial differential equations (PDEs). The structural optimization problem is then posed as a suitably constrained PDE optimization problem, which can be solved numerically using a gradient approach. As a main contribution to the thesis, we derive expressions for gradients (sensitivities) of different objective functionals. This is done in both the continuous and discrete setting using the Riesz representation theorem and adjoint analysis. The sensitivities derived in this way are then tested computationally using simple minimization algorithms and some standard two-dimensional test problems. / Thesis / Master of Science (MSc)

Topology optimization tools are useful for distributing material in a geometric domain to match targets for mass, displacement, structural stiffness, and other characteristics as closely as possible. Topology optimization tools are especially applicable to additive manufacturing applications, which provide nearly unlimited freedom for customizing the internal and external architecture of a part. Existing topology optimization tools, however, do not take full advantage of the capabilities of additive manufacturing. Prominent tools use micro- or meso-scale voids or artificial materials to parameterize the topology optimization problem, but they use filters, penalization functions, and other schemes to force convergence to regions of fully dense (solid) material and fully void (open) space in the final structure as a means of accommodating conventional manufacturing processes. Since additive manufacturing processes are capable of fabricating intermediate densities (e.g., via porous mesostructures), significant performance advantages could be achieved by preserving and exploiting those features during the topology optimization process. Towards this goal, a topology optimization tool has been created by combining homogenization with parametric smoothing functions. Rectangular mesoscale voids are used to represent material topology. Homogenization is used to analyze its properties. B-spline based parametric smoothing functions are used to control the size of the voids throughout the design domain, thereby smoothing the topology and reducing the number of required design variables relative to homogenization-based approaches. Resulting designs are fabricated with selective laser sintering technology, and their geometric and elastic properties are evaluated experimentally. / text

Em áreas que demandam componentes de alto desempenho como a indústria automotiva, aeronáutica e aeroespacial, a otimização do desempenho dinâmico de estruturas é buscada através de diferentes abordagens, como o projeto de materiais específicos à aplicação, ou otimização estrutural topológica. Em particular, o método de otimização estrutural evolucionária bidirecional BESO (Bi-directional Evolutionary Structural Optimization) tem sido utilizado no projeto simultâneo de estruturas hierárquicas, o que significa que o domínio estrutural consiste não somente na estrutura como também na topologia microestrutural dos materiais empregados. O objetivo desse trabalho consiste em aplicar a metodologia BESO na resolução de problemas multiescala bidimensionais visando à maximização da frequência fundamental de estruturas, assim como a minimização de sua resposta quando sujeitas a excitações forçadas numa determinada faixa de frequências. O método da homogeneização é introduzido e aplicado na integração entre as diferentes escalas do problema. Em especial, o modelo de interpolação material é generalizado para o uso de dois materiais no caso de otimização da resposta no domínio da frequência. A metodologia BESO foi aplicada a casos de otimização tomando como domínio estrutural somente a macroescala (projeto estrutural), somente a microescala (projeto material), assim como ambas as escalas concomitantemente (projeto multiescala). Para os casos estudados, a redistribuição de material na macroescala levou a resultados melhores em relação à otimização que modifica a microestrutura. Para a maximização da frequência fundamental, a otimização multiescala obteve os melhores resultados, já para a minimização da resposta em frequência, a otimização somente na macroescala se mostrou mais eficiente. / In areas which demand high performance components, such as automotive, aeronautics and aerospace, the design of application deppendent materials and structural topology optimization are two approaches used in order to optimize structures‟ dynamic behaviour. In particular, the Bi-directional Evolutionary Structural Optimization (BESO) method has been applied to the simultaneous project of hierarchical structures, meaning that the project‟s domain consists not only on the structure on the macroscale, but also on the representative volume element (RVE) associated with the microstructure of the employed materials. The objective of this work is to apply the BESO method in order to solve multiscale bidimensional problems, more specifically, topology optimization problems for fundamental frequency maximization and minimization of the response in the frequency domain under harmonic excitation. The homogenization method is introduced and used to integrate the macro and microscales considered. Furthermore, the material interpolation model in generalized for two material domains in the response minimization problem. The BESO method was applied to optimizations problems where the structural domain was eiher the macrostructure (structural project), microstructure (material project), or both scales simultaneously (multiscale project). In general, material distribution at the macroscale lead to better results in comparison to optimization at the microscale. For fundamental frequency maximization, the multiscale approach obtained better results, while for minimization of the frequency response the results were optimal when the structural domain was restricted to the macrostructure.

This paper describes an intuitive way of defining geometry design variables for solving structural topology optimization problems using a genetic algorithm (GA). The geometry representation scheme works by defining a skeleton that represents the underlying topology/connectivity of the continuum structure. As the effectiveness of any GA is highly dependent on the chromosome encoding of the design variables, the encoding used here is a directed graph which reflects this underlying topology so that the genetic crossover and mutation operators of the GA can recombine and preserve any desirable geometric characteristics through succeeding generations of the evolutionary process. The overall optimization procedure is tested by solving a simulated topology optimization problem in which a 'target' geometry is pre-defined with the aim of having the design solutions converge towards this target shape. The procedure is also applied to design a straight-line compliant mechanism : a large displacement flexural structure that generates a vertical straight line path at some point when given a horizontal straight line input displacement at another point. / Singapore-MIT Alliance (SMA)