Improving the design of flow channels in a liquid-cooled heat sink is critical for boosting the capabilities of electronic components as well as reducing energy usage by the pump. This work explores the use of topology optimization to minimize the pressure difference across a heat sink and consequently, the energy used to supply the liquid. Topology optimization involves solving mathematical equations to obtain the optimal design for a defined cost function, here the total pressure difference between the inlet and outlet. A design variable called the porosity is defined for each cell in the mesh. The porosity features in a sink term in the momentum equation, which 'solidifies' cells by velocity suppression when deemed to be counterproductive to the cost function. The adjoint method of topology optimization, in particular, is a well-established tool for use in flow network problems and includes non-physical parameters such as the adjoint velocity and pressure. The method isn't without its drawbacks, such as the numerical instability of the adjoint equations, and the absence of boundary layers or wall functions at the interface of high and low porosity. The strength of the adjoint method lies in the ease with which it calculates the gradient of the cost function with respect to the porosity. When applied to the geometries in this work, it is observed that the problem is non-convex and results in multiple optimums with similar cost values. Thus the objective becomes seeking solutions with the simplest shape and at the same time having a minimized pressure difference. Interesting techniques are tested, namely an interpolation function, a velocity tolerance, and a volume constraint. The work is accomplished by modifying an existing adjoint optimization solver in the open-source CFD software, OpenFOAM.

Here explored is a method by which designers can use the tool of topology optimization to numerically improve barriers to reverse engineering. Recently developed metrics, which characterize the time (T) to reverse engineer a product, enable this optimization. A key parameter use din the calculation of T is information content (K). The method presented in this thesis pursues traditional topology optimization objectives while simultaneously maximizing K, and thus T, in the resulting topology. This thesis presents new algorithms to 1) evaluate K for any topology, 2)increase K for a topology by manipulating macro-scale geometry and micro-scale crystallographic information for each element, and 3) simultaneously maximize K and minimize structural compliance(a traditional topology optimization objective). These algorithms lead designers to desirable topologies with increased barriers to reverse engineering. It is concluded that barriers to reverse engineering can indeed be increased without sacrificing the desirable structural characteristic of compliance. This has been shown through the example of a novel electrical contact for a consumer electronics product.

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Indiana University-Purdue University Indianapolis (IUPUI) / In this project, a chassis concept has been developed for a small electric vehicle ’minibus’. The vehicle is intended to be used as a transport between agricultural locations in Ethiopia to cities where the products can be sold. The objective is to develop a chassis that can house several different modular structures for the purposes of transporting refrigerated goods, a mobile power grid, or people. Literature studies have been conducted on current electric vehicle markets, battery markets, chassis materials, and optimal cross-sections. The battery housings have also been analyzed from an environmental perspective to account for conditions in Ethiopia. Based on this, it was found that a four-wheeled ’minibus’ design including space for approximately fourteen custom batteries is optimal. It is essential to keep in mind that this project has been carried out both on a conceptual level within the framework of a degree project as well as a production project for use in Ethiopian rural areas. This master thesis project aims to provide a solid benchmark for further development and research within the subject.

To analyze the impact of different objective functions and additive manufacturing (AM)constraints on structural topology optimization, it is necessary to perform an in-depth comparative study. This analysis should consider specific structural design factors, such as compliance, volume, or stress minimization, and assess their effects on the topology optimization for AM. In addition, the inclusion of AM constraints can have a significant influence on various aspects, including optimal part geometry, part volume, support structure volume, and structural performance. Thus, it is essential to examine and compare these factors to determine the optimal part design for AM. This study focuses on comparing topology optimization results obtained using compliance, stress, or multi-objective minimization, with and without AM constraints. The comparative analysis is conducted in the study, utilizing four structural design examples: cantilever beam, bridge-shaped structure, L-shaped beam and connecting rod. The comparison results provide insights into the effects of build orientation, AM constraints such as overhang, and different design objectives on the structural topology optimization for AM

Although additive manufacturing technologies are often referred to as "3D printing," the family of technologies typically deposit material on a layer-by-layer basis. For material extrusion (ME) in particular, the deposition process results in weak inter- and intra-layer bonds that reduce mechanical performance in those directions. Despite this shortcoming, ME offers the opportunity to specifically and preferentially align the reinforcement of a composite material throughout a part by customizing the toolpath. Recent developments in multi-axis deposition have demonstrated the ability to place material outside of the XY-plane, enabling depositions to align to any 3D (i.e., non-planar) vector. Although mechanical property improvements have been demonstrated, toolpath planning capabilities are limited; the geometries and load paths are restricted to surface-based structures, rather than fully 3D load paths. By specifically planning deposition paths (roads) where the composite reinforcement is aligned to the load paths within a structure, there is an opportunity for a step-change in the mechanical properties of ME parts. To achieve this goal for arbitrary geometries and load paths, the author presents a design and process planning workflow that concurrently optimizes the topology of the part and the toolpath used to fabricate it. The workflow i) identifies the optimal structure and road directions using topology optimization (TO), ii) plans roads aligned to those optimal directions, iii) orders those roads for collision-free deposition, and iv) translates that ordered set of roads to a robot-interpretable toolpath. A TO algorithm, capable of optimizing 3D material orientations, is presented and demonstrated in the context of 2D and 3D load cases. The algorithm achieved a 38% improvement in final solution compliance for a 3D Wheel problem relative to existing TO algorithms with planar orientation optimization considerations. Optimized geometries and their associated orientation fields were then propagated with the presented alignment-focused deposition path planner and conventional toolpath planners. The presented method resulted in a 97% correlation between the road directions and the orientation field, while the conventional methods only achieved 77%. A planar multi-load case was then fabricated using each of these methods and tested in both tension and bending; the presented alignment-focused method resulted in a 108.24% and 29.25% improvement in each load case, respectively. To evaluate the workflow in a multi-axis context, an inverted Wheel problem was optimized and processed by the workflow. The resulting toolpaths were then fabricated on a multi-axis deposition platform and mechanically evaluated relative to geometrically similar structures using a conventional toolpath planner. While the alignment in the multi-axis specimen was improved from the conventional method, the mechanical properties were reduced due to limitations of the multi-axis deposition platform. / Doctor of Philosophy / The material extrusion additive manufacturing process is widely used by hobbyists and industry professionals to produce demonstration parts, but the process is often overlooked for end-use, load bearing parts. This is due to the layer-by-layer fabrication method used to create the desired geometries; the bonding between layers is weaker than the direction material is deposited. If load paths acting on the printed structure travel across those layer interfaces, the part performance will decrease. Whereas gantry-based systems are forced into this layer-by-layer strategy, robotic arms allow the deposition head to rotate, which enables depositions to be placed outside of the XY-plane (i.e., the typical layer). If depositions are appropriately planned using this flexibility, the layer interfaces can be oriented away from the load paths such that all of the load acts on the (stronger) depositions. Although this benefit has been demonstrated in literature, the existing methods for planning robotic toolpaths have limits on printability; certain load paths and geometries cannot be printed due to concerns that the robotic system will collide with the part being printed. This work focuses on increasing the generality of these toolpath planning methods by enabling any geometry and set of load paths to be printed. This is achieved through three objectives: i) identify the load paths within the structure, ii) plan roads aligned to those load paths, iii) order those roads such that collisions will not occur. The author presents and evaluates a design workflow that addresses each of these three objectives by simultaneously optimizing the geometry of the part as well as the toolpath used to fabricate it. Planar and 3D load cases are optimized, processed using the presented workflow, and then fabricated on a multi-axis deposition platform. The resulting specimens are then mechanically tested and compared to specimens fabricated using conventional toolpath planning methods.

It is a common practice when designing a system to apply safety factors to the critical failure load or event. These safety factors provide a buffer against failure due to the random or un-modeled behavior, which may lead the system to exceed these limits. However these safety factors are not directly related to the likelihood of a failure event occurring. If the safety factors are poorly chosen, the system may fail unexpectedly or it may have a design which is too conservative. Reliability-Based Design Optimization (RBDO) is an alternative approach which directly considers the likelihood of failure by incorporating a reliability analysis step such as the First-Order Reliability Method (FORM). The FORM analysis requires the solution of an optimization problem however, so implementing this approach into an RBDO routine creates a double-loop optimization structure. For large problems such as Reliability-Based Topology Optimization (RBTO), numeric sensitivity analysis becomes computationally intractable. In this thesis, a general approach to the sensitivity analysis of nested functions is developed from the Lagrange Multiplier Theorem and then applied to several Reliability-Based Design Optimization problems, including topology optimization. The proposed approach is computationally efficient, requiring only a single solution of the FORM problem each iteration. / Master of Science

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.

When building aircrafts, structural components must be designed for high strength, low cost, and easy assembly.To meet these conditions structural components are often based upon previous designs, even if a new component is developed.Refining previous designs can be a good way of preserving knowledge but can also limit the exploration of new design concepts. Currently the design process for structural aircraft components at SAAB is managed by design engineers. The design engineer is responsible for ensuring the design meets requirements from several different disciplines such as structural analysis, manufacturing, tool design, and assembly.Therefore, the design engineer needs to have good communication with all disciplines and an effective flow of information. The previous design is refined, it is then reviewed and approved by adjacent disciplines.Reviewing designs is an iterative process, and when several disciplines are involved it quickly becomes time consuming.Any time the design is altered it has to be reviewed once more by all disciplines to ensure the change is acceptable.So there is a need for further customizing the design concept to decrease the number of iterations when reviewing. Design Space Exploration DSE is a well known method to explore design alternatives before implementation and is used to find new concepts.This thesis investigates if DSE can be used to facilitate the design process of structural aircraft components and if it can support the flow of information between different disciplines.To find a suitable discipline to connect with design a prestudy is conducted, investigating what information affect structural design and how it is managed.The information flow is concluded in a schematic diagram where structural analysis is chosen as additional discipline. By using topology optimization in a DSE, design and structural analysis are connected.The design space can be explored with regards to structural constraints.The thesis highlights the possibilities of using DSE with topology optimization for developing structural components and proposes a method for including it in the design process.

Este trabalho apresenta a aplicação do Método de Otimização Topológica (MOT) considerando restrição de tensão mecânica em dois problemas de Engenharia: o projeto de estruturas mecânicas sujeitas a restrição de tensão e o projeto da distribuição de material em estruturas constituídas por Materiais com Gradação Funcional (MsGF). O MOT é um método numérico capaz de fornecer de forma automática o leiaute básico de uma estrutura mecânica para que esta atenda a um dado requisito de projeto, como o limite sobre a máxima tensão mecânica no componente. Os MsGF são materiais cujas propriedades variam gradualmente com a posição. Este gradiente de propriedades é obtido através da variação contínua da microestrutura formada por dois materiais diferentes. Neste trabalho o MOT foi implementado utilizando o modelo de material Solid Isotropic Microstructure with Penalization (SIMP) e o campo de densidades foi parametrizado utilizando a abordagem Aproximação Contínua da Distribuição de Material (ACDM). O modelo de material e utilizado em conjunto com um localizador de tensões, de modo a representar as tensões nas regiões com densidade intermediária. O projeto de estruturas tradicionais através do MOT possui dois problemas centrais aqui tratados: o fenômeno das topologias singulares, que consiste na incapacidade do algoritmo de otimização de retirar material de certas regiões da estrutura, onde a tensão mecânica supera o limite de tensão quando os valores da densidade tendem a zero, e o problema do grande número de restrições envolvidas, pois que a tensão mecânica é uma grandeza local e deve ser restrita em todos os pontos da estrutura. Para tratar o primeiro problema é utilizado o conceito de relaxação. Para o segundo são utilizadas duas abordagens: uma é a substituição das restrições locais por uma restrição global e a outra é a aplicação do Método do Lagrangeano Aumentado. Ambas foram implementadas e aplicadas para o projeto de estruturas planas e axissimétricas. No projeto da distribuição de material em estruturas constituídas por MsGF é utilizado um modelo de material baseado na interpolação dos limites de Hashin-Shtrikman. A partir deste modelo as tensões em cada fase são obtidas a partir das matrizes localizadoras de tensão. Para tratar o fenômeno das topologias singulares é proposto um índice estimativo de falha, baseado nas tensões de von Mises em cada fase da microestrutura, que evita tal problema. O grande número de restrições é tratado através da restrição global de tensão. Em ambos os problemas as formulações são apresentadas e sua eficiência é discutida através de exemplos numéricos. / This work presents the Topology Optimization Method (TOM) with stress constraint applied to two Engineering problems: the design of mechanical structures subjected to stress constraint and the design of material distribution in structures made of Functionally Graded Materials (FGMs). The TOM is a numerical method capable of synthesizing the basic layout of a mechanical structure accomplishing to a given design requirement, for example the maximum stress in the structure. The FGMs are materials with spatially varying properties, which are obtained through a continuum change of the microstructuremade of two different materials. In this work, the TOM was implemented with Solid Isotropic Microstructure with Penalization (SIMP) material model and the density field was parameterized with the Continuous Approximations of Material Distribution. To obtain the intermediate density stresses, the material model is applied together with a stress localization matrix. The design of mechanical structures through the TOM has two major problems: the singular topology phenomenon, which is characterized by the optimization algorithm impossibility of removing material from certain regions, where the stress overpasses the limiting stress when the density goes to zero, and the large number of constraints, once the stress is a local value that must be constrained everywhere in the structure. To deal with the first problem, it is applied the \"-realaxation concept, and for the second one two approaches are considered: one is to change the local stress constraint into a global stress constraint and the other is to apply the Augmented Lagrangian Method. Both approaches were implemented and applied to the design of plane and axisymmetric structures. In the design of material distribution in structures made of FGMs a material model based on Hashin-Shtrikman bounds is applied. From this model, stresses in each phase are obtained by the stress localization matrix. To deal with the singular topology phenomenon it is proposed a modified von Mises failure criteria index that avoids such problem. A global stress constraint is applied to deal with the large number of constraints. In both problems formulations are presented and their performance are discussed through numerical examples.