This master’s thesis deals with analysis and following optimisation of a Sigma TN sports car suspension. Knowledge of vehicle dynamics and strength of materials was used during the optimisation. Kinematic and force analysis was carried out in software ADAMS Car. A FEM analysis was processed in Ansys Workbench environment. Three design concepts were worked out, in which Topology optimisation also found use.

Level set method is a boundary tracking method that uses an implicit function to define the boundary location. By using the implicit function to define the structural boundary the level set method can be used for topology optimisation. The level set method has previously been used to solve a range of structural optimisation problems. The aim of this thesis is to extend the application of the level set method to additional applications of structural optimisation. A robust method of 3D level set topology optimisation is developed and tested. The use of a hole insertion method was found to be advantageous, but not vital, for 3D level set topology optimisation. The level set method is used to optimise the internal structure of a proximal femur. Similarities between the optimal structure and real internal trabecular bone architecture suggest that the internal bone structure may be mechanically optimal. Stress constrained level set topology optimisation is performed in 2D. Stress shape sensitivities are derived and interpolated to obtain smooth boundary sensitivity, resulting in feasible stress constrained solution in numerical examples. A new generic objective hole insertion method is used to reduce dependence on the initial solution. A level set method for optimising the design of fibre angles in composite structures is also introduced. Fibre paths are implicitly defined using the level set function. Sensitivity analysis is used to update the level set function values and optimise the fibre path. The method implicitly ensures continuous fibre paths in the optimum solution, that could be manufactured using advanced fibre placement.

Adsorption is a retention mechanism of fluid molecules on solid surfaces and presents a wide range of applications, such as refrigeration, separation processes and fuel storage. This work describes the modelling of gas adsorption on porous media and presents an optimisation approach for the design of adsorption systems based on topology optimisation. A comprehensive formulation for the adsorption and desorption phenomena is presented, detailing the derivation of their weak forms and assembling the matrices for the implementation of the Finite Element Method (FEM). The sensitivities of objective functions to topology optimisation design variables are obtained by the adjoint method, which is presented in detail. The numerical implementation is aided by FEniCS and Dolfin Adjoint packages, resulting in a generic software for the optimisation of adsorption systems. The method is applied for the design of Adsorbed Natural Gas (ANG) tanks for on-demand consumption. Optimised tank layouts are proposed and compared with standard tanks, presenting improvement of the design objectives. / Adsorção é um mecanismo de retenção de moléculas de um fluido em superfícies sólidas e apresenta um vasto campo de aplicações, como em refrigeração, processos de separação e armazenamento de combustível. Este trabalho descreve o modelo de adsorção de gás em meios porosos e define uma abordagem de otimização de sistemas de adsorção baseada no Método de Otimização Topológica (MOT). Uma formulação abrangente para os fenômenos de adsorção e dessorção é apresentada, detalhando a dedução de seus formas fracas e montagem das matrizes para a implementação do Método dos Elementos Finitos (MEF). As sensibilidades das funções-objetivo em relação às variáveis de projeto são obtidas pelo método adjunto, que também é apresentado em detalhe. A implementação numérica é auxiliada pelos pacotes FEniCS e Dolfin Adjoint, originando uma ferramenta genérica para a otimização de sistemas de adsorção. Este método é aplicado ao projeto de tanques de Gás Natural Adsorvido (GNA) visando transporte, armazenamento e consumo. Tanques otimizados são propostos e comparados com tanques tradicionais, apresentando melhora dos objetivos de projeto.

Adsorption is a retention mechanism of fluid molecules on solid surfaces and presents a wide range of applications, such as refrigeration, separation processes and fuel storage. This work describes the modelling of gas adsorption on porous media and presents an optimisation approach for the design of adsorption systems based on topology optimisation. A comprehensive formulation for the adsorption and desorption phenomena is presented, detailing the derivation of their weak forms and assembling the matrices for the implementation of the Finite Element Method (FEM). The sensitivities of objective functions to topology optimisation design variables are obtained by the adjoint method, which is presented in detail. The numerical implementation is aided by FEniCS and Dolfin Adjoint packages, resulting in a generic software for the optimisation of adsorption systems. The method is applied for the design of Adsorbed Natural Gas (ANG) tanks for on-demand consumption. Optimised tank layouts are proposed and compared with standard tanks, presenting improvement of the design objectives. / Adsorção é um mecanismo de retenção de moléculas de um fluido em superfícies sólidas e apresenta um vasto campo de aplicações, como em refrigeração, processos de separação e armazenamento de combustível. Este trabalho descreve o modelo de adsorção de gás em meios porosos e define uma abordagem de otimização de sistemas de adsorção baseada no Método de Otimização Topológica (MOT). Uma formulação abrangente para os fenômenos de adsorção e dessorção é apresentada, detalhando a dedução de seus formas fracas e montagem das matrizes para a implementação do Método dos Elementos Finitos (MEF). As sensibilidades das funções-objetivo em relação às variáveis de projeto são obtidas pelo método adjunto, que também é apresentado em detalhe. A implementação numérica é auxiliada pelos pacotes FEniCS e Dolfin Adjoint, originando uma ferramenta genérica para a otimização de sistemas de adsorção. Este método é aplicado ao projeto de tanques de Gás Natural Adsorvido (GNA) visando transporte, armazenamento e consumo. Tanques otimizados são propostos e comparados com tanques tradicionais, apresentando melhora dos objetivos de projeto.

Disc brake calipers are subjected to complex mechanical loading and interaction of individual components in a typical brake assembly makes design improvement very challenging. To analyse caliper behaviour, complex Finite Element models were created and successfully validated using a variety of experimental techniques, including exceptionally suitable Digital Image Correlation. A novel methodology to optimise caliper design was developed, using non-linear contact Finite Element Analysis and topology optimisation, to generate lightweight, high performance brake calipers. The method was used on a Formula 1 brake assembly and significant improvement in structural design was achieved, with the new caliper being lighter and stiffer than the original. The same approach was used on more conventional 4 pistons calipers using various boundary conditions with particular focus on mass reduction and considerably lighter designs were achieved. The influence of specific features of the optimised calipers on the structural performance was also successfully investigated.

Additive manufacturing methods has been prevailing for several decades and the recent technological advancements brings in the flexibility and consideration for large-scale production in the industries. The components manufactured with these methods have wide variety of applications and therefore, it is crucial to investigate the mechanical performance of the printed parts. There have been many researches done to investigate the mechanical behaviour of polymer material but the studies are limited when it comes to the fatigue performance of the polymer parts printed using multi-jet fusion technology. The aim of the master thesis is to investigate the fatigue behaviour of polyamide12 (PA12) material with the components manufactured using HP’s multi-jet fusion 3D printing machine. Fatigue life is influenced by several factors such as the loading condition, the topology of the specimen, material properties, print quality and the environmental conditions. It is therefore essential to consider all these factors when developing the experiments for fatigue life prediction. The master thesis work can be divided into three sections. The first section focuses on evaluating the mechanical properties of polyamide12. This includes the quasi-static test for determining the tensile properties of specimens with the geometrical influence, the difference in properties in relation to the print directions, the influence of humidity and porosity over the mechanical performance of the material and finally the effect of internal heat generation and the surrounding temperature. The results show that the temperature and the quality of the specimens are the two major factors affecting the mechanical and fatigue performance of PA12. That being said, the next section focuses on setting up the fatigue experiments based on the data obtained from the static tests. When carrying out the experiment, both the test frequency and the surrounding temperature were foundto have a greater impact over the fatigue results. High test frequency showed a dramatic increase in the temperature of the specimen which caused an early failure. Hence, the experiments were developed in such a way that the influence of the thermal fatigue can be ignored by controlling the temperature of the specimen through a compressed air cooling system. The final section presents the findings, the conclusions about the material behaviour and the development of a finite element model to predict the fatigue life of a topology optimised demonstrator part using the data gathered from the experiments. / Additiva tillverkningsmetoder har använts i flera decennier och de senaste tekniska framstegen möjliggör flexibilitet och storskaliga produktionsprocesser. Komponenter tillverkade med dessa metoder har många olika tillämpningar inom industrin och därför är det avgörande att undersöka de tillverkade materialens mekaniska prestanda. Det har gjorts många undersökningar av det mekaniska beteendet hosmaterial som metaller och polymerer, men studierna är begränsade när det gäller utmattnings prestandan hos detaljer som tillverkats med multi-jet fusionsteknik.  Syftet med examensarbetet är att undersöka utmattnings beteendet hos polyamid-12 (PA12) tillverkat med hjälp av HP multi-jet fusion 3D-utskriftsteknik. Utmattnings livslängden påverkas av flera parametrar såsom belastnings tillståndet, provets topologi, materialegenskaper, utskrifts kvalitet och miljöförhållanden. Det är därför viktigt att ta hänsyn till alla dessa faktorer när man utvecklar experimenten för utmattnings karakterisering. Examensarbetet kan delas in i tre avsnitt. Det första avsnittet fokuserar på att utvärdera de mekaniska egenskaperna hos PA12. Detta inkluderar kvasi statisk provning för att bestämma drag egenskaperna hos prover med olika geometrier, skillnaden i egenskaper i förhållande till utskrifts riktningarna, inverkan av fukt och porositet på materialets mekaniska prestanda och slutligen effekten av yttre temperatur. Resultaten visar att temperaturen och kvaliteten på proverna är de faktorer som har störst inverkan på den mekaniska prestandan hos PA12. Med detta som utgångspunkt fokuserar nästa avsnitt på att sätta upp utmattnings experimenten baserat på data som erhållits från de statiska testerna. Under utformningen av experimenten visade sig test frekvensen och den omgivande temperaturen ha en stor inverkan på utmattnings resultaten. Hög test frekvens bidrog till en dramatisk ökning av temperaturen hos provet vilket resulterade i tidigt brott. Experimenten utformades därför på ett sätt så att termisk inverkan kan undvikas, genom att kontrollera provets yttre temperatur med ett trycklufts kylsystem. Det sista avsnittet presenterar resultaten, slutsatser om materialets beteende och utvecklingen av en finita element modell för att förutsäga utmattnings livslängden för en topologioptimerad demonstratören med hjälp av data som samlats in från experimenten.

Thesis (MScEng (Mechanical and Mechatronic Engineering))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: The development of light and sti aerospace structural panels is very important in the aerospace industry, e.g. a lighter satellite requires less fuel to launch it into space which in turn saves money for the owner of the satellite. This thesis describes the design, optimisation, manufacturing and testing of a ribbed light alloy core - carbon bre face sheets, sandwich-type, satellite panel operating at launch loading conditions (115 m/s2 accelerations and requiring a minimum structural natural frequency of 90 Hz) to determine the optimum sti ness per mass ratio of the panel. The panel layout was based on a satellite panel designed by SunSpace and Information Systems for the Sumbandila satellite. Only the black box mounting positions of the original panel were used in the optimisation of the new panel. The core of the evaluation panel was manufactured from aluminium (6082-T6). The carbon bre skins were manufactured from unidirectional high modulus carbon bre (K63712) in a [0/90/0] wet layup with the 0± direction in the longitudinal direction of the panel. A three-dimensional model of the panel consisting of 3D wedge elements and containing all the boundary conditions was modelled with the use of the nite element software MSC Patran. The model was optimised with the use of optimisation software Genesis to locate the rib positions. Genesis removes all the elements containing the least amount of stress; only 30% of the core elements were kept while restricting the elements to form an extruded con guration (for milling machining) throughout the thickness of the panel. The rib elements remaining were replaced in MSC Patran by shell elements and the shell element thicknesses were optimised with the use of Genesis to ensure the lightest and sti est possible structure. The optimised rib thicknesses were imported into MSC Patran and the numerically optimised model could then be analysed with MSC Nastran. The numerical model was converted into a manufacturable structure and the core was machined from a solid aluminium sheet. The ribs were machined in the shape of an Ibeam to allow for minimum weight and a su cient bonding area for the two carbon bre face sheets. Elevated circular surfaces, protruding through the carbon bre sheets, were machined in the position of the black box mountings to allow for better heat transfer away from the black boxes. The carbon bre face sheets were bonded to the metal core (3M Scotch-Weld 9323 B/A). The nished panel was put through various tests to determine whether it is suitable for use in the aviation industry. The tests included modal testing, random vibration testing and temperature testing to determine if the structure is durable enough for use in satellites. The test results are promising and show that a substantive amount of money can be saved by reducing the mass on the structure. By using optimisation software and ribbed light alloy - carbon bre face sheets sandwich structures the performance of the structures can be improved without adding mass to the structure. / AFRIKAANSE OPSOMMING: Die ontwikkeling van ligter en stywer lugvaartstruktuur panele is baie belangrik in die lugvaart-industrie, bv. 'n ligter satelliet benodig minder brandstof om tot in 'n wentelbaan lanseer te word. Dit bespaar sodoende lanseerkostes vir die eienaar van die satelliet. In die verslag word die ontwerp, optimering, vervaardiging en toets van 'n gewebde, ligte allooi kern - koolstofveselvel, saamgestelde materiaal, satelliet struktuurpaneel wat onderwerp word aan lanseer belastingstoestande van ongeveer 115 m/s2 versnellings ondersoek. Die tegnieke word gebruik om die optimale styfheid per eenheidsmassa-verhouding te bepaal. Die paneel benodig 'n minimum strukturele eerste natuurlike frekwensie van 90 Hz. Die basiese paneel uitleg is verkry vanaf 'n satellietpaneel wat deur SunSpace and Information Systems ontwerp is vir die basisplaat van die Sumbandila satelliet. Die enigste geometrie wat van die oorspronklike struktuur behou is om die nuwe struktuur te optimeer is die vashegtingspunt-posisies van die swart-kassies. Die kern van die ge-optimeerde struktuur is vervaardig uit gemasjieneerde aluminium (6082-T6). Die koolstofvesel-velle is vervaardig uit enkelrigting hoë-modulus koolstofvesel-doek (K63712). Die oplegging is gedoen met 'n nat-opleggingsproses waar die drie lae van elke vel 'n [0/90/0] oriëntasie het met, die 0± lae in die langsrigting van die paneel. 'n Drie-dimensionele eindige element model van die paneel is geskep met behulp van die MSC Patran sagteware pakket met die model hoofsaaklik opgebou uit 3D wig-elemente. Al die lanseertuig vashegtingsrandwaardes is in die eindige element model ingebou. Om die web posisies te bepaal is die Genesis optimeringsagteware pakket gebruik. Verskeie ontwerpsvoorwaardes is gespesi seer waaraan die optimeringsproses moes voldoen. Slegs 30% van die wig-elemente mag behoue bly in die optimeringsproses en al die elemente deur die dikte van die paneel moet of behou of verwyder word. Dit verseker dat die resultaat masjieneerbaar is met 'n freesmasjien. Die oorblywende wig-elemente is in MSC Patran vervang met dop-elemente. Die dopelemente se diktes is ge-optimeer met Genesis om die ligste en styfste struktuur moontlik te kry. Die ge-optimeerde dop-element diktes is in die MSC Patran model ingetrek. Die numeries ge-optimeerde model is daarna met behulp van MSC Nastran ge-analiseer. Nadat die numeriese model omgeskakel is in 'n vervaardigbare struktuur is die kern gemasjieneer uit 'n soliede blok aluminium. Die webbe is ontwerp en vervaardig in 'n I-balk vorm. Dit laat toe dat die webbe 'n minimum gewig en genoegsame area het waarop die koolstofvesel velle geheg kan word. Verhewe vlakke is gemasjieneer op die aluminium kern in die posisies van die swart-kassie vashegtingpunte. Hierdie verhewe vlakke steek deur die koolstofvesel-vel aan die kant waar die swart-kassies vasgeheg word. Dit verseker 'n metaal-op-metaal verbinding tussen die kern en die swart-kassies vir beter hittegeleiding. 3M Scotch-Weld 9323 B/A epoksie is gebruik om die koolstofvesel-velle aan die aluminium kern te heg. Die voltooide struktuur is aan 'n reeks toetse onderwerp om te bepaal of dit geskik is om in die ruimtevaart-industrie gebruik te kan word. Dit sluit modale toetse, lukrake vibrasie toetse en temperatuursverandering toetse in. Die toetsresultate sal bepaal of die struktuur duursaam genoeg is om in satelliete gebruik te word. Die toetsresultate is belowend en dui daarop dat deur massa te bespaar op die struktuur, 'n aansienlike bedrag op satelliet lanseer-kostes bespaar kan word. Deur optimeringsagteware tesame met gewebde ligte allooi kern - koolstofvesel vel, saamgestelde materiaal strukture te gebruik kan die werksverrigting van die strukture verbeter sonder dat massa bygevoeg word.

We present a level-set algorithm for topology optimisation and demonstrate its capabilities and advantages in a variety of settings. The algorithm uses discrete element densities so that interpolation schemes are avoided and the boundary of the design is always well defined. A review of the level-set method for topology optimisation, and a description of the mathematical concepts behind the level-set algorithm are given in the introductory chapters. A compact Matlab implementation of the algorithm provides explicit implementation details for the simple example of compliance minimisation with a volume constraint. The remainder of the thesis presents original results obtained using the level-set algorithm. As a new application, we use topology optimisation to maximise fracture resistance. Fracture resistance is assumed to be related to the elastic energy released by a crack propagating in a normal direction from parts of the boundary that are in tension. We develop a suitable fracture resistance objective functional, derive its shape derivative and apply the level-set algorithm to simple examples. Topology optimisation methods that involve intermediate density elements are not suitable to solve this problem because the boundary of the design is not well defined. Our results indicate that the algorithm correctly optimises for fracture resistance. As the method is computationally intensive, we suggest simpler objective functionals that could be used as a proxy for fracture resistance. For example, a perimeter penalty could be added to the compliance objective functional in conjunction with a non-linear elasticity law where the Young's modulus in tension is lower than in compression. The level-set method has only recently been applied to fluid flow problems. We utilise the level-set algorithm to minimise energy dissipation in Stokes flows in both two and three dimensions. The discrete element densities allow the no-slip boundary condition to be applied directly. The Stokes equations therefore need only be solved in the fluid region of the design: this results in significant computational savings compared to conventional material distribution approaches. In order to quantify the computational savings the optimisation problems are resolved using an interpolation scheme to simulate the no-slip boundary condition. This significant advantage of the level-set method for fluid flow problems has not been noted by other authors. The algorithm produces results consistent with those obtained by other topology optimisation approaches, and solves large-scale three dimensional problems with modest computational cost. The first examples of three dimensional periodic microstructure design with the level-set method are presented in this thesis. The level-set algorithm is extended to deal with multiple constraints. This is needed so that materials can be designed with symmetry requirements imposed on their effective properties. To demonstrate the capabilities of the approach, unit cells are designed separately to maximise conductivity and bulk modulus with an isotropy requirement. The resulting materials have properties very close to the relevant Hashin-Shtrikman bounds. The algorithm is then applied to multifunctional material design: unit cells are designed to give isotropic materials that have maximum bulk modulus and maximum conductivity. Cross-property bounds indicate the near-optimality of the microstructures obtained. The design space of the problem is extensively explored with different coefficients of the conductivity and bulk modulus in the objective and different volume constraints. We hypothesise the existence of theoretically optimal single-scale microstructures with the topologies of the computationally optimised microstructures we have found. Structures derived from the Schwartz primitive (P) and diamond (D) minimal surfaces have previously been presented as good multifunctional composites. These structures are elastically anisotropic. Although they have similar conductivity, they have stiffness properties inferior to several of the isotropic optimised microstructures.

We present a level-set algorithm for topology optimisation and demonstrate its capabilities and advantages in a variety of settings. The algorithm uses discrete element densities so that interpolation schemes are avoided and the boundary of the design is always well defined. A review of the level-set method for topology optimisation, and a description of the mathematical concepts behind the level-set algorithm are given in the introductory chapters. A compact Matlab implementation of the algorithm provides explicit implementation details for the simple example of compliance minimisation with a volume constraint. The remainder of the thesis presents original results obtained using the level-set algorithm. As a new application, we use topology optimisation to maximise fracture resistance. Fracture resistance is assumed to be related to the elastic energy released by a crack propagating in a normal direction from parts of the boundary that are in tension. We develop a suitable fracture resistance objective functional, derive its shape derivative and apply the level-set algorithm to simple examples. Topology optimisation methods that involve intermediate density elements are not suitable to solve this problem because the boundary of the design is not well defined. Our results indicate that the algorithm correctly optimises for fracture resistance. As the method is computationally intensive, we suggest simpler objective functionals that could be used as a proxy for fracture resistance. For example, a perimeter penalty could be added to the compliance objective functional in conjunction with a non-linear elasticity law where the Young's modulus in tension is lower than in compression. The level-set method has only recently been applied to fluid flow problems. We utilise the level-set algorithm to minimise energy dissipation in Stokes flows in both two and three dimensions. The discrete element densities allow the no-slip boundary condition to be applied directly. The Stokes equations therefore need only be solved in the fluid region of the design: this results in significant computational savings compared to conventional material distribution approaches. In order to quantify the computational savings the optimisation problems are resolved using an interpolation scheme to simulate the no-slip boundary condition. This significant advantage of the level-set method for fluid flow problems has not been noted by other authors. The algorithm produces results consistent with those obtained by other topology optimisation approaches, and solves large-scale three dimensional problems with modest computational cost. The first examples of three dimensional periodic microstructure design with the level-set method are presented in this thesis. The level-set algorithm is extended to deal with multiple constraints. This is needed so that materials can be designed with symmetry requirements imposed on their effective properties. To demonstrate the capabilities of the approach, unit cells are designed separately to maximise conductivity and bulk modulus with an isotropy requirement. The resulting materials have properties very close to the relevant Hashin-Shtrikman bounds. The algorithm is then applied to multifunctional material design: unit cells are designed to give isotropic materials that have maximum bulk modulus and maximum conductivity. Cross-property bounds indicate the near-optimality of the microstructures obtained. The design space of the problem is extensively explored with different coefficients of the conductivity and bulk modulus in the objective and different volume constraints. We hypothesise the existence of theoretically optimal single-scale microstructures with the topologies of the computationally optimised microstructures we have found. Structures derived from the Schwartz primitive (P) and diamond (D) minimal surfaces have previously been presented as good multifunctional composites. These structures are elastically anisotropic. Although they have similar conductivity, they have stiffness properties inferior to several of the isotropic optimised microstructures.

PhD by portfolio. Research aim: To investigate if topology optimisation can be used for the development of mechanical structures exposed to large (non-linear) deformations. Research objectives: 1. Analyse and critically evaluate the potential for using state of the art commercially available Finite Element software (and associated topology optimisation algorithms) for topology optimisation of structures exposed to large-deformations. 2. Based on 1 (where feasible) suggest, develop and critically appraise opportunities, methodologies and tools for enhancing the accuracy and precision of current state of the art topology optimisation algorithms for non-linear applications. 3. Based on the outcomes of 1 and 2 define / refine and integrate a topology optimisation algorithm / methodology with enhanced levels of accuracy for structures exposed to large (non-linear) deformations. 4. Critically analyse and assess the outcomes of the tool developed in 3 to competing algorithms and “sound engineering judgement” using case-studies and objectively evaluate the potential for further development/refinement of the proposed algorithm/methodology.