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

Intelligent methods for optimization design of lightweight fiber-reinforced composite structures: A review and the-state-of-the-art

As the application of lightweight fiber-reinforced composite structures reaches an unprecedented scale in industry, design technology for composite structures becomes crucial for enhancing performance, improving productivity, and reducing cost. In recent years, the rapid development of intelligent technology, such as big data, deep learning, and machine learning, has promoted the development of design technology. However, the current situation and intellectualization of the design technology is not well summarized. This paper reviews the advance in design technologies for fiber-reinforced composite structures, including prediction and optimization methods for composite properties. Then, their intellectualization development is overviewed. Finally, the development trend of intelligent design technologies and intelligent composite structures are discussed. This work can provide a reference for researchers in the related field

Development of a multi-objective optimization algorithm based on lichtenberg figures

This doctoral dissertation presents the most important concepts of multi-objective optimization and a systematic review of the most cited articles in the last years of this subject in mechanical engineering. The State of the Art shows a trend towards the use of metaheuristics and the use of a posteriori decision-making techniques to solve engineering problems. This fact increases the demand for algorithms, which compete to deliver the most accurate answers at the lowest possible computational cost. In this context, a new hybrid multi-objective metaheuristic inspired by lightning and Linchtenberg Figures is proposed. The Multi-objective Lichtenberg Algorithm (MOLA) is tested using complex test functions and explicit contrainted engineering problems and compared with other metaheuristics. MOLA outperformed the most used algorithms in the literature: NSGA-II, MOPSO, MOEA/D, MOGWO, and MOGOA. After initial validation, it was applied to two complex and impossible to be analytically evaluated problems. The first was a design case: the multi-objective optimization of CFRP isogrid tubes using the finite element method. The optimizations were made considering two methodologies: i) using a metamodel, and ii) the finite element updating. The last proved to be the best methodology, finding solutions that reduced at least 45.69% of the mass, 18.4% of the instability coefficient, 61.76% of the Tsai-Wu failure index and increased by at least 52.57% the natural frequency. In the second application, MOLA was internally modified and associated with feature selection techniques to become the Multi-objective Sensor Selection and Placement Optimization based on the Lichtenberg Algorithm (MOSSPOLA), an unprecedented Sensor Placement Optimization (SPO) algorithm that maximizes the acquired modal response and minimizes the number of sensors for any structure. Although this is a structural health monitoring principle, it has never been done before. MOSSPOLA was applied to a real helicopter’s main rotor blade using the 7 best-known metrics in SPO. Pareto fronts and sensor configurations were unprecedentedly generated and compared. Better sensor distributions were associated with higher hypervolume and the algorithm found a sensor configuration for each sensor number and metric, including one with 100% accuracy in identifying delamination considering triaxial modal displacements, minimum number of sensors, and noise for all blade sections.Esta tese de doutorado traz os conceitos mais importantes de otimização multi-objetivo e uma revisão sistemática dos artigos mais citados nos últimos anos deste tema em engenharia mecânica. O estado da arte mostra uma tendência no uso de meta-heurísticas e de técnicas de tomada de decisão a posteriori para resolver problemas de engenharia. Este fato aumenta a demanda sobre os algoritmos, que competem para entregar respostas mais precisas com o menor custo computacional possível. Nesse contexto, é proposta uma nova meta-heurística híbrida multi-objetivo inspirada em raios e Figuras de Lichtenberg. O Algoritmo de Lichtenberg Multi-objetivo (MOLA) é testado e comparado com outras metaheurísticas usando funções de teste complexas e problemas restritos e explícitos de engenharia. Ele superou os algoritmos mais utilizados na literatura: NSGA-II, MOPSO, MOEA/D, MOGWO e MOGOA. Após validação, foi aplicado em dois problemas complexos e impossíveis de serem analiticamente otimizados. O primeiro foi um caso de projeto: otimização multi-objetivo de tubos isogrid CFRP usando o método dos elementos finitos. As otimizações foram feitas considerando duas metodologias: i) usando um meta-modelo, e ii) atualização por elementos finitos. A última provou ser a melhor metodologia, encontrando soluções que reduziram pelo menos 45,69% da massa, 18,4% do coeficiente de instabilidade, 61,76% do TW e aumentaram em pelo menos 52,57% a frequência natural. Na segunda aplicação, MOLA foi modificado internamente e associado a técnicas de feature selection para se tornar o Seleção e Alocação ótima de Sensores Multi-objetivo baseado no Algoritmo de Lichtenberg (MOSSPOLA), um algoritmo inédito de Otimização de Posicionamento de Sensores (SPO) que maximiza a resposta modal adquirida e minimiza o número de sensores para qualquer estrutura. Embora isto seja um princípio de Monitoramento da Saúde Estrutural, nunca foi feito antes. O MOSSPOLA foi aplicado na pá do rotor principal de um helicóptero real usando as 7 métricas mais conhecidas em SPO. Frentes de Pareto e configurações de sensores foram ineditamente geradas e comparadas. Melhores distribuições de sensores foram associadas a um alto hipervolume e o algoritmo encontrou uma configuração de sensor para cada número de sensores e métrica, incluindo uma com 100% de precisão na identificação de delaminação considerando deslocamentos modais triaxiais, número mínimo de sensores e ruído para todas as seções da lâmina

Free vibration analysis and design optimization of SMA/Graphite/Epoxy composite shells in thermal environments

Composite shells, which are being widely used in engineering applications, are often under thermal loads. Thermal loads usually bring thermal stresses in the structure which can significantly affect its static and dynamic behaviors. One of the possible solutions for this matter is embedding Shape Memory Alloy (SMA) wires into the structure. In the present study, thermal buckling and free vibration of laminated composite cylindrical shells reinforced by SMA wires are analyzed. Brinson model is implemented to predict the thermo-mechanical behavior of SMA wires. The natural frequencies and buckling temperatures of the structure are obtained by employing Generalized Differential Quadrature (GDQ) method. GDQ is a powerful numerical approach which can solve partial differential equations. A comparative study is carried out to show the accuracy and efficiency of the applied numerical method for both free vibration and buckling analysis of composite shells in thermal environment. A parametric study is also provided to indicate the effects of like SMA volume fraction, dependency of material properties on temperature, lay-up orientation, and pre-strain of SMA wires on the natural frequency and buckling of Shape Memory Alloy Hybrid Composite (SMAHC) cylindrical shells. Results represent the fact that SMAs can play a significant role in thermal vibration of composite shells. The second goal of present work is optimization of SMAHC cylindrical shells in order to maximize the fundamental frequency parameter at a certain temperature. To this end, an eight-layer composite shell with four SMA-reinforced layers is considered for optimization. The primary optimization variables are the values of SMA angles in the four layers. Since the optimization process is complicated and time consuming, Genetic Algorithm (GA) is performed to obtain the orientations of SMA layers to maximize the first natural frequency of structure. The optimization results show that using an optimum stacking sequence for SMAHC shells can increase the fundamental frequency of the structure by a considerable amount

Adaptive chaotic particle swarm algorithm for isogeometric multi-objective size optimization of FG plates

An effective multi-objective optimization methodology that combines the isogeometric analysis (IGA) and adaptive chaotic particle swarm algorithm is presented for optimizing ceramic volume fraction (CVF) distribution of functionally graded plates (FGPs) under eigenfrequencies. The CVF distribution is represented by the B-spline basis function. Mechanical behaviors of FGPs are obtained with NURBS-based IGA and the recently developed simple first-order shear theory. The design variables are the CVFs at control points in the thickness direction, and the optimization objective is to minimize the mass of structure and maximize the first natural frequency. A recently developed multi-objective adaptive chaotic particle swarm algorithm with high efficiency is employed as an optimizer. All desirable features of the developed approach will be illustrated through four numerical examples, confirming its effectiveness and reliability

Form Follows Force: A theoretical framework for Structural Morphology, and Form-Finding research on shell structures

The springing up of freeform architecture and structures introduces many challenges to structural engineers. The main challenge is to generate structural forms with high structural efficiency subject to the architectural space constraints during the conceptual structural design process. Structural Morphology is the study of the relation between form and force, which can be considered the guiding theory for this challenge. The relation between form and force is important for all types of structures during the entire structural design process. Thus, Structural Morphology has a wide range of related research subjects and multiple research approaches. Therefore, Structural Morphology has gained neither a clear definition nor a unified methodology. In the present research, a theoretical framework for Structural Morphology has been proposed, that provides an effective solution to the challenge mentioned above. To enrich the proposed framework of Structural Morphology, systematic Form-Finding research on shell structures is conducted. Shell structures, the structural efficiency of which depends strongly on their 3D shape, have particular problems regarding the relationship between form and force. To obtain a structurally efficient shell, the form should follow the flow of forces, and a process of Form-Finding can achieve this. In this thesis, Form-Finding of shells indicates a process of generating the equilibrium structural forms of hanging, tent or pneumatic physical models. In Chapters 2 and 3, a theoretical framework for Structural Morphology is established. Structural systems are divided into two categories based on their responses under the loads: ‘Force-Active’ and ‘Force-Passive’. A ‘Force-Active’ structural system can significantly and actively adjust its shape due to the loads, while a ‘Force-Passive’ system cannot. A generic conceptual model of the numerical analysis process of structural systems is presented, which is suitable to both categories of structural systems. This conceptual model includes three parts: (1) the initial system described by five categories of parameters: geometry, material distribution, material properties, boundary conditions and forces; (2) the setup of equations and calculation methods to handle the above parameters; and (3) the structural performance described by two categories of parameters: the structural form and its mechanical behaviour (Chapter 2). A conceptual model of Structural Morphology is proposed by adding further requirements of the structural form or the mechanical behaviour and an optimisation process into the above conceptual model of the numerical analysis process of structural systems. Then, a corresponding conceptual formula of Structural Morphology is concluded. Thus, a theoretical framework of Structural Morphology is established. Subsequently, its feasibility is validated by a comprehensive discussion of the two main aspects of Structural Morphology, including ‘Form-Finding’ and ‘Structural Optimisation’. In this research, Form- Finding relates to Force-Active structural systems, which means the generation of multiple equilibrium shapes subject to architectural space constraints. Structural Optimisation relates to Force-Passive structural systems, which indicates the adjustment of relevant parameters of the initial structural system with the aim of improving its mechanical behaviour. The methodology of both aspects is presented. Research achievements completed by the author’s research groups from Harbin Institute of Technology (HIT) and Delft University of Technology (TU Delft) are presented to validate the feasibility. These achievements cover the research on Form-Finding of cable-nets and membrane structures, and on the Structural Optimisation of shells and gridshells (Chapter 3). In Chapters 4 to 7, the proposed theoretical framework for Structural Morphology is enriched by systemic Form-Finding research on shell structures. To study the form of shell structures, the curvature analysis of the surface is displayed. To study the mechanical behaviour of shell structures during the conceptual structural design process, an assessment strategy based on its linear static behaviour and buckling behaviour under two different load cases is proposed. To comprehensively study the linear static behaviour of a shell structure where bending moments may or may not be dominant in this shell, the membrane over the total stress ratios and strain-energy ratio are introduced (Chapter 4). The Vector Form Intrinsic Finite Element (VFIFE) method is a recently developed numerical analysis method. At the beginning of this research, few studies on the Form-Finding of shell structures using the VFIFE method were found in the literature. The VFIFE method is applied to generate equilibrium shapes of Force-Active structural systems and thus the structural geometries of shells. A MATLAB script and a plug-in in the Rhino-Grasshopper platform are developed (Chapter 5). Form-Control of Force-Active structural systems aims to generate form-found structural forms subject to the required architectural space constraints. Two Form-Control strategies are developed by combining two simple optimisation algorithms (the Newton-Raphson method and the inverse iteration method) with the VFIFE method. These strategies can help designers determine the structurally efficient forms more easily and more efficiently than some relatively complicated and time-consuming optimisation algorithms (Chapter 6). Based on the proposed theoretical framework of Structural Morphology, multiple structural forms of form-found shell structures are obtained by adjusting the five categories of parameters of the initial structural systems. This work can efficiently and effectively provide multiple structural forms with reasonable mechanical behaviour for designers from the perspective of structural engineers (Chapter 7). In Chapters 8 and 9, the specific influence of curved supports on the structural forms and the mechanical behaviour of these shells is studied. Intuitively and qualitatively, designers may be able to select the correct shapes for the supports of shells. However, there was a need to quantify the consequences of designing particular shell supports. In this work, form-found shells with slightly different support shapes are analysed numerically and experimentally. Four hexagonal form-found shells generated from hanging models with different support shapes but with the same target point are generated. The following four support shapes are considered: straight supports, outwardcurved supports, inward-curved supports and strongly inward-curved supports. From the numerical comparison, slight changes of the support shapes have a relatively small influence on the equilibrium structural forms but have a considerable influence on the mechanical behaviour of these form-found shells. It is concluded that we can improve structural efficiency by slightly curving the supports during the Form-Finding process, which would not significantly change the architect’s design scheme (Chapter 8). In the experimental research, three scaled plastic shell models (with straight supports, outward-curved supports, and inward-curved supports) are tested, and the shadow Moiré method is used in the observation of the deformation of the shells. Form these tests, the influence of the support shapes on form-found shells is studied visually by these obtained Moiré patterns, which represent the buckling modes of these shell models influenced by the curvature distribution near the supports as well as thickness distribution (Chapter 9). There are still issues that need to be solved in future research. For instance, the theoretical framework for Structural Morphology needs to be enriched with Structural Optimisation work, more complicated design constraints need to be considered in the Form-Finding process of shell structures (for example, the stress level or distribution in the shell), and more influence factors of the form-found shells need to be researched (for example, the number or length of the supports, and edge beams)

Form Follows Force:

The springing up of freeform architecture and structures introduces many challenges to structural engineers. The main challenge is to generate structural forms with high structural efficiency subject to the architectural space constraints during the conceptual structural design process. Structural Morphology is the study of the relation between form and force, which can be considered the guiding theory for this challenge. The relation between form and force is important for all types of structures during the entire structural design process. Thus, Structural Morphology has a wide range of related research subjects and multiple research approaches. Therefore, Structural Morphology has gained neither a clear definition nor a unified methodology. In the present research, a theoretical framework for Structural Morphology has been proposed, that provides an effective solution to the challenge mentioned above. To enrich the proposed framework of Structural Morphology, systematic Form-Finding research on shell structures is conducted. Shell structures, the structural efficiency of which depends strongly on their 3D shape, have particular problems regarding the relationship between form and force. To obtain a structurally efficient shell, the form should follow the flow of forces, and a process of Form-Finding can achieve this. In this thesis, Form-Finding of shells indicates a process of generating the equilibrium structural forms of hanging, tent or pneumatic physical models. In Chapters 2 and 3, a theoretical framework for Structural Morphology is established. Structural systems are divided into two categories based on their responses under the loads: ‘Force-Active’ and ‘Force-Passive’. A ‘Force-Active’ structural system can significantly and actively adjust its shape due to the loads, while a ‘Force-Passive’ system cannot. A generic conceptual model of the numerical analysis process of structural systems is presented, which is suitable to both categories of structural systems. This conceptual model includes three parts: (1) the initial system described by five categories of parameters: geometry, material distribution, material properties, boundary conditions and forces; (2) the setup of equations and calculation methods to handle the above parameters; and (3) the structural performance described by two categories of parameters: the structural form and its mechanical behaviour (Chapter 2). A conceptual model of Structural Morphology is proposed by adding further requirements of the structural form or the mechanical behaviour and an optimisation process into the above conceptual model of the numerical analysis process of structural systems. Then, a corresponding conceptual formula of Structural Morphology is concluded. Thus, a theoretical framework of Structural Morphology is established. Subsequently, its feasibility is validated by a comprehensive discussion of the two main aspects of Structural Morphology, including ‘Form-Finding’ and ‘Structural Optimisation’. In this research, Form- Finding relates to Force-Active structural systems, which means the generation of multiple equilibrium shapes subject to architectural space constraints. Structural Optimisation relates to Force-Passive structural systems, which indicates the adjustment of relevant parameters of the initial structural system with the aim of improving its mechanical behaviour. The methodology of both aspects is presented. Research achievements completed by the author’s research groups from Harbin Institute of Technology (HIT) and Delft University of Technology (TU Delft) are presented to validate the feasibility. These achievements cover the research on Form-Finding of cable-nets and membrane structures, and on the Structural Optimisation of shells and gridshells (Chapter 3). In Chapters 4 to 7, the proposed theoretical framework for Structural Morphology is enriched by systemic Form-Finding research on shell structures. To study the form of shell structures, the curvature analysis of the surface is displayed. To study the mechanical behaviour of shell structures during the conceptual structural design process, an assessment strategy based on its linear static behaviour and buckling behaviour under two different load cases is proposed. To comprehensively study the linear static behaviour of a shell structure where bending moments may or may not be dominant in this shell, the membrane over the total stress ratios and strain-energy ratio are introduced (Chapter 4). The Vector Form Intrinsic Finite Element (VFIFE) method is a recently developed numerical analysis method. At the beginning of this research, few studies on the Form-Finding of shell structures using the VFIFE method were found in the literature. The VFIFE method is applied to generate equilibrium shapes of Force-Active structural systems and thus the structural geometries of shells. A MATLAB script and a plug-in in the Rhino-Grasshopper platform are developed (Chapter 5). Form-Control of Force-Active structural systems aims to generate form-found structural forms subject to the required architectural space constraints. Two Form-Control strategies are developed by combining two simple optimisation algorithms (the Newton-Raphson method and the inverse iteration method) with the VFIFE method. These strategies can help designers determine the structurally efficient forms more easily and more efficiently than some relatively complicated and time-consuming optimisation algorithms (Chapter 6). Based on the proposed theoretical framework of Structural Morphology, multiple structural forms of form-found shell structures are obtained by adjusting the five categories of parameters of the initial structural systems. This work can efficiently and effectively provide multiple structural forms with reasonable mechanical behaviour for designers from the perspective of structural engineers (Chapter 7). In Chapters 8 and 9, the specific influence of curved supports on the structural forms and the mechanical behaviour of these shells is studied. Intuitively and qualitatively, designers may be able to select the correct shapes for the supports of shells. However, there was a need to quantify the consequences of designing particular shell supports. In this work, form-found shells with slightly different support shapes are analysed numerically and experimentally. Four hexagonal form-found shells generated from hanging models with different support shapes but with the same target point are generated. The following four support shapes are considered: straight supports, outwardcurved supports, inward-curved supports and strongly inward-curved supports. From the numerical comparison, slight changes of the support shapes have a relatively small influence on the equilibrium structural forms but have a considerable influence on the mechanical behaviour of these form-found shells. It is concluded that we can improve structural efficiency by slightly curving the supports during the Form-Finding process, which would not significantly change the architect’s design scheme (Chapter 8). In the experimental research, three scaled plastic shell models (with straight supports, outward-curved supports, and inward-curved supports) are tested, and the shadow Moiré method is used in the observation of the deformation of the shells. Form these tests, the influence of the support shapes on form-found shells is studied visually by these obtained Moiré patterns, which represent the buckling modes of these shell models influenced by the curvature distribution near the supports as well as thickness distribution (Chapter 9). There are still issues that need to be solved in future research. For instance, the theoretical framework for Structural Morphology needs to be enriched with Structural Optimisation work, more complicated design constraints need to be considered in the Form-Finding process of shell structures (for example, the stress level or distribution in the shell), and more influence factors of the form-found shells need to be researched (for example, the number or length of the supports, and edge beams)

Optimization of the natural frequency of hybrid, multi-scale graphene/fibre reinforced nanocomposite laminates.

Masters Degree. University of KwaZulu-Natal, Durban.The optimal solution of the natural vibration problem is investigated in this thesis, for a hybrid, multi-scale graphene/fibre reinforced composite laminate plate. Although several research outputs have been published on the optimization of traditional fibre reinforced composites, the investigation of the reinforcement of these composites by adding a nanomaterial, is still an open topic. The fundamental frequency is optimized within a Sequential Quadratic Programming algorithm. Micromechanics equations are used to produce the effective material properties of the 3-phase laminate plate and finite element analysis is adopted to derive the natural frequencies. Several design variables are considered in the optimization problem, emphasizing in the influence of graphene nanoplatelets‘ weight on the optimal vibration response. Results indicate the optimal distribution of graphene in the laminate for several stacking sequences, boundary conditions and different fibre types (glass or carbon). It is shown that a non-uniform distribution of graphene along the layers of the laminate, results in optimal vibration response. The boundary conditions, as well as the type of fibres (glass or carbon) also affect significantly the natural frequencies

Active thermography for the investigation of corrosion in steel surfaces

The present work aims at developing an experimental methodology for the analysis of corrosion phenomena of steel surfaces by means of Active Thermography (AT), in reflexion configuration (RC). The peculiarity of this AT approach consists in exciting by means of a laser source the sound surface of the specimens and acquiring the thermal signal on the same surface, instead of the corroded one: the thermal signal is then composed by the reflection of the thermal wave reflected by the corroded surface. This procedure aims at investigating internal corroded surfaces like in vessels, piping, carters etc. Thermal tests were performed in Step Heating and Lock-In conditions, by varying excitation parameters (power, time, number of pulse, ….) to improve the experimental set up. Surface thermal profiles were acquired by an IR thermocamera and means of salt spray testing; at set time intervals the specimens were investigated by means of AT. Each duration corresponded to a surface damage entity and to a variation in the thermal response. Thermal responses of corroded specimens were related to the corresponding corrosion level, referring to a reference specimen without corrosion. The entity of corrosion was also verified by a metallographic optical microscope to measure the thickness variation of the specimens