[pt] Este trabalho tem por objetivo apresentar um sistema integrado para otimização de forma de estruturas planas que tenham comportamento elasto-plástico. A metodologia implementada propõe uma alternativa à forma conservadora com que tradicionalmente as estruturas têm sido otimizadas, ou seja, admitindo-se que as mesmas possuam comportamento linear elástico. O sistema computacional é denominado integrado pois reúne diversos módulos distintos para o tratamento do problema, como modelagem geométrica, geração de malhas de elementos finitos, análise não-linear da resposta da estrutura, análise de sensibilidade,programação matemática e otimização de estruturas. A geometria do contorno da estrutura plana é definida por meio de curvas (paramétricas)B-splines cúbicas. Estas, por sua vez, são determinadas em função de um conjunto de pontos de interpolação (pontos-chave) e condições de contorno em seus vértices extremos. A correta definição da geometria da estrutura é responsável pelo sucesso do processo de otimização. A resposta da estrutura às solicitações do carregamento externo é avaliada pelo método dos elementos finitos. Para isso, é necessário que o domínio da estrutura seja discretizado. No presente trabalho foi empregado um gerador automático de malhas não estruturadas de elementos finitos isoparamétricos. A configuração de equilíbrio da estrutura é obtida através de um procedimento iterativo/incremental envolvendo o método de Newton-Raphson. Localmente, o equilíbrio é satisfeito pela aplicação de um algoritmo implícito de integração de tensões nos pontos que violarem o critério de plastificação do material. A matriz tangente de rigidez é atualizada a cada iteração da análise e é obtida de forma consistente com o algoritmo de integração das tensões, preservando as características de convergência quadrática assintótica inerentes ao método de Newton- Raphson. No procedimento iterativo de otimização é empregado um algoritmo de programac¸ ão quadrática recursiva que requer a avaliação dos gradientes da função-objetivo e restrições. Para tal, foi implementado um método semi-analítico para a determinação das sensibilidades da resposta estrutural envolvidas nas expressôes dos gradientes citados. O método leva em consideração os efeitos da plastificação ocorrida durante o carregamento da estrutura e é dito -exato- por apresentar imprecisões apenas nos casos em que a magnitude da perturbação da variável é muito pequena, não podendo ser representada corretamente pelo hardware. Os exemplos analisados mostram que a consideração do comportamento elastoplástico da estrutura na otimização de sua forma leva a configurações mais eficientes do que aquelas obtidas admitindo-se a relação linear elástica entre deformações e tensões. / [en] The main goal of this work is to present an integrated system for the optimization of plane structures with elastoplastic behavior. The methodology proposes an alternative for the conservative way in which structures traditionally have been optimized, i.e., that they present linear elastic behavior. The computational system is said to be integrated because it congregates distinct modules for the solution of the problem, such as geometric modelling, finite element mesh generation, non-linear structural response analysis, sensitivity analysis, mathematical programming and optimization of structures. The geometry of the plane structure`s boundary is defined by cubic (parametric) B-splines curves. Those, in turn, are determined by a set of interpolation points (key points) and boundary constraints at their ends. The correct definition of the structure`s geometry is responsible for the success of the optimization process.The structural response to the applied loading is evaluated by the finite element method. For that, the domain of the structure must be discretized. In the present work, an automatic unstructured mesh generator of isoparametric finite elements has been used. The equilibrium layout of the structure is obtained by an iterative/incremental procedure using the standard Newton-Raphson method. Locally, the equilibrium is satisfied by applying an implicit stress return mapping algorithm at points which violate the yield criterion of the material. The tangent stiffness matrix is updated at each analysis iteration and it is obtained in a way which is consistent with the return mapping algorithm, so that the asymptotic quadratic rate of convergence of the Newton-Raphson method is preserved. The use of a quadratic recursive programming algorithm in the optimization procedure involves the gradient evaluation of the objective function and constraints. For that, a semi-analytical method for the calculation of the response sensitivities, which appear in the gradient expressions, has been implemented. The technique takes into account the plastic effects which take place during the loading of the structure and is considered - exact- up to round-off errors, which occurs when the magnitude of the perturbation is so small that the hardware cannot accurately represent it.The examples presented demonstrate that the consideration of the elastoplastic behavior of the material during the optimization process leads to structural layouts which are more efficient than of those obtained under the assumption of linear elastic relationship between strains and stresses. / [es] Este trabajo tiene por objetivo presentar un sistema integrado para otimización de forma de extructuras planas que tengan comportamiento elástico-plástico. LA metodología implementada propone una alternativa a la forma conservadora con que tradicionalmente las extructuras han sido optimizadas, o sea, admitiendo que las poseen um comportamiento lineal-elástico. EL sistema computacional se denomina integrado pues reúne diversos módulos para el tratamiento del problema, como modelage geométrica, generación de mallas de elementos finitos, análisis no lineal de la respuesta de la extructura, análisis de sensibilidad,programación matemática y otimización de extructuras. LA geometría del contorno de la extructura plana es definida por medio de curvas (paramétricas)B splines cúbicas. Estas, por su vez, son determinadas en función de un conjunto de puntos de interpolación (puntos claves) y condiciones de contorno en sus vértices extremos. La definición correta de la geometría de la extructura es responsable por el éxito del proceso de otimización. La respuesta de la extructura a las solicitudes de carga externa se evalúa por el método de los elementos finitos. Para esto, es necesario que el dominio de la extructura sea discretizado. En este trabajo se utiliza un generador automático de mallas no extructuradas de elementos finitos isoparamétricos. La configuración de equilíbrio de la extructura se obtiene a través de un procedimiento iterativo/incremental que envuelve el método de Newton Raphson. Localmente, el equilíbrio es satisfecho por la aplicación de un algoritmo implícito de integración de tensiones en los puntos que violen el critério de plastificación del material. La matriz tangente de rigidez se actualiza a cada iteración del análisis y se obtiene de forma consistente con el algoritmo de integración de las tensiones, preservando las características de convergencia cuadrática asintótica inherentes al método de Newton Raphson. En el procedimiento iterativo de otimización se utiliza un algoritmo de programación cuadrática recursiva que requiere la evaluación de los gradientes de la función objetivo y restricciones. Para tal, se implementó un método semi analítico para la determinación de las sensibilidades de la respuesta extructural envolvidas en las expresóes de los gradientes citados. EL método lleva en consideración el hecho de que la plastificación que ocurre durante la carga de la extructura y se dice exacta por presentar imprecisiones apenas en los casos en que la magnitud de la perturbación de la variable es muy pequeña, no puede ser representada correctamente por el hardware. Los ejemplos analizados muestran que la consideración del comportamiento elástico-plástico de la extructura en la otimización de su forma lleva la configuraciones más eficientes de que aquellas obtenidas admitiendo la relación lineal elástica entre deformaciones y tensiones.

[pt] Este trabalho consiste no desenvolvimento e implementação de um sistema computacional integrado para Modelagem Geo- étrica, Geração de Malhas, Análise Numérica, Auto- Adaptação do tipo h e Otimização de Forma e Espessura em Cascas. O Modelo Geométrico adotado consiste em representar a superfície por meio de B-Splines Racionais Recortadas, admitindo variação de espessura segundo as mesmas funções que descrevem a superfície. Para a utilização nos módulos de Auto-Adaptação e Otimização, Geradores de Malhas Não-Estruturadas sobre superfícies paramétricas foram empregados. Com base em um gerador de malhas triangulares que utiliza a técnica de avanço de Fronteira, dois geradores de malhas quadrilaterais foram desenvolvidos. Os elementos finitos empregados são baseados nas hipóteses de Reissner-Mindlin e no conceito de degeneração de sólidos. São considerados os elementos tradicionais, baseados puramente em deslocamentos, bem como elementos de formulação mais robusta, com base em campos assumidos de deformação. Um procedimento para Auto-Adaptação de Malhas do tipo foi desenvolvido para o Modelo Geométrico e para os elementos considerados. As malhas obtidas a partir de níveis de erro prescritos permitem aos modelos a obtenção de suas taxas de convergência mesmo em problemas com singularidades e efeitos de fronteira. A Análise de Sensibilidade, ferramenta essencial nos procedimentos de Otimização, é feita com a utilização do Método Semi-Analítico, considerando as características especiais dos elementos de casca. Foi desenvolvida para elementos degenerados de casca uma versão do Método Semi- Analítico que elimina sua imprecisão eventual, através da diferenciação exata das componentes de deslocamento de corpo rígido. Para os elementos baseados puramente em deslocamentos, o Método Analítico também foi desenvolvido. Os módulos de Otimização de Forma e Espessura trabalham sobre diversas possibilidades de definição das variáveis de projeto e com diferentes algoritmos de Programação Matemá tica. Permitem também a Otimização de Forma com consideração de Auto-Adaptatividade para obter as malhas durante o processo de mudança de forma. Devido à interconexão entre os diversos módulos e com o objetivo de facilitar a comunicação e a implementação dos mesmos, o sistema computacional foi completamente desenvolvido utilizando técnicas de Programação Orientada para Objetos. / [en] The purpose of this thesis is the development of an integrated computational system for Geometric Modelling, Unstructured Mesh Generation, Numerical Analysis, Adaptivity and Shape Optimization of Shells.The Geometric Model is composed of Non-Uniform Rational B-Spline Surfaces (NURBS), further modified by trimming loops described in the parametric plane. Smooth thickness variations may be modelled by means of the same functions that describe the surface geometry.For Unstructured Mesh Generation, two algorithms were implemented for quadrilateral elements and one for triangles. The triangular Mesh Generator is based on the Advancing Front Technique applied to parametric surfaces. The quadrilateral Mesh Generators employ the indirect approach for converting the triangular meshes to pure quadrilateral ones. The Finite Element formulation is based on the degenerated isoparametric approach. Pure displacement based elements, as well as assumed strain robust shell elements, are employed in the Analysis, Adaptivity and Optimization modules. A procedure for h-Adaptive Mesh Refinement was developed for the shell models. For this purpose an Error Estimator scheme, based upon a Zienkiewicz-Zhu Patch Recovery Technique, adapted to handle curved shell surfaces, was employed. The adaptive procedure allows the convergence rates of the Finite Element Model to be maintained even in the presence of singularities and boundary layers.For the Sensitivity Evaluation, the well- known Semi-Analytical Method is employed and adapted for the degenerated solid shell element approach. In order to solve the inaccuracy problems inherent to the application of the method for certain types of structures, the recent Refined Semi- Analytical Method, is extended for degenerated shell elements. For the pure displacement-based elements, the Analytical Method is also developed. The Shape and Thickness Optimization modules work with a wide variety of design variable descriptions, different mathematical Programming algorithms, Sensitivity schemes and Finite Element Models. The possibility of h-Adaptive Mesh refinement in conjunction with Shape Optimization is also considered in this stage. In order to ease up code expansion, communication and data exchange between the modules,the computational system was fully developed employing Object-Oriented Programming techniques.

This report focuses on the practicality and results of using the COMSOL 6.0 Optimization Module on a HVDC bushing corona shield model provided by Hitachi Energy to minimize electric field. The Optimization Module has several functions and parameters for altering the geometry of a model. Parameter Optimization, Polynomial Boundary and Free Shape Boundary was the primary methods used. The best results in minimizing the electric field was found with the Polynomial Boundary. The optimized shape decreased the maximum electric field by about 15% and when run with constraints to the change in volume the optimization showed similar results. Tests with Parameter Optimization did decrease the electric field but lacked the ability to fine-tune the shape like Polynomial Boundary can. Free Shape Boundaryseemed to have great potential in the documentation but we did not finda successful way of implementing the method. Through testing of different setups for methods and solvers we have concluded that the Optimization Module is both useful and practical for the given model and a clear improvement in electric field was observed in the new shape. Polynomial Boundary is the best option for the given model but more research is needed about Free Shape Boundary.

This thesis utilizes the Immersed Interface Finite Element Method (IIFEM) for shape optimization and material design, while also investigating the modeling and parameterization of lung tissue for Diver Underwater Explosion (UNDEX) simulations. In the first part, a shape optimization scheme utilizing a four-noded rectangular immersed-interface element is presented. This method eliminates the need for interface fitted mesh or mesh morphing, reducing computational costs while maintaining solution accuracy. Analytical design sensitivity analysis is performed to obtain gradients for the optimization formulation, and various parametrization techniques are explored. The effectiveness of the approach is demonstrated through verification and case studies. For material design, the study combines topological shape optimization with IIFEM, providing a computational approach for architecting materials with desired effective properties. Numerical homogenization evaluates effective properties, and level set-based topology optimization evolves boundaries within the unit cell to generate optimal periodic microstructures. The design space is parameterized using radial basis functions, facilitating a gradient-based optimization algorithm for optimal coefficients. The method produces geometries with smooth boundaries and distinct interfaces, demonstrated through numerical examples. The thesis then delves into modeling the mechanical response of lung tissues, particularly focusing on hyperelastic and hyperviscoelastic models. The research adopts a phased approach, emphasizing hyperelastic model parametrization while reserving hyperviscoelastic model parametrization for future studies. Alternative methods are used for parametrization, circumventing direct experimental tests on biological materials. Representative material properties are sourced from literature or refit from existing experimental data, incorporating both empirically derived data and practical values suitable for simulations. Damage parameter quantification relies on asserted quantitative relationships between injury levels and the regions or percentages of affected lung tissue. / Doctor of Philosophy / This research explores the following themes: optimizing shapes, designing materials using repetitive identical building blocks, and understanding how divers' lungs respond to underwater explosions. When computationally analyzing structures with multiple materials, the conventional method involves creating meshes that align with material interfaces, which can be intricate and time-consuming. The Immersed Interface Finite Element Method (IIFEM) is introduced as a computational approach that simplifies this process, utilizing a uniform grid for analysis regardless of interface shape. Consider a plate with a hole or other inclusions. Shape optimization seeks the optimal hole/inclusion shape for withstanding specific loading. Traditional optimization processes necessitate iterative mesh recreation, a step circumvented by employing IIFEM. This technique also extends to creating micro-building blocks of materials, enabling the architectural design of materials with desired qualities. Materials with specific properties, like strength or flexibility can be achieved. This thesis also addresses the challenge of understanding how divers' lungs respond to underwater explosions, a crucial aspect of safety. Advanced computer models are used to mimic the behavior of lung tissue under shock loads. Directly testing materials and tissues can be difficult and restricted. Techniques like gathering data from scientific papers and refitting existing experimental data are utilized to obtain the information needed. Also, it is hard to directly measure how much damage an underwater explosion does to a diver's lungs. Thus, the level of damage was quantified based on assertions about the relationship between different injury severities and how much lung tissue is affected.

Yes

As worldwide energy consumption continues to increase, so does the demand for renewable energy sources. The total available wave energy resource for the United States alone is 2,640 TWh/yr; nearly two thirds of the 4,000 TWh of electricity used in the United States each year. It is estimated that nearly half of that available energy is recoverable through wave energy conversion techniques. In this thesis, a two-body 'point absorber' type wave energy converter with a mechanical power-takeoff is investigated. The two-body wave energy converter extracts energy through the relative motion of a floating buoy and a neutrally buoyant submerged body. Using a linear frequency-domain model, analytical solutions of the optimal power and the corresponding power-takeoff components are derived for the two-body wave energy converter. Using these solutions, a case study is conducted to investigate the influence of the submerged body size on the absorbed power of the device in regular and irregular waves. Here it is found that an optimal mass ratio between the submerged body and floating buoy exists where the device will achieve resonance. Furthermore, a case study to investigate the influence of the submerged body shape on the absorbed power is conducted using a time-domain numerical model. Here it is found that the submerged body should be designed to reduce the effects of drag, but to maintain relatively large hydrodynamic added mass and excitation force. To validate the analytical and numerical models, a 1/30th scale model of a two-body wave energy converter is tested in a wave tank. The results of the wave tank tests show that the two-body wave energy converter can absorb nearly twice the energy of a single-body 'point absorber' type wave energy converter. / Master of Science

One key outcome of this research is the design for a 3-D tractor-trailer base-drag reduction device that predicts a 41% reduction in wind-averaged drag coefficient at 57 mph (92 km/h) and that is relatively insensitive to uncertain wind speed and direction and uncertain deflection angles due to mounting accuracy and static aeroelastic loading; the best commercial device of non-optimized design achieves a 12% reduction at 65 mph. Another important outcome is the process by which the optimized design is obtained. That process includes verification and validation of the flow solver, a less complex but much broader 2-D pathfinder study, and the culminating 3-D aerodynamic shape optimization under uncertainty (OUU) study. To gain confidence in the accuracy and precision of a computational fluid dynamics (CFD) flow solver and its Reynolds-averaged Navier-Stokes (RANS) turbulence models, it is necessary to conduct code verification, solution verification, and model validation. These activities are accomplished using two commercial CFD solvers, Cobalt and RavenCFD, with four turbulence models: Spalart-Allmaras (S-A), S-A with rotation and curvature, Menter shear-stress transport (SST), and Wilcox 1998 k-ω. Model performance is evaluated for three low subsonic 2-D applications: turbulent flat plate, planar jet, and NACA 0012 airfoil at α = 0°. The S-A turbulence model is selected for the 2-D OUU study. In the 2-D study, a tractor-trailer base flap model is developed that includes six design variables with generous constraints; 400 design candidates are evaluated. The design optimization loop includes the effect of uncertain wind speed and direction, and post processing addresses several other uncertain effects on drag prediction. The study compares the efficiency and accuracy of two optimization algorithms, evolutionary algorithm (EA) and dividing rectangles (DIRECT), twelve surrogate models, six sampling methods, and surrogate-based global optimization (SBGO) methods. The DAKOTA optimization and uncertainty quantification framework is used to interface the RANS flow solver, grid generator, and optimization algorithm. The EA is determined to be more efficient in obtaining a design with significantly reduced drag (as opposed to more efficient in finding the true drag minimum), and total predictive uncertainty is estimated as ±11%. While the SBGO methods are more efficient than a traditional optimization algorithm, they are computationally inefficient due to their serial nature, as implemented in DAKOTA. Because the S-A model does well in 2-D but not in 3-D under these conditions, the SST turbulence model is selected for the 3-D OUU study that includes five design variables and evaluates a total of 130 design candidates. Again using the EA, the study propagates aleatory (wind speed and direction) and epistemic (perturbations in flap deflection angle) uncertainty within the optimization loop and post processes several other uncertain effects. For the best 3-D design, total predictive uncertainty is +15/-42%, due largely to using a relatively coarse (six million cell) grid. That is, the best design drag coefficient estimate is within 15 and 42% of the true value; however, its improvement relative to the no-flaps baseline is accurate within 3-9% uncertainty. / Ph. D.

Hydrogen fuel cells are devices used to generate electricity from the electrochemical reaction between air and hydrogen gas. An attractive advantage of these devices is that their byproduct is water, which is very safe to the environment. However, hydrogen fuel cells still lack some improvements in terms of increasing their life time and electricity production, decreasing power losses, and optimizing their operating conditions. In this thesis, the cathode part of the hydrogen fuel cell will be considered. This part mainly consists of an air gas channel and a gas diffusion layer. To simulate the fluid dynamics taking place in the cathode, we present two models, a general model and a simple model both based on a set of conservation laws governing the fluid dynamics and chemical reactions. A numerical method to solve these models is presented and verified in terms of accuracy. We also show that both models give similar results and validate the simple model by recovering a polarization curve obtained experimentally. Next, a shape optimization problem is introduced to find an optimal design of the air gas channel. This problem is defined from the simple model and a cost functional, $E$, that measures efficiency factors. The objective of this functional is to maximize the electricity production, uniformize the reaction rate in the catalytic layer and minimize the pressure drop in the gas channel. The impact of the gas channel shape optimization is investigated with a series of test cases in long and short fuel cell geometries. In most instances, the optimal design improves efficiency in on- and off-design operating conditions by shifting the polarization curve vertically and to the right. The second primary goal of the thesis is to analyze mathematical issues related to the introduced shape optimization problem. This involves existence and uniqueness of the solution for the presented model and differentiability of the state variables with respect to the domain of the air channel. The optimization problem is solved using the gradient method, and hence the gradient of $E$ must be found. The gradient of $E$ is obtained by introducing an adjoint system of equations, which is coupled with the state problem, namely the simple model of the fuel cell. The existence and uniqueness of the solution for the adjoint system is shown, and the shape differentiability of the cost functional $E$ is proved.

Hydrogen fuel cells are devices used to generate electricity from the electrochemical reaction between air and hydrogen gas. An attractive advantage of these devices is that their byproduct is water, which is very safe to the environment. However, hydrogen fuel cells still lack some improvements in terms of increasing their life time and electricity production, decreasing power losses, and optimizing their operating conditions. In this thesis, the cathode part of the hydrogen fuel cell will be considered. This part mainly consists of an air gas channel and a gas diffusion layer. To simulate the fluid dynamics taking place in the cathode, we present two models, a general model and a simple model both based on a set of conservation laws governing the fluid dynamics and chemical reactions. A numerical method to solve these models is presented and verified in terms of accuracy. We also show that both models give similar results and validate the simple model by recovering a polarization curve obtained experimentally. Next, a shape optimization problem is introduced to find an optimal design of the air gas channel. This problem is defined from the simple model and a cost functional, $E$, that measures efficiency factors. The objective of this functional is to maximize the electricity production, uniformize the reaction rate in the catalytic layer and minimize the pressure drop in the gas channel. The impact of the gas channel shape optimization is investigated with a series of test cases in long and short fuel cell geometries. In most instances, the optimal design improves efficiency in on- and off-design operating conditions by shifting the polarization curve vertically and to the right. The second primary goal of the thesis is to analyze mathematical issues related to the introduced shape optimization problem. This involves existence and uniqueness of the solution for the presented model and differentiability of the state variables with respect to the domain of the air channel. The optimization problem is solved using the gradient method, and hence the gradient of $E$ must be found. The gradient of $E$ is obtained by introducing an adjoint system of equations, which is coupled with the state problem, namely the simple model of the fuel cell. The existence and uniqueness of the solution for the adjoint system is shown, and the shape differentiability of the cost functional $E$ is proved.

The development of a shape optimization solver using the existing Computational Fluid Dynamics (CFD) codes is taken up as topic of research in this thesis. A shape optimizer was initially developed based on Genetic Algorithm (GA) coupled with a CFD solver in an earlier work. The existing CFD solver is based on Kinetic Flux Vector Splitting and uses least squares discretization. This solver requires a cloud of points and their connectivity set, hence this CFD solver is a meshless solver. The advantage of a meshless solver is utilised in avoiding re-gridding (only connectivity regeneration is required) after each shape change by the shape optimizer. The CFD solver is within the optimization loop, hence evaluation of CFD solver after each shape change is mandatory. Although the earlier shape optimizer developed was found to be robust, but it was taking enoromous amount of time to converge to the optimum solution (details in Appendix). Hence a new evolving method, Ant Colony Optimization (ACO), is implemented to replace GA. A shape optimizer is developed coupling ACO and the meshless CFD solver. To the best of the knowledge of the present author, this is the first time when ACO is implemented for aerodynamic shape optimization problems. Hence, an exhaustive validation has become mandatory. Various test cases such as regeneration problems of (1) subsonic - supersonic nozzle with a shock in quasi - one dimensional flow (2) subsonic - supersonic nozzle in a 2-dimensional flow field (3) NACA 0012 airfoil in 2-dimensional flow and (4) NACA 4412 airfoil in 2-dimensional flow have been successfully demonstrated. A comparative study between GA and ACO at algorithm level is performed using the travelling salesman problem (TSP). A comparative study between the two shape optimizers developed, i.e., GA-CFD and ACO-CFD is carried out using regeneration test case of NACA 4412 airfoil in 2-dimensional flow. GA-CFD performs better in the initial phase of optimization and ACO-CFD performs better in the later stage. We have combined both the approaches to develop a hybrid GA-ACO-CFD solver such that the advantages of both GA-CFD and ACO-CFD are retained with the hybrid method. This hybrid approach has 2 stages, namely, (Stage 1) initial optimum search by GA-CFD (coarse search), the best members from the optimized solution from GA-CFD are segregated to form the input for the fine search by ACO-CFD and (Stage 2) final optimum search by ACO-CFD (fine search). It is observed that this hybrid method performs better than either GA-CFD or ACO- CFD, i.e., hybrid method attains better optimum in less number of CFD calls. This hybrid method is applied to the following test cases: (1) regeneration of subsonic-supersonic nozzle with shock in quasi 1-D flow and (2) regeneration of NACA 4412 airfoil in 2-dimensional flow. Two applications on shape optimization, namely, (1) shape optimization of a body in strongly rotating viscous flow and (2) shape optimization of a body in supersonic flow such that it enhances separation of binary species, have been successfully demonstrated using the hybrid GA-ACO-CFD method. A KFVS based binary diffusion solver was developed and validated for this purpose. This hybrid method is now in a state where industrial shape optimization applications can be handled confidently.