An inverse method is developed to analyze the transient heat source from arc erosion. The temperature at the contour of arc erosion is assumed as melting point. And the temperature in grid points at the last time is calculated by interpolation, which include measurement errors. Then, the unknown parameters of transient heat source can be solved by linear least-squares error method. These parameters are plasma radius at the anode surface grows with time, arc power, and plasma flushing efficiency on the anode. Because the temperature in measuring points includes measurement errors, the exact solution can be found when fewer unknowns are considered. The inverse method is sensitivity to measurement errors.

Accurate values of thermophysical transport properties of particle beds are necessary to accurately model heat and mass transfer processes in particle beds that under-go preferred processes and changes. The objective of this study is to use a proven analytical/numerical methodology to estimate the unknown transport properties within test cells filled with silicagel particles and compare the results with the previously published data. An experimental test cell was designed and constructed to carry out transient heat transfer tests for both step change conduction and convection heat transfer within a packed bed of silicagel particles. For a known step change in the test cell temperature boundary condition, the temporal temperature distribution within the bed during heat conduction depends only on the effective heat conduction coefficient and the thermal capacity of the particle bed. The central problem is to, using only the boundary conditions and a few time-varying temperature sensors in the test cell of particles, determine the effective thermal conductivity of the test bed and specify the resulting measurement uncertainty. A similar problem occurs when the heat convection coefficient is sought after a step change in the airflow inlet temperature for the test cell. These types of problems are known as inverse heat transfer problems (IHTP). In this thesis, IHTP method was used to estimate the convective heat transfer coefficient. Good agreement was seen in experimental and numerical temperature profiles, which were modeled by using the estimated convective heat transfer coefficient. The same methodology was used to estimate the effective thermal conductivity of the particle bed. Comparison between the experimental temperature distribution and numerical temperature distribution, which was modeled by using the estimated effective conductivity, illustrated good agreement. On the other side, applying the effective thermal conductivity, obtained from a direct steady state measurement, in the numerical simulation could not present agreement between the numerical and experimental results. It was concluded that the IHTP methodology was a successful approach to find the thermophysical properties of the particle beds, which were hard to measure directly.

This study is concerned with whiplash injuries resulting from the sudden acceleration and deceleration of the head relative to the torso in vehicle collisions. Whiplash is the most common automobile injury, yet it is poorly understood. The objective of this thesis is to develop a representative rigid linkage lumped parameter model using Lagrangian mechanics to capture the relative motion of the head and cervical spine. Joint locations corresponding to the intervertebral centers of rotation are used to simulate the normal spinal movements and an inverse analysis is applied to determine the viscoelastic parameters for the spine, based on cadaver test results. The model is further validated using ANSYS dynamic finite element analysis and experimentally validated using a newly designed and fully instrumented whiplash test fixture. Our findings reveal the effectiveness of the simplified model which can be easily scaled to accommodate differences in collision severity, posture, gender, and occupant size.

This study is concerned with whiplash injuries resulting from the sudden acceleration and deceleration of the head relative to the torso in vehicle collisions. Whiplash is the most common automobile injury, yet it is poorly understood. The objective of this thesis is to develop a representative rigid linkage lumped parameter model using Lagrangian mechanics to capture the relative motion of the head and cervical spine. Joint locations corresponding to the intervertebral centers of rotation are used to simulate the normal spinal movements and an inverse analysis is applied to determine the viscoelastic parameters for the spine, based on cadaver test results. The model is further validated using ANSYS dynamic finite element analysis and experimentally validated using a newly designed and fully instrumented whiplash test fixture. Our findings reveal the effectiveness of the simplified model which can be easily scaled to accommodate differences in collision severity, posture, gender, and occupant size.

No desenvolvimento de projetos de iluminação de ambientes, um dos objetivos que se destaca é a busca pelo conforto visual, que emprega metodologias de resolução conhecidas, como o Método dos Lumens e o Método Ponto a Ponto. A luz visível está contida no espectro da radiação térmica e, portanto, o fluxo luminoso pode ser relacionado ao fluxo de radiação térmica. Determinar as posições e as competências das fontes de luz necessárias na superfície de projeto ganha importância quando o comportamento, em termos de uniformidade ou de fluxo radiante, é especificado. O presente trabalho visa a estabelecer diferentes valores de fluxo em duas regiões distintas da superfície do projeto. Por meio do posicionamento das fontes de luz, é estabelecido um fluxo maior na região denominada principal e um fluxo menor na região denominada secundária. A modelagem matemática da radiação térmica (Método das Radiosidades) é aplicada ao projeto de iluminação, considerando-se as características da visão humana e o comportamento das fontes de luz. Na modelagem, é considerada uma cavidade retangular tridimensional com superfícies cinza e com condição de parede fria, na qual o poder emissivo das paredes é nulo. As fontes de luz são representadas por unidades de malha no teto. A relação de equações é resolvida por metodologia inversa, usando o algoritmo de Otimização Extrema Generalizada (GEO). Este algoritmo é classificado como um método de otimização estocástica de busca global para a resolução de sistemas considerados inicialmente mal condicionados. A posição e a potência das fontes luminosas são determinadas pela resolução do sistema de equações, de forma a proporcionar um fluxo de radiação duas vezes maior na região principal em relação à região secundária. A função objetivo do processo consiste em minimizar a diferença entre o fluxo desejado e os valores de fluxo de radiação incidente nas duas regiões da superfície de projeto. Em virtude das características de simetria do problema, a relação é estabelecida para apenas um quarto da cavidade. Assim, por exemplo, aplicar a metodologia com 9 fontes de luz a um quarto da região resulta em 36 fontes de luz em toda a cavidade. Os resultados mostram que é possível encontrar um arranjo de fontes de luz preestabelecendo-se duas condições de potência. / In the development of environmental illumination projects, one of the main goals to be achieved is the visual comfort, which is usually done by known methodologies, like the Lumens Method and the Point by Point Method. Since the visible light is contained in the spectrum of thermal radiation, the luminous flux can be related to the thermal radiation flux. The determination of the position and power of the light sources required by the design surface gains an higher importance whenever a behavior is specified, should it be in terms of uniformity or in therms of radiant flux. In this work, we describe a method that allows the establishment of different flux values in two distinct regions of the design surface, which are referred by the names main region and secondary region. Through the spatial arrangement of the light sources, the method sets a more intense flux in the main region and a less intense one in the secondary region. The mathematical model of thermal radiation, known as Radiosity Method, is applied to the illumination design, along with the characteristics of the human vision and the behavior of light sources. In this model, a rectangular three-dimensional cavity is considered. It has gray surfaces and exhibits the conditions of a cold wall, in which the emissivity power of the walls is null. The light sources are represented by a mesh unit in the ceiling. The system of equations is solved by inversemethodology, using the Generalized Extremal Optimization (GEO) algorithm. This algoritm is classified as being a stochastic optimization method of global search to solve systems that are initially considered ill-conditioned. By solving this system, the position and power of light sources can be determined, and this is done in such a way that the flux radiation in the main region is twice more intense then the one in the secondary region. The target function of the whole process is to minimize the difference between the desired flux and the incident flux radiation values for each one of the two design surface regions. We further explore the problem symmetry, solving the equation system for only a quarter of the cavity. This way, if the methodology is applied with nine light sources into a quarter of the region, the entire cavity will behave as if it has 36 light sources. Our results show that, given two prescribed conditions of power, it is possible to find an arrangement of light sources.

Um método híbrido aplicado é proposto para um problema inverso que trata de uma cavidade tridimensional preenchida com meio transparente. As paredes são assumidas cinza e difusas, e o único mecanismo de transferência de calor presente é a radiação térmica. É um caso idealizado, mas que encontra ampla aplicação em sistemas de engenharia. Prescrevem-se duas condições de contorno na base da cavidade – temperatura e fluxo de calor – e, para satisfazêlas, buscam-se o fluxo de calor e a distribuição espacial dos aquecedores. Na superfície superior, que contêm os aquecedores, nenhuma condição de contorno é imposta. Este tipo de problema, quando solucionado através de técnicas convencionais, envolve um procedimento de tentativa e erro, que, além de demandar um elevado tempo computacional, conduz a resultados pouco precisos. Na análise inversa, opta-se por otimização ou pela aplicação de um método de regularização, pois o problema resultante é mal condicionado por envolver a equação integral de Fredholm de primeira espécie. Neste trabalho, optou-se por acoplar otimização e regularização como uma alternativa baseada no emprego distinto dessas duas formas de abordagem. A tarefa de busca por posições para os aquecedores ficou por conta do método da Otimização Extrema Generalizada, enquanto o método de regularização da Decomposição em Valores Singulares Truncada calcula o fluxo de calor dos aquecedores para cada configuração gerada pelo processo de otimização. A aplicação da técnica híbrida conduziu a resultados mais precisos do que aqueles que normalmente se obtêm apenas com regularização, reduzindo consideravelmente o tempo computacional da solução baseada apenas na otimização. / This work considers the inverse analysis in a three-dimensional rectangular enclosure with diffuse-gray surfaces. The locations and powers of the heaters sources are left unconstrained and two conditions are imposed on the design surface – uniform heat flux and temperature distributions. The solution to this kind of problem by conventional techniques is possible only with trial-and-error procedure and in this case, the forward solution will be run oftentimes without guarantee to find out a good answer. The aim is determine the powers and locations of the heaters to attain both uniform heat flux and temperature on the design surface. A new solution procedure – termed hybrid solution – which couples two methods, the Generalized Extremal Optimization (GEO) and the Truncated Singular Value Decomposition (TSVD) is proposed. The search of locations is treated as an optimization problem, by GEO algorithm, whereas the solution of the system equation, that embodies the Fredholm integral equation of first kind and, therefore, is expected to be ill-conditioned, is build up through a TSVD regularization method. The hybrid method provides better results than TSVD and, when compared with GEO, reduces the computational time substantially.

No projeto de um forno, normalmente busca-se uma configuração para a posição dos aquecedores que resulte em aquecimento uniforme na superfície inferior, a superfície de projeto. Neste trabalho, o fluxo de calor e a temperatura são prescritos na superfície de projeto e os elementos aquecedores devem ser projetados em um conjunto de quatro filamentos, ou um filamento em cada quarto simétrico do forno, a fim de satisfazer às condições prescritas. O forno é modelado como uma cavidade tridimensional preenchida com meio transparente; assume-se que as paredes sejam cinzas e difusas e que o único mecanismo de transferência de calor presente é a radiação térmica. Esse problema, convencionalmente, é solucionado através de um procedimento de tentativa-e-erro; neste trabalho, a solução é obtida através da análise inversa, uma técnica mais versátil e eficaz de projeto, embora exija tratamentos matemáticos especiais. O problema inverso é resolvido nesta pesquisa de forma implícita, como um problema de otimização. A solução é obtida através do método da Otimização Extrema Generalizada (GEO), um método de otimização estocástico e global, utilizado para encontrar as posições para os aquecedores respeitando a condição de formar um filamento. A metodologia é aplicada para se obter a configuração geométrica e posição do filamento aquecedor, uma abordagem inédita na literatura, conduzindo a resultados com desvio máximo inferior a 2%. Por fim, nesta pesquisa, realiza-se um estudo acerca do fator de forma dos elementos aquecedores que indica a aplicabilidade da solução obtida para filamentos com diferentes espessuras. / In the design of a oven is desired to obtain the positions for the heaters that results in a uniform heating to the bottom surface, the design surface. The heat flux and temperature are prescribed in the design surface and the heating elements are positioned in a single filament so as to satisfy prescribed conditions. The oven is modeled as a three-dimensional cavity filled with transparent medium, it is assumed that the walls are gray and diffuse and the dominant heat transfer mechanism is thermal radiation. This problem, conventionally, is solved through a trial and error procedure, in this work, the solution is obtained by inverse analysis. The inverse problem is solved implicitly, as an optimization problem. The solution is obtained by the method of optimization extreme (GEO) a stochastic global optimization method used to find the locations for the heaters respecting the condition of build a filament. The methodology leads to satisfactory results, with maximum error less than 2%. Finally, this research, realized a study of the view factor of the elements heaters that indicates the applicability of the solution into filaments with different thicknesses.

No desenvolvimento de projetos de iluminação de ambientes, um dos objetivos que se destaca é a busca pelo conforto visual, que emprega metodologias de resolução conhecidas, como o Método dos Lumens e o Método Ponto a Ponto. A luz visível está contida no espectro da radiação térmica e, portanto, o fluxo luminoso pode ser relacionado ao fluxo de radiação térmica. Determinar as posições e as competências das fontes de luz necessárias na superfície de projeto ganha importância quando o comportamento, em termos de uniformidade ou de fluxo radiante, é especificado. O presente trabalho visa a estabelecer diferentes valores de fluxo em duas regiões distintas da superfície do projeto. Por meio do posicionamento das fontes de luz, é estabelecido um fluxo maior na região denominada principal e um fluxo menor na região denominada secundária. A modelagem matemática da radiação térmica (Método das Radiosidades) é aplicada ao projeto de iluminação, considerando-se as características da visão humana e o comportamento das fontes de luz. Na modelagem, é considerada uma cavidade retangular tridimensional com superfícies cinza e com condição de parede fria, na qual o poder emissivo das paredes é nulo. As fontes de luz são representadas por unidades de malha no teto. A relação de equações é resolvida por metodologia inversa, usando o algoritmo de Otimização Extrema Generalizada (GEO). Este algoritmo é classificado como um método de otimização estocástica de busca global para a resolução de sistemas considerados inicialmente mal condicionados. A posição e a potência das fontes luminosas são determinadas pela resolução do sistema de equações, de forma a proporcionar um fluxo de radiação duas vezes maior na região principal em relação à região secundária. A função objetivo do processo consiste em minimizar a diferença entre o fluxo desejado e os valores de fluxo de radiação incidente nas duas regiões da superfície de projeto. Em virtude das características de simetria do problema, a relação é estabelecida para apenas um quarto da cavidade. Assim, por exemplo, aplicar a metodologia com 9 fontes de luz a um quarto da região resulta em 36 fontes de luz em toda a cavidade. Os resultados mostram que é possível encontrar um arranjo de fontes de luz preestabelecendo-se duas condições de potência. / In the development of environmental illumination projects, one of the main goals to be achieved is the visual comfort, which is usually done by known methodologies, like the Lumens Method and the Point by Point Method. Since the visible light is contained in the spectrum of thermal radiation, the luminous flux can be related to the thermal radiation flux. The determination of the position and power of the light sources required by the design surface gains an higher importance whenever a behavior is specified, should it be in terms of uniformity or in therms of radiant flux. In this work, we describe a method that allows the establishment of different flux values in two distinct regions of the design surface, which are referred by the names main region and secondary region. Through the spatial arrangement of the light sources, the method sets a more intense flux in the main region and a less intense one in the secondary region. The mathematical model of thermal radiation, known as Radiosity Method, is applied to the illumination design, along with the characteristics of the human vision and the behavior of light sources. In this model, a rectangular three-dimensional cavity is considered. It has gray surfaces and exhibits the conditions of a cold wall, in which the emissivity power of the walls is null. The light sources are represented by a mesh unit in the ceiling. The system of equations is solved by inversemethodology, using the Generalized Extremal Optimization (GEO) algorithm. This algoritm is classified as being a stochastic optimization method of global search to solve systems that are initially considered ill-conditioned. By solving this system, the position and power of light sources can be determined, and this is done in such a way that the flux radiation in the main region is twice more intense then the one in the secondary region. The target function of the whole process is to minimize the difference between the desired flux and the incident flux radiation values for each one of the two design surface regions. We further explore the problem symmetry, solving the equation system for only a quarter of the cavity. This way, if the methodology is applied with nine light sources into a quarter of the region, the entire cavity will behave as if it has 36 light sources. Our results show that, given two prescribed conditions of power, it is possible to find an arrangement of light sources.

Um método híbrido aplicado é proposto para um problema inverso que trata de uma cavidade tridimensional preenchida com meio transparente. As paredes são assumidas cinza e difusas, e o único mecanismo de transferência de calor presente é a radiação térmica. É um caso idealizado, mas que encontra ampla aplicação em sistemas de engenharia. Prescrevem-se duas condições de contorno na base da cavidade – temperatura e fluxo de calor – e, para satisfazêlas, buscam-se o fluxo de calor e a distribuição espacial dos aquecedores. Na superfície superior, que contêm os aquecedores, nenhuma condição de contorno é imposta. Este tipo de problema, quando solucionado através de técnicas convencionais, envolve um procedimento de tentativa e erro, que, além de demandar um elevado tempo computacional, conduz a resultados pouco precisos. Na análise inversa, opta-se por otimização ou pela aplicação de um método de regularização, pois o problema resultante é mal condicionado por envolver a equação integral de Fredholm de primeira espécie. Neste trabalho, optou-se por acoplar otimização e regularização como uma alternativa baseada no emprego distinto dessas duas formas de abordagem. A tarefa de busca por posições para os aquecedores ficou por conta do método da Otimização Extrema Generalizada, enquanto o método de regularização da Decomposição em Valores Singulares Truncada calcula o fluxo de calor dos aquecedores para cada configuração gerada pelo processo de otimização. A aplicação da técnica híbrida conduziu a resultados mais precisos do que aqueles que normalmente se obtêm apenas com regularização, reduzindo consideravelmente o tempo computacional da solução baseada apenas na otimização. / This work considers the inverse analysis in a three-dimensional rectangular enclosure with diffuse-gray surfaces. The locations and powers of the heaters sources are left unconstrained and two conditions are imposed on the design surface – uniform heat flux and temperature distributions. The solution to this kind of problem by conventional techniques is possible only with trial-and-error procedure and in this case, the forward solution will be run oftentimes without guarantee to find out a good answer. The aim is determine the powers and locations of the heaters to attain both uniform heat flux and temperature on the design surface. A new solution procedure – termed hybrid solution – which couples two methods, the Generalized Extremal Optimization (GEO) and the Truncated Singular Value Decomposition (TSVD) is proposed. The search of locations is treated as an optimization problem, by GEO algorithm, whereas the solution of the system equation, that embodies the Fredholm integral equation of first kind and, therefore, is expected to be ill-conditioned, is build up through a TSVD regularization method. The hybrid method provides better results than TSVD and, when compared with GEO, reduces the computational time substantially.

Doctor of Philosophy / Department of Civil Engineering / Dunja Peric / A low ratio between the compressive strength of concrete and its cost makes concrete one of the most widely used construction materials in civil engineering. Despite of a very good response to compressive stress, concrete exhibits a low tensile strength and limited tensile strain capacity. Adding short discrete fibers to a cementitious matrix can significantly improve its performance under tensile stress, thus ultimately exhibiting a ductile behavior. Nevertheless, in spite of their beneficial properties fiber reinforced cementitious composites remain underutilized in engineering practice. One of the main reasons for this is a lack of an adequate characterization of the tensile behavior as well as a lack of analysis methods that would allow engineers to incorporate fiber reinforced structural concrete elements into their design. Therefore, this dissertation has four key objectives: 1) to computationally model a stress-strain response of high performance fiber reinforced cementitious composites in uniaxial tension and uniaxial compression prior to macro-crack localization, 2) to develop and perform a diagnostic strain localization analysis for high performance fiber reinforced cementitious composites, the results of which can characterize effects of fibers on failure precursors, 3) to devise and perform an experimental program for characterization of ultra-high performance fiber reinforced cementitious composites, and 4) to characterize a full-fledged behavior including stress-strain and stress-crack opening displacement responses of ultra-high performance fiber reinforced cementitious composites in uniaxial tension. To quantify effects of fibers on onset of strain localization in fiber reinforced cementitious composites a combined computational/analytical models have been developed. To this end, linear-elastic multi-directional fibers were embedded into a cementitious matrix. The resulting composite was described by different types of two-invariant non-associated Drucker-Prager plasticity models. In order to investigate effects of a shape of a yield surface and hardening type linear and nonlinear yield surfaces, and linear and nonlinear hardening rules were considered. Diagnostic strain localization analyses were conducted for several plane stress uniaxial tension and uniaxial compression tests on non-reinforced cementitious composites as well as on high performance fiber-reinforced cementitious composites. It was found that presence of fibers delayed the inception of strain localization in all tests on fiber-reinforced composites. Furthermore, presence of fibers exerted a more significant effect on the strain localization direction and mode in uniaxial compression than in uniaxial tension. The main objective of experimental program was to facilitate characterization of the post-cracking tensile behavior of ultra-high performance fiber reinforced cementitious composites. To this end, five different mixes of fiber-reinforced cementitious composites were cast, whereby volumetric fiber content, fiber shape and water to binder ratio were the experimental variables. Two testing methods were adopted, a direct uniaxial tension test and four-point prism bending test. Two different post-cracking behaviors were observed in direct tension tests, softening and strain hardening accompanied with multiple cracking. On the other hand, the response from prism bending tests was less scattered. Several different inverse analyses were carried out to predict stress-strain and stress-crack opening displacement responses in uniaxial tension based on the prism bending tests. The analyses resulted in worthy correlations with the experimental data, thus suggesting that the prism bending test is a viable alternative to a much more challenging to perform direct tension test for ultra-high performance fiber reinforced composites.