Reactivity ratios for the homogeneous free radical initiated copolymerization of acrylonitrile and methyl acrylate were measured by NMR on isolated, low conversion copolymers and by real time in situ FTIR. The system utilized azobisisobutyronitrile (AIBN) initiator in dimethyl formamide (DMF) at 62°. The FTIR technique allowed rapid generation of extensive copolymer compositions, which permitted application of nonlinear least squares methodology for the first time to this copolymer system. Thus, reactivity ratios at the 95% confidence level were determined to be 1.29 ± 0.2 and 0.96 ± 0.2 for acrylonitrile and methyl acrylate, respectively. The results are useful for the development of acrylonitrile (<90%) melt processable copolymer fibers and films, which could include precursors for carbon fibers. / Master of Science

The thesis of this study is that modern optimization theory is a natural extension of classical optimization theory. As such, modern optimization theory will be applied to administrative problems only after interpretive studies are made that provide (1) an explanation of the general theoretical development of the techniques of modern optimization theory, (2) computational algorithms for implementing the techniques of modern optimization theory, (3) detailed demonstrations of the computational aspects of each technique and its corresponding algorithm, and (4) an identification of the types of problems to which these techniques are applicable.

O objetivo principal deste trabalho é o desenvolvimento de uma formulação e sua implementação computacional para se analisar, via Método dos Elementos Finitos (MEF),o comportamento dinâmico não linear geométrico de sólidos bidimensionais. Trata-se o comportamento geometricamente não linear através de uma formulação posicional classificada como lagrangeana total com cinemática exata. No estudo do comportamento dinâmico utiliza-se um algoritmo de integração temporal baseado na família de integradores temporais de Newmark. Para a consideração do impacto adota-se uma técnica que utiliza como integrador temporal o algoritmo de Newmark, modificado de forma a garantir sua estabilização, e limita-se a posição de cada nó da estrutura que por ventura sofra impacto. O código computacional desenvolvido é validado através de exemplos tradicionais da literatura científica. Analisam-se exemplos com comportamento apenas não linear geométrico e não linear geométrico dinâmico com ou sem impacto / The main goal of this work is the development of a formulation and its computational implementation, based on the finite element method (FEM), to analyze the dynamic geometrically nonlinear behavior of bidimensional solids. The geometrically nonlinear behavior is treated with a positional formulation classified as total Lagrangean with exact kinematics. In the study of the dynamic behavior, a time integration algorithm based on the family of time integrators of Newmark is applied. In order to consider the impact, a technique based on the time integrator of Newmark, modified to assure its stabilization, is used. This technique limits the position of each node that suffers impact. The developed computational code is validated through benchmarks of scientific literature. Examples with static geometrically nonlinear and dynamic geometrically nonlinear behavior, with or without impact, are analyzed

A pesquisa foi desenvolvida com a finalidade de se analisar o comportamento elástico e inelástico de estruturas de cabos, sob carregamento estático, pela técnica dos elementos finitos. Para a discretização das estruturas de cabos adotou-se um elemento retilíneo isoparamétrico, e na formulação dos princípios variacionais foram considerados a não linearidade física do material e a não linearidade geométrica, inerente às estruturas de cabos. Empregou-se o método incrementai-iterativo de Newton-Raphson para a resolução do sistema de equações não lineares. Alternativamente a solução foi obtida da minimização direta da função energia potencial total da estrutura de cabos, utilizando-se o método do Gradiente Conjugado. Vários exemplos de estruturas de cabos comumente empregadas em coberturas de grandes vãos foram estudados. Os resultados obtidos segundo os dois procedimentos foram analisados e a eficiência elos métodos foi comprovada. / The research was developed with the purpose of analyzing the elaslic and the inelaslic behaviour of cable slructures, under static load. The finite element method with straight isoparametric element was used. In the formulation of the variational principles, the material and the geometric non-linearity were considered. The Newton-Raphson method was used to resolve the non-linear equations system. Alternatively the solution was obtained of the direct minimization of the total potential energy of the cable structure; in this case using the Conjugated Gradient Method. Several examples of cable structures, commonly employed in roofs of large spaces were studied. The results were obtained according to both processes and the efficiency of the methods was verified.

A Cronobiologia estuda a origem e a manifestação de ritmos biológicos nos mais diversos táxons. A análise dos dados obtidos experimentalmente, contudo, é bastante complexa, haja vista a restrita gama de métodos disponíveis para tal. Os osciladores que determinam a existência dos ritmos biológicos são exemplos de sistemas dinâmicos não-lineares, os quais estão amplamente distribuídos nos seres vivos. Esses sistemas, por suas peculiaridades, são melhor analisados por métodos não-lineares. O objetivo deste trabalho é testar diferentes métodos de análise séries temporais, tanto alguns classicamente empregados na Cronobiologia quanto métodos não-lineares, verificando sua empregabilidade e funcionalidade para dados cronobiológicos, bem como as propriedades que permitem ou não seu uso. Para tanto, foram utilizados dados de ritmos de consumo de O2 obtidos para diferentes grupos etários de operárias de Melipona quadrifasciata (Hymenoptera, Meliponini). Tais dados foram submetidos às seguintes análises: Transformada Rápida de Fourier (TRF), Análise de Potência Espectral (PSA), Estatística Circular (teste de Rayleigh), Teste de Estacionariedade (Teste da Raiz Unitária de Dickey-Fuller Aumentado - ADF), Plot de Poincaré, Entropia Aproximada (ApEn) e Entropia Aproximada Volumétrica (vApEn). Os resultados obtidos demonstram que os métodos não-lineares de análise detectam a existência de ritmo metabólico, assim como os métodos lineares utilizados por Teixeira (2006) e Camargo (em andamento) indicam sua presença. Ressalta-se, contudo, que há certa dificuldade em distinguir se a variabilidade existente nas séries deve-se, possivelmente, a seu comportamento determinístico ou a ruídos externos a elas, cuja detecção não é possível. Outro importante fator limitante da aplicabilidade das análises não-lineares é o número de pontos das séries temporais em questão, que era bastante reduzido nesse estudo. Dessa maneira, conclui-se que alguns métodos não-lineares, e.g. TRF, também são eficazes na detecção de ritmos biológicos, devendo ser observada a restrição devido ao tamanho da série temporal. / Chronobiology is the study of the origin and manifestation of rhythmical phenomena in all sorts of taxons. The analysis of the experimental obtained data is, however, still very complex due to the lack of availability of methods and techniques. The oscillators that determine the existence of rhythmical biological phenomena are examples of non-linear dynamic systems, which are widely spread among organisms. This research intends to present the result of a sort of temporal series analysis methods, some already used for Chronobiology research, as non-linear methods, testing their use and functionality for chronobiological data as well as determining their gaps and limitations for this purpose. For this research, data regarding to rhythm of O2 consumption were obtained from different age groups of Melipona quadrifasciata (Hymenoptera, Meliponini) workers. Such data were submitted to the following analysis: Fast Fourier Transform (FFT), Power Spectrum Analysis (PSA), Circular Statistics (Rayleigh\'s test), Stationarity Test (Unit Root Augmented Dickey-Fuller Test - ADF), Poincaré Plot, Approximate Entropy (ApEn) e Volumetric Approximate Entropy (vApEn). The results indicate that nonlinear methods detect the presence of metabolic rhythm, such as previous researches where linear methods used by Teixeira (2006) and Camargo (ongoing research) indicate its presence. However, there is some difficulty in determining if the variability present in the series is possibly due to its deterministic behavior or to the external noise, from which the determination is still not possible. Another limiting factor is the number of points of analyzed temporal series, which was very small. We conclude that some nonlinear methods, e.g. FFT, are effective to detect biological rhythms, but the constraint to time series length must be observed.

Trata de formulações e algoritmos para a análise não linear em problemas de impacto bidirecional entre estruturas reticuladas. São apresentadas novas formulações posicionais para problemas não lineares geométricos para os casos estático e dinâmico, baseadas no método dos elementos finitos. As formulações desenvolvidas são estendidas para problemas de impacto bidirecional entre estruturas reticuladas e anteparo rígido. Utiliza-se o método do multiplicador de Lagrange para impor as restrições de contato. Uma pesquisa foi realizada para se encontrar integrador temporal estável para análises de impacto. Desenvolveu-se uma nova estratégia de previsão do impacto, através da teoria de problemas potenciais e do método dos elementos de contorno. Por fim, a formulação é adaptada para o estudo de impacto bidirecional entre estruturas reticuladas, adotando-se algoritmo de retorno geométrico, no qual consideram-se situações com e sem atrito. São apresentados diversos exemplos numéricos, comparando-se resultados obtidos com soluções analíticas e numéricas de outros trabalhos. A formulação desenvolvida ainda considera efeitos elastoplásticos nos membros estruturais e ligações com deslocamentos livres nas conexões nodais, possibilitando a análise de mecanismos flexíveis / This work deals with formulations and algorithms for nonlinear bi-directional impact analysis between reticulated structures. New positional formulations for static and dynamic nonlinear cases are presented, both based on the finite element method. The developed formulations are extended to bi-directional impact problem between reticulated structures and rigid wall, using the Lagrange multiplier method to impose contact conditions. An appropriated time integration scheme is used to alleviate the numerical errors due high frequency vibrations occurring in the impact. Finally, the formulation is adapted for the bi-directional impact between reticulated structures. During the thesis several numerical examples are presented, comparing the obtained results with analytical and other numerical responses. The developed formulation also considers elastoplastic effects in structural members and nodal connections with free displacements

The frame tube buildings have been the most efficient structural system used for building which is in the range of 40-100storey. The soaring heights and the demanding structural efficiency have led to them having smaller reserves of stiffness and consequently stability. In this thesis a Non-linear analysis and stability check of frame-tube building is done. Nonlinear analysis offers several options for addressing problems of nonlinearity and in this work focus is on Geometric Non-linearity. The main sources can be identified as P-Æ’´ effect of gravity loading acting on a transversely displaced structure due to lateral loading and can also be due to member imperfections, such as member camber and out of plumb erection of the frame. During analysis the element response keep continuously changing as a function of the applied load so simple step computing methods have been employed instead of direct analytical methods. The problem here is dealt in a piece wise linear way and solved. In this thesis a program using the matrix approach has been developed. The program developed can calculate the buckling load and can do Linear and Non-linear analysis using the Mat-lab as the computing platform. Numerical results obtained from the program have been compared with the Finite Element software Mastan2. The comparative solutions presented later on in the report clearly prove the accuracy of the program and go on to show, how exploiting simple matrix equation can help solve the most complex structures in fraction of seconds. The program is modular in structure. It provides opportunity for user to make minor manipulation or can append his own module to make it work for his specific needs and will get reliable results.

As vigas mistas de aço e concreto, por empregarem cada um desses materiais dentro de suas melhores características mecânicas, são uma boa solução estrutural para vários problemas de engenharia. Em função da geometria, carregamento e restrições de deslocamentos essas vigas apresentam vários modos de falhas que precisam ser verificados no seu dimensionamento. Nesse contexto, esse trabalho tem como objetivo estudar o comportamento das vigas mistas em situações onde a aplicação da não linearidade geométrica pode a priori ser importante. Em vigas simplesmente apoiadas, com a linha neutra localizada no perfil de aço e em vigas contínuas na região de momentos negativos, o perfil de aço está sujeito à compressão. Nessas situações os modos de falha de flambagem local, flambagem lateral por torção e flambagem distorcional (no caso de perfis I enrijecidos) podem ocorrer principalmente quando o perfil de aço é do tipo não compacto. Em vigas mistas com aberturas no perfil de aço, por exemplo, para passagem de tubulações, também há modos de falhas adicionais que devem ser investigados. O trabalho em questão foi conduzido empregando-se o código desenvolvido no CEMACOM com pequenas alterações para a priori permitir analisar problemas com pequenas não linearidades geométricas. Em paralelo empregou-se o software ANSYS customizado para analisar problemas com não linearidades geométricas significativas. Vários exemplos foram analisados empregando-se ambos os softwares e os resultados obtidos mostram o bom funcionamento do ANSYS customizado e do script para modelar vigas mistas. Por outro lado, algumas vigas analisadas demonstraram a carência de alguns recursos do programa desenvolvido no CEMACOM. / The steel - concrete composite beams are a good structural solution to various engineering problems. The main advantage of steel - concrete composite beams is to employ each of these materials within their best mechanical characteristics, which results in a more efficient stiffness/ weight ratio. Due to the geometry, loading and displacement constraints, these beams present several failure modes that need to be verified in their design. In simply supported beams, the steel profile is subjected to compression when the neutral line is located in the steel profile. In continuous beams, the steel profile is subject to compression in the hogging moment region. In these situations, local buckling, lateral - torsional buckling, and distortional buckling failure modes (in the case of I stiffened profiles) may occur. Local buckling becomes important when the steel profile is of the non-compact type. In several practical situations it is also common to use composite beams with openings in the steel profile, for example, for passage of pipes. This solution also introduces failure modes that must be investigated. A priori these problems require the use of a nonlinear geometric analysis to be studied. The work in question was conducted using the code developed in CEMACOM with small changes to a priori allow analyzing problems with small geometric nonlinearities. In parallel, the customized ANSYS software was used to analyze problems with significant geometric nonlinearities. Several examples were analyzed using both software and the results obtained show the proper functioning of the customized ANSYS and the script to model mixed beams. On the other hand, some analyzed beams demonstrated the lack of some resources of the program developed in CEMACOM.

This thesis investigates the flexural behavior of interlocking compressed earth block (ICEB) shear walls. In-plane cyclic tests were conducted to evaluate the performance of three flexure dominant large scale ICEB specimens: a slim wall with a 2:1 height to width aspect ratio, a flanged wall, and a wall with an opening at the center. Following the experimental investigation, two types of analyses were conducted for calculating the ultimate strength of flexure dominant ICEB walls: a nonlinear static analysis model assuming lumped plasticity and a plastic analysis model. In addition, incremental dynamic analysis was conducted to address the seismic performance of flexure dominant ICEB buildings. Based on the database from the incremental dynamic analysis, the collapse potential of demonstration ICEB buildings were compared for the countries of interest.

In the first part of this dissertation, we produce and study a generalized mathematical model of solid combustion. Our generalized model encompasses two special cases from the literature: a case of negligible heat diffusion in the product, for example, when the burnt product is a foam-like substance; and another case in which diffusivities in the reactant and product are assumed equal. In addition to that, our model pinpoints the dynamics in a range of settings, in which the diffusivity ratio between the burned and unburned materials varies between 0 and 1. The dynamics of temperature distribution and interfacial front propagation in this generalized solid combustion model are studied through both asymptotic and numerical analyses. For asymptotic analysis, we first analyze the linear instability of a basic solution to the generalized model. We then focus on the weakly nonlinear case where a small perturbation of a neutrally stable parameter is taken so that the linearized problem is marginally unstable. Multiple scale expansion method is used to obtain an asymptotic solution for large time by modulating the most linearly unstable mode. On the other hand, we integrate numerically the exact problem by the Crank-Nicolson method. Since the numerical solutions are very sensitive to the derivative interfacial jump condition, we integrate the partial differential equation to obtain an integral-differential equation as an alternative condition. The result system of nonlinear algebraic equations is then solved by the Newton’s method, taking advantage of the sparse structure of the Jacobian matrix. By a comparison of our asymptotic and numerical solutions, we show that our asymptotic solution captures the marginally unstable behaviors of the solution for a range of model parameters. Using the numerical solutions, we also delineate the role of the diffusivity ratio between the burned and unburned materials. We find that for a representative set of this parameter values, the solution is stabilized by increasing the temperature ratio between the temperature of the fresh mixture and the adiabatic temperature of the combustion products. This trend is quite linear when a parameter related to the activation energy is close to the stability threshold. Farther from this threshold, the behavior is more nonlinear as expected. Finally, for small values of the temperature ratio, we find that the solution is stabilized by increasing the diffusivity ratio. This stabilizing effect does not persist as the temperature ratio increases. Competing effects produce a “cross-over” phenomenon when the temperature ratio increases beyond about 0.2. In the second part, we study the existence and decay rate of a transmission problem for the plate vibration equation with a memory condition on one part of the boundary. From the physical point of view, the memory effect described by our integral boundary condition can be caused by the interaction of our domain with another viscoelastic element on one part of the boundary. In fact, the three different boundary conditions in our problem formulation imply that our domain is composed of two different materials with one condition imposed on the interface and two other conditions on the inner and outer boundaries, respectively. These transmission problems are interesting not only from the point of view of PDE general theory, but also due to their application in mechanics. For our mathematical analysis, we first prove the global existence of weak solution by using Faedo-Galerkin’s method and compactness arguments. Then, without imposing zero initial conditions on one part of the boundary, two explicit decay rate results are established under two different assumptions of the resolvent kernels. Both of these decay results allow a wider class of relaxation functions and initial data, and thus generalize some previous results existing in the literature.