In this research the stochastic nonlinear dynamic behaviors and probability density function of ship rolling are studied by nonlinear dynamic method and probability theory. The probability density function of rolling response is evaluated through solving the stochastic differential equations by using path integral method based on Gauss-Legendre interpolation scheme. The time-dependent probability of ship rolling restricted within the safe domain is provided and capsizing is investigated in the probability‟s view. The random differential equation of ships‟ rolling motion is established considering the nonlinear damping, nonlinear restoring moment, the white noise wave excitation, and the colored noise wave excitation. As an example, an ocean survey vessel T-AGOS is considered to sail in the seas of Pierson-Moskowitz wave spectrum. It is found that the probability decreases as time progresses and it decreases much more quickly for the high intensity of the noise. The ship will finally leave the safe domain and capsize in the probability‟s view. It is also shown the similarity of probability density contours between the case of white noise wave excitation and the case of colored noise wave excitation.

In this research project, the Boundary Element Method (BEM) is developed and formulated for the solution of two-dimensional convection-diffusion-reaction problems. A combined approach with the dual reciprocity boundary element method (DRBEM) has been applied to solve steady-state problems with variable velocity and transient problems with constant and variable velocity fields. Further, the radial integration boundary element method (RIBEM) is utilised to handle non-homogeneous problems with variable source term. For all cases, a boundary-only formulation is produced. Initially, the steady-state case with constant velocity is considered, by employing constant boundary elements and a fundamental solution of the adjoint equation. This fundamental solution leads to a singular integral equation. The conservation laws, usually applied to avoid this integration, do not hold when a chemical reaction is taking place. Then, the integrals are successfully computed using Telles' technique. The application of the BEM for this particular equation is discussed in detail in this work. Next, the steady-state problem for variable velocity fields is presented and investigated. The velocity field is divided into an average value plus a perturbation. The perturbation is taken to the right-hand-side of the equation generating a non-homogeneous term. This nonhomogeneous equation is treated by utilising the DRM approach resulting in a boundary-only equation. Then, an integral equation formulation for the transient problem with constant velocity is derived, based on the DRM approach utilising the fundamental solution of the steady-state case. Therefore, the convective terms will be encompassed by the fundamental solution and lie within the boundary integral after application of Greens's second identity, leaving on the right-hand-side of the equation a domain integral involving the time-derivative only. The proposed DRM method needs the time-derivative to be expanded as a series of functions that will allow the domain integral to be moved to the boundary. The expansion required by the DRM uses functions which take into account the geometry and physics of the problem, if velocity-dependent terms are used. After that, a novel DRBEM model for transient convection-diffusion-reaction problems with variable velocity field is investigated and validated. The fundamental solution for the corresponding steady-state problem is adopted in this formulation. The variable velocity is decomposed into an average which is included into the fundamental solution of the corresponding equation with constant coefficients, and a perturbation which is treated using the DRM approximation. The mathematical formulation permits the numerical solution to be represented in terms of boundary-only integrals. Finally, a new formulation for non-homogeneous convection-diffusion-reaction problems with variable source term is achieved using RIBEM. The RIM is adopted to convert the domain integrals into boundary-only integrals. The proposed technique shows very good solution behaviour and accuracy in all cases studied. The convergence of the methods has been examined by implementing different error norm indicators and increasing the number of boundary elements in all cases. Numerical test cases are presented throughout this research work. Their results are sufficiently encouraging to recommend the use of the techniques developed for solution of general convection-diffusion-reaction problems. All the simulated solutions for several examples showed very good agreement with available analytical solutions, with no numerical problems of oscillation and damping of sharp fronts.

No description available.

This thesis presents the numerical algorithms to carry out the face transformation. The main efforts are denoted to the finite volume method (FVM) with the Delaunay triangulation to solve the Laplace equations in the harmonic transformation undergone in face images. The advantages of the FVM with the Delaunay triangulation are: (1) Easy to formulate the linear algebraic equations, (2) Good to retain the geometric and physical properties, (3) less CPU time needed. The numerical and graphical experiments are reported for the face transformations from a female to a male, and vice versa. The computed sequential and absolute errors are and , where N is division number of a pixel into subpixels. Such computed errors coincide with the analysis on the splitting-shooting method (SSM) with piecewise constant interpolation in [Li and Bui, 1998c].

Algebro-Differentialgleichungen (engl. differential-algebraic equations - DAEs) sind implizite singuläre gewöhnliche Differentialgleichungen, die restringierte dynamische Prozesse beschreiben. Sie unterscheiden sich von expliziten gewöhnlichen Differentialgleichungen dahingehend, dass Anfangswerte nicht beliebig vorgegeben werden können. Weiterhin sind in einer DAE neben Integrations- auch Differentiationsaufgaben involviert. Der Differentiationsindex gibt an, wieviele Differentiationen zur Lösung notwendig sind. Seit den 1980er Jahren wird vorwiegend an der Charakterisierung und Klassifizierung regulärer DAEs und der Konstruktion nebst Fundierung von Integrationsmethoden gearbeitet. I. Higueras, R. März und C. Tischendorf haben gezeigt, dass man lineare DAEs mit properem Hauptterm, A(t)(D(t)x(t))'' + B(t)x(t) = q(t), die regulär mit Traktabilitätsindex 2 sind, zuverlässig numerisch integrieren kann - im Unterschied zu linearen DAEs in Standardform. In Publikationen von R. Riaza und R. März wird die Klassifizierungen kritischer Punkten von linearen DAEs an die Verletzung bestimmter Rangbedingungen von Matrixfunktionen im Rahmen des Traktabilitätsindexes geknüpft. Im wesentlichen heißt ein kritischer Punkt harmlos, wenn der durch die inhärente Differentialgleichung beschriebene Fluß nicht tangiert ist. Gegenstand der vorliegenden Arbeit sind lineare quasi-proper formulierte DAEs. Es werden Index 2 DAEs mit harmlosen kritischen Punkten charakterisiert. Unter Verwendung von quasi-zulässigen Projektorfunktionen können neben DAEs, die fast überall gleiche charakteristische Werte haben, nun erstmalig auch solche mit Indexwechseln behandelt werden. Der Hauptteil der Arbeit besteht im Nachweis von Durchführbarkeit, Konvergenz und nur schwacher Instabilität von numerischen Integrationsmethoden (BDF, IRK(DAE)) für lineare Index 2 DAEs mit harmlosen kritischen Punkten, sowie in der Entwicklung von Fehlerschätzern und Schrittweitensteuerung. / Differential-algebraic equations (DAEs) are implicit singular ordinary differential equations, which describe dynamical processes that are restricted by some constraints. In contrast to explicit regular ordinary differential equations, for a DAE not any value can be imposed as an initial condition. Furthermore, DAEs involve not only integration problems but also differentiation problems. The differentiation index of a DAE indicates the number of differentiations required in order to solve a DAE. Since the 1980th, research focuses primarily on the characterization and classification of regular problem classes and the construction and foundation of integration methods for simulation software. I. Higueras, R. Maerz, and C. Tischendorf have shown that one can reliably integrate a general linear DAE with a properly stated leading term, A(t)(D(t)x(t))'' + B(t)x(t) = q(t), which is regular with tractability index 2 - in contrast to linear standard form DAEs. The first classification of critical points of linear DAEs has been published by R. Riaza and R. Maerz. Based on the tractability index, critical points are classified according to failures of certain rank conditions of matrix functions. Essentially, a critical point is said to be harmless, if the flow described by the inherent differential equation is not affected. The subject of this work are quasi-proper linear DAEs. Index-2 DAEs with harmless critical points are characterized. Under the application of quasi-admissible projector functions. Besides DAEs which have almost everywhere the same characteristic values, DAEs with index changes can now be discussed for the first time. The main part of the work is to provide a proof of feasibility, convergence, and only weak instability of numerical integration methods (BDF, IRK (DAE)) for linear index-2 DAEs with harmless critical points, as well as the development and testing of error estimators and stepsize control.

Orientador: Aloisio Ernesto Assan / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo / Made available in DSpace on 2018-08-07T16:33:50Z (GMT). No. of bitstreams: 1 Volpini_EstevaoXavier_M.pdf: 3994255 bytes, checksum: 682eea9ccb0ec139a6d062e4466cd140 (MD5) Previous issue date: 2006 / Resumo: Este estudo tem por objetivo implementar, em programa já existente para a análise de placas laminadas de compósitos, a análise dinâmica de placas laminadas sob ação de carregamento forçado com integração direta pelo algoritmo de Newmark. O programa inicial de elementos finitos, que realiza a análise estática, foi desenvolvido por Tápia (1998), usando o elemento finito de Kosmatka (1994), formulado com a teoria de deformação por cisalhamento de primeira ordem de Reissner-Mindlin. Cassiano (2002) implementou nesse programa o cálculo das freqüências naturais. Neste trabalho foi introduzida a análise dinâmica forçada, através da integração direta no tempo, empregando o método de Newmark. Exemplos comparativos com variações das espessuras das placas, do número de lâminas, das orientações das fibras e das vinculações das bordas, mostram o excelente comportamento do elemento finito aqui empregado / Abstract: : The aim of this study is the dynamic analysis of laminated composite plates under forced transverse vibration with time direct-integration method. The original program, with the static analysis, was developed by Tapia (1998) using the element proposed by Kosmatka (1994), formulated with first-order shear deformation theory of Reissner-Mindlin. Later Cassiano (2002) introduced into this finite element code the evaluation of the natural frequencies. In this thesis the dynamic analysis by means of a direct time integration method, which was formulated by Newmark, was performed. Comparative examples with several plates thicknesses, number of laminates, orientation of the fibers and boundary constraints, show the excellent performance of the finite element used herein / Mestrado / Estruturas / Mestre em Engenharia Civil

In this study, a computer code is developed in MATLAB&reg / to compute the Radar Cross Section (RCS) of arbitrary shaped complex targets by using Physical Optics (PO) and Modified PO. To increase the computational efficiency of the code, a novel fast integration procedure for oscillatory integrals, called Levin&rsquo / s integration, is applied to PO integrals. In order to improve the performance of PO near grazing angles and to model diffraction effects, a method called PO with Modified Surface Normal Vectors is implemented. In this method, new surface normals are defined to model the diffraction mechanism. Secondary scattering mechanisms like multiple scattering and shadowing algorithms are also included into the code to obtain a complete RCS prediction tool. For this purpose, an iterative version of PO is used to account for multiple scattering effects. Indeed, accounting for multiple scattering effects automatically solves the shadowing problem with a minor modification. Therefore, a special code for shadowing problem is not developed. In addition to frequency domain solutions of scattering problems, a waveform analysis of scattered fields in time domain is also comprised into this thesis. Instead of direct time domain methods like Time Domain Physical Optics, a Fourier domain approach is preferred to obtain the time domain expressions of the scattered fields. Frequency and time domain solutions are obtained for some simple shapes and for a complex tank model for differently polarized incident fields. Furthermore, a statistical analysis for the scattered field from the tank model is conducted.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The need for transmission lines expansion (TL) is evident in the face of growing electrical energy demand in Brazil as well as the great distances between generation and consumption centers. It is known that numerous failures can interrupt the energy transmission and the towers collapse is among the main reasons, causing huge losses to both electrical energy companies and final users. Thus, it is crucial to understand the mechanical behavior of these structures, considering the different actions that they can act so that the energy transmission can take place in a safe, efficient and economical way. In this context, this paper deals with the static and dynamic response evaluation of guyed lattice metallic towers of TLs submitted to broken conductor and broken lightning-rod cable. For this purpose, numerical models of isolated tower and completed stretch of TL were developed, including all components, towers, insulator chains, lightning-rod cables, conductor cables and prestressed stay cables. The models are subjected to static analysis through "equivalent static loads" application coming from the broken cable and dynamic analysis, in the time domain, using the method of direct integration of equations of motion explicitly, with central finite differences. The static and dynamic responses are given in terms of nodal displacements at the top and normal stresses in the tower bars. Finally, the results of the dynamic analysis in the time domain are compared with those determined by static analysis, employed in the usual design practice, that is, the peak and final values (after the structure stops vibrating) are compared with the static response values in order to verify the validity of the model used in the design practice. / A necessidade da expansão de linhas de transmissão (LTs) fica evidente diante da crescente demanda por energia elétrica no Brasil, além das grandes distâncias entre a geração e os centros consumidores. Sabe-se que inúmeras falhas podem interromper a transmissão da energia, e o colapso de torres está entre as principais, causando enormes prejuízos, tanto as companhias de energia elétrica quanto aos consumidores finais. Dessa forma, torna-se fundamental o conhecimento do comportamento mecânico destas estruturas, frente às diferentes ações que podem atuar, para que o transporte de energia ocorra de maneira segura, eficiente e econômica. Neste contexto, o presente trabalho trata da avaliação da resposta estática e dinâmica de torres metálicas treliçadas estaiadas de LTs submetidas à ruptura de cabo condutor e de cabo para-raios. Para isso, foram desenvolvidos modelos numéricos de torre isolada e de um trecho completo de LT, incluindo todos componentes, torres, cadeias de isoladores, cabos para-raios, cabos condutores e cabos de estais pré-tensionados. Os modelos são submetidos a análises estáticas, através da aplicação de cargas estáticas equivalentes oriundas da ruptura de cabo, e análises dinâmicas, no domínio do tempo, empregando o método de integração direta das equações do movimento, de forma explícita, com diferenças finitas centrais. As respostas estática e dinâmica são dadas em termos de deslocamentos nodais no topo e esforços normais nas barras da torre. Por fim, os resultados da análise dinâmica no domínio do tempo são comparados com os determinados por meio da análise estática, empregada na prática usual de projeto, ou seja, são comparados os valores de pico e os valores finais (após a estrutura parar de vibrar) com os valores da resposta estática, a fim de verificar a validade do modelo empregado na prática de projeto.

This diploma thesis deals with the measurement of flow rate in flumes type PARS P2, P3 and P4. First, there is a search for a convenient profile in confusor for research and consequently to construct graphical dependences from which to read the value of the correction coefficient for many water depths in flumes. Then, there are constructed graphical dependences from which to read the value of measurement uncertainty for many flow rates in flumes.

[pt] A resposta dinâmica de sistemas estruturais não lineares tem sido um item de grande interesse nas pesquisas em engenharia civil. Problemas onde há interação base flexível-estrutura são de grande importância na análise estrutural, já que a maioria das estruturas civis é apoiada sobre sistemas flexíveis (solo ou sistemas de apoio com dissipação de energia). Nesta área, o estudo de sistemas submetidos a ações sísmicas é um tópico relevante, já que estas solicitações têm um grande conteúdo de frequências, o que pode influenciar consideravelmente as respostas da estrutura. Neste contexto, o conhecimento da resposta em frequência de estruturas não lineares sob uma excitação de base é uma ferramenta útil para avaliar os potenciais efeitos de ações sísmicas sobre estes sistemas. Na presente tese é desenvolvida uma metodologia de análise não linear dinâmica de sistemas estruturais reticulados sob excitações de base, considerando não linearidade geométrica e apoios flexíveis, representados por molas unidimensionais, com comportamento elasto-plástico. Através de uma análise paramétrica é avaliada a variabilidade das respostas de sistemas esbeltos submetidos a ações sísmicas reais, sismos artificiais, assim como ações sísmicas sucessivas. O problema no espaço é resolvido pelo método dos elementos finitos. Para a análise em frequência, é apresentada uma metodologia baseada no método do balanço harmônico e no método de Galerkin, juntamente com técnicas de continuação para a obtenção das curvas de ressonância não lineares. O problema no tempo é abordado através da integração das equações de movimento pelos métodos de Runge-Kutta e Newmark, associado ao método de Newton-Raphson. / [en] The dynamic response of nonlinear structures has been a topic of interest in civil engineering research. Problems in which base-structure interaction is present have a great importance in structural analysis, since most structures rests on flexibel systems (soil or supports with dissipation). In this research area, the study of structures under the action of seismic loads represent a relevant topic, since this kind of excitations may excite several vibration modes and thus influence strongly the dynamic response. In this context, the prediction of the nonlinear structural behavior in frequency domain of structures under base excitation is a useful resource to assess the potential effects of sismic loads on these systems. In this thesis, a methodology for nonlinear dynamic analysis of plane frame structures under base excitation is presented considering geometric nonlinearity and elastic supports represented by elasto-plastic unidimensional springs. Trough a parametric analysis, the variability of the dynamic responses of slender structural systems under the actions of real earthquakes, synthetics earthquakes, as well as the action of multiple earthquakes is assessed. The structural systems here analyzed are discretized in space using a nonlinear finite element formulation. For the response in frequency domain, a scheme based on the Balance Harmonic Method and the Galerkin method, in conjunction with continuation methods, is formulated to obtain the nonlinear resonance curves. The nonlinear dynamic response in the time domain is calculated by direct integration of the equations of motion. For this, the Runge-Kutta method and the Newmark method in association with the iterative Newton-Raphson scheme are employed.