This dissertation is composed of three parts of contributions. Systems of a fully penetrating pumping well in a confined aquifer near a fully penetrating stream with and without streambeds are discussed in Chapter II. In Chapter III, stream-aquifer systems with a fully penetrating pumping well in a confined aquifer between two parallel fully penetrating streams with and without streambeds are discussed. Stream depletion rates in Chapter II are solved using Laplace and Fourier transform methods, and stream depletion rates in Chapter III are solved using the potential method. Chapter II presents analytical solutions in the Laplace domain for general stream depletion rates caused by a pumping well and caused by stream stage fluctuations. For seasonal case, the stream stage is a function of time. For an individual flood wave, the stream stage is a function of time and distance along the stream. Semi-analytical solutions of seasonal stream depletion rates in time domain, using a cosine function to simulate stream stage fluctuations, are presented. The stream depletion rate caused by pumping is solved analytically, while the stream depletion rate caused by stream stage fluctuations is solved numerically. Various parameters affecting stream depletion rates, such as flood period and streambed, are analyzed. For a short-term case, the pumping rate is assumed to be constant, and a Gaussian function is used as an example of floodwaves. This part is solved using the same method as used in the seasonal case. Early time and late time approximations of the stream depletion rates are also presented. This approximation leads to an interesting finding that the stream depletion rate caused by seasonal stream stage fluctuations can be neglected if the stream aquifer system has a long time to equilibrate. In Chapter III, analytical stream depletion rates caused by a pumping well between two parallel streams with and without streambeds are presented. In this chapter, stream stage is assumed to be constant. Capture zone delineations were analyzed in the case without streambed. For the case with streambed, streambed conductance, which is an important factor controlling stream depletion, is analyzed. All solutions discussed in this dissertation can be used to predict stream depletion rates and to estimate parameters controlling stream depletion rates, which is crucial for water management. In addition to the stream depletion, the derived semi-analytical solutions in the Laplace-Fourier domain can also be used to predict drawdown in the aquifer near the stream. The derived solutions may also be used inversely to find the streambed and aquifer parameters if the stream stage fluctuation can be well described.

This dissertation is composed of three parts of contributions. Systems of a fully penetrating pumping well in a confined aquifer near a fully penetrating stream with and without streambeds are discussed in Chapter II. In Chapter III, stream-aquifer systems with a fully penetrating pumping well in a confined aquifer between two parallel fully penetrating streams with and without streambeds are discussed. Stream depletion rates in Chapter II are solved using Laplace and Fourier transform methods, and stream depletion rates in Chapter III are solved using the potential method. Chapter II presents analytical solutions in the Laplace domain for general stream depletion rates caused by a pumping well and caused by stream stage fluctuations. For seasonal case, the stream stage is a function of time. For an individual flood wave, the stream stage is a function of time and distance along the stream. Semi-analytical solutions of seasonal stream depletion rates in time domain, using a cosine function to simulate stream stage fluctuations, are presented. The stream depletion rate caused by pumping is solved analytically, while the stream depletion rate caused by stream stage fluctuations is solved numerically. Various parameters affecting stream depletion rates, such as flood period and streambed, are analyzed. For a short-term case, the pumping rate is assumed to be constant, and a Gaussian function is used as an example of floodwaves. This part is solved using the same method as used in the seasonal case. Early time and late time approximations of the stream depletion rates are also presented. This approximation leads to an interesting finding that the stream depletion rate caused by seasonal stream stage fluctuations can be neglected if the stream aquifer system has a long time to equilibrate. In Chapter III, analytical stream depletion rates caused by a pumping well between two parallel streams with and without streambeds are presented. In this chapter, stream stage is assumed to be constant. Capture zone delineations were analyzed in the case without streambed. For the case with streambed, streambed conductance, which is an important factor controlling stream depletion, is analyzed. All solutions discussed in this dissertation can be used to predict stream depletion rates and to estimate parameters controlling stream depletion rates, which is crucial for water management. In addition to the stream depletion, the derived semi-analytical solutions in the Laplace-Fourier domain can also be used to predict drawdown in the aquifer near the stream. The derived solutions may also be used inversely to find the streambed and aquifer parameters if the stream stage fluctuation can be well described.

Made available in DSpace on 2014-10-09T12:54:34Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T14:09:26Z (GMT). No. of bitstreams: 0 / Dissertação (Mestrado) / IPEN/D / Instituto de Pesquisas Energéticas e Nucleares - IPEN/CNEN-SP

Made available in DSpace on 2014-10-09T12:54:34Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T14:09:26Z (GMT). No. of bitstreams: 0 / Este trabalho apresenta uma solução analítica obtida pelo método de expansão para cinética espacial usando o modelo de difusão e considerando meios homogêneos multiplicativos subcríticos acionados por fonte externa. Em particular, partindo de modelos mais simples e aumentando a complexidade do sistema, resultados foram obtidos para diferentes tipos de transientes. Inicialmente, uma solução analítica foi obtida considerando um grupo de energia sem nêutrons atrasados, em seguida considerou-se um sistema de um grupo de energia e uma família de precursores. A solução para o caso G grupos de energia e R famílias de precursores em forma fechada é obtida, apesar do fato que não possa ser resolvido analiticamente, uma vez que não existe forma explícita para os autovalores e métodos numéricos devem ser utilizados para resolver tal problema. Para ilustrar a solução geral um problema de multigrupo (três grupos de energia) dependente do tempo sem precursores é apresentada e os resultados numéricos obtidos usando um código de diferenças finitas são comparados com os resultados exatos para diferentes tipos de transientes. / Dissertação (Mestrado) / IPEN/D / Instituto de Pesquisas Energéticas e Nucleares - IPEN/CNEN-SP

The transient temperature fields induced by welding processes largely determine the size of the fusion and heat-affected zones, the microstructures, residual stresses and distortion both in the vicinity of the weld and in the final component as a whole. An accurate prediction of these fields relies heavily on the representation of the welding heat source, both in space and in time. The double-ellipsoidal heat source model proposed by Goldak and co-workers has been widely used to simulate the heat transferred from an electric arc to a component and to compute the induced transient temperature fields. This double-ellipsoidal distribution has worked well for many welding applications, but it is less appropriate when representing the heat transfer at the base of a groove whose width is narrow in relation to its depth. Similarly the conical heat source models used to represent the electron beam welding process, when applied in keyhole mode, are less appropriate when the keyhole terminates within the component, such as in the case of a partial penetration weld. In this work, the double-ellipsoidal heat source model is extended, and alternatives presented, to account for a wider set of welding scenarios, including narrow weld groove geometries and keyhole welding scenarios. A series of mathematically robust novel heat source models is presented and the models are validated against experimental data obtained during the application of various welding processes to an important grade of pressure vessel steel, namely SA508 Grade 3 class 1 steel. The calculation of the transient temperature fields during welding is extremely computationally expensive using numerical methods. Where available, and appropriate, analytical solutions are presented for these novel welding heat source models, coupled with analytical methods for accounting for time dependent heat input rates, to not only reduce computational cost but also to achieve precise predictions of the temperature fields. This, in turn, has the potential to contribute to improvements in safety assessments on critical welded infrastructure through improved predictions for the evolution of microstructure, mechanical properties and the levels of residual stress and distortion in welded joints.

The Eshelby-Stroh formalism is used to analyze the generalized plane strain quasistatic deformations of an anisotropic, linear elastic laminated plate.The formulation admits any set of boundary conditions on the edges and long faces of the laminate. Each lamina may be generally anisotropic with as many as 21 independent elastic constants. The three dimensional governing differential equations are satisfied at every point of the body.The boundary conditions and interface continuity conditions are satisfied in the sense of a Fourier series. Results are presented for three sample problems to illustrate the versatility of the method. The solution methodology is generalized to study the deformation of finite rectangular plates subjected to arbitrary boundary conditions. The effect of truncation of the series on the accuracy of the solution is carefully examined. Results are presented for thick plates with two opposite edges simply supported and the other two subjected to eight different boundary conditions. The results are compared with three different plate theories.The solution exhibits boundary layers at the edges except when they are simply supported. Results are presented in tabular form for different sets of edge boundary conditions to facilitate comparisons with predictions from various plate theories and finite element formulations. The Eshelby-Stroh formalism is also extended to study the generalized plane deformations of piezothermoelastic laminated plates. The method is capable of analyzing laminated plates with embedded piezothermoelastic patches. Results are presented for a thermoelastic problem and laminated elastic plates with piezothermoelastic lamina attached to its top surface. When a PZT actuator patch is attached to an elastic cantilever substrate, it is observed that the transverse shear stress and transverse normal stress are very large at the corners of the PZT-substrate interface. This dissertation is organized in the form of three self-contained chapters each of which will be submitted for possible publication in a journal. / Ph. D.

No / The advection–dispersion equation (ADE) is one of the most widely used methods for estimating natural stream pollution at different locations and times. In this paper, variational iteration method (VIM) is utilized to obtain a semianalytical solution for 1D ADE in a temporally dependent solute dispersion within uniformsteady flow. Through a computational validation, the effect of different parameters such as uniform flow velocity and dispersion coefficient on the solute concentration values has been investigated. Results show that the change in velocity has a strong effect on fluid density variation. However, when the diffusion coefficient has been increased, the change in flow and velocity behaviors is negligible. To verify the proposed semianalytical solution, the results were compared to analytical solutions and errors were found to be <0.7% in all simulations.

Yes / Solutions for dam-break flow mainly developed for rectangular channels are not applicable to prediction of the propagation of the dam-break wave in frictional triangular channels. This study presents an approximate solution considering the frictional effect on the dam-break flow in a dry horizontal triangular channel. Wave tip velocity is solved by an implicit formula for the product of time and resistance coefficients. All other hydraulic properties in the wave tip region can be expressed as explicit functions of wave tip velocity. Meanwhile, laboratory experiments have been performed for obtaining water surface profiles of dam-break flow from which the position and velocity of the wave tip front have been derived. Results show that retardation of the wave front position is more significant with the increases in both resistance and time. The proposed analytical solution shows satisfactory agreement with measurements, and clarifies how the behavior of the dam-break wave tip is affected by channel geometry.

An Analytical Strip Method (ASM) for the analysis of stiffened and non-stiffened antisymmetric laminated composite plates is derived by considering the bending-extension coupling effect for bending, free vibration and buckling. A system of three equations of equilibrium, governing the general response of arbitrarily laminated composite plates, is reduced to a single eighth order partial differential equation in terms of a displacement function. The displacement function is solved in a single series form to determine the displacement, fundamental frequency, and buckling load of antisymmetric cross-ply and angle-ply laminated composite plates. The solution is applicable to rectangular plates with two opposite edges simply supported, while the other edges are simply supported, clamped, free, beam supported, or any combinations of these boundary conditions. This method overcomes the limitations of other analytical methods (Navier’s and Lévy’s), and provides an alternative to numerical, semi-numerical, and approximate methods of analysis. Numerical examples of bending, free vibration, and buckling of antisymmetric laminated composite plates are presented in tabular and graphical form. Whenever possible, the results of the present study are compared with those published in the literature and/or ANSYS solutions. The comparison firmly establishes that this method could be used for the analysis of antisymmetric laminated composite plates. Future research needs are identified for the aspects that have not been reached by the present study and others.

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