Na presente tese é resolvida a equação de difusão de nêutrons estacionária, bem como problemas de cinética, em geometria unidimensional cartesiana multi-região considerando o modelo de multigrupos de energia. Um dos objetivos e inovação neste trabalho é a obtenção de uma solução aproximada com estimativa de erro, controle de precisão e na forma de uma expressão analítica. Com esse tipo de solução não há a necessidade de recorrer a esquemas de interpolação, geralmente necessários em caso de discretizações do domínio. O fluxo de nêutrons é expandido em uma série de Taylor cujos coeficientes são encontrados utilizando a equação diferencial e as condições de contorno e interface. O domínio é dividido em várias células, cujo tamanho e o grau do polinômio são ajustáveis de acordo com a precisão requerida. Para resolver o problema de autovalor é utilizado o método da potência. A metodologia é aplicada em um benchmark que consiste na solução da equação de difusão como condição inicial e na solução de problemas de cinética para diferentes transientes. Os resultados são comparados com sucesso com resultados da literatura. A convergência da série é garantida pela aplicação de um raciocínio baseado no critério de Lipschitz para funções contínuas. Cabe ressaltar que a solução obtida, em conjunto com a análise da convergência, mostra a solidez e a precisão dessa metodologia. / In the present dissertation the one-dimensional neutron diffusion equation for stationary and kinetic problems in a multi-layer slab has been solved considering the multi-group energy model. One of the objectives and innovation in this work is to obtain an approximate solution with error estimation, accuracy control and in the form of an analytical expression. With this solution there is no need for interpolation schemes, which are usually needed in case of discretization of the domain. The neutron flux is expanded in a Taylor series whose coefficients are found using the differential equation and the boundary and interface conditions. The domain is divided into several layers, whose size and the polynomial order can be adjusted according to the required accuracy. To solve the eigenvalue problem the conventional power method has been used. The methodology is applied in a benchmark problem consisting of the solution of the diffusion equation as an initial condition and solving kinetic problems for different transients. The results are compared successfully with the ones in the literature. The convergence of the series is guaranteed by applying a criterion based on the Lipschitz criterion for continuous functions. Note that the solution obtained, together with the convergence analysis, shows the robustness and accuracy of this methodology.

Design optimization of truss structures is a popular topic in aerospace, mechanical, civil, and structural engineering due to benefits to industry. Common design problem for the structures is the weight minimization. Especially in aerospace engineering the minimization of the weight of the total structure gets the highest importance in the design. This study focuses on the design optimization of 2D and 3D truss structures. The objective function is the total mass of the structure which is subjected to stress and nodal displacement constraints. To optimize the design, Genetic Algorithm (GA) is preferred due to its efficiency in dealing with problems with discrete design variables as in the case of truss structures. This technique yields more realistic results than linear programming methods. In the thesis, a finite element code is developed for the analysis of planar and space truss structures. The developed finite element solver is coupled with a genetic algorithm optimization code which is also developed as a part of the thesis study. Different truss optimization case studies are performed to demonstrate the performance of the finite element solver and the genetic algorithm optimization code that are developed. It is shown that with the use of adaptive penalty function employing scaled fitnesses, the arbitrariness issue of the factor multiplying the error term in the augmented fitness function can be resolved. It is also shown that significant weight reduction can v be achieved by employing shape optimization together with size optimization compared to pure size optimization.

Structural optimization is achieving the best objective function from a predefined medium, well bounded by constraints. Optimization methods have been utilized on different engineering applications to minimize the conceptual design effort that creates the necessity of new optimization techniques. Evolutionary Structural Optimization (ESO) is a topological optimization algorithm, which is defined as removing of inefficient elements from a design domain. ESO stress based method is applied to linear elastic, isotropic aircraft components for multiple load case. The bulk structure is modeled and discretized into three dimensional solid hexahedron or tetrahedron mesh, afterwards constraints, load and boundary conditions are defined in MSC.PATRAN. MSC.NASTRAN is utilized as finite element solver. The stress results are collected and evaluated by program developed in MICROSOFT VISUAL BASIC. The elements which are below the stress limit are eliminated. The remaining elements are operated after increasing the stress limit. The iteration process continued until prescribed rejection ratio is reached. Well known examples in literature are solved using program code and similar results are obtained which is a check for the code developed. Four generic aircraft components, the clevis, the lug, the main landing fitting and power control unit fitting were structurally optimized. The stress distribution in optimized results and existing aircraft designs are compared.

In this study, the structural optimization of a cruise missile wing is accomplished for the aerodynamic loads for four different flight conditions. The flight conditions correspond to the corner points of the V-n diagram. The structural analysis and optimization is performed using the ANSYS finite element program. In order to construct the flight envelope and to find the pressure distribution in each flight condition, FASTRAN Computational Fluid Dynamics program is used. The structural optimization is performed for two different wing configurations. In the first wing configuration all the structural members are made up of aluminum material. In the second wing configuration, the skin panels are all composite material and the other members are made up of aluminum material. The minimum weight design which satisfies the strength and buckling constraints are found for both wings after the optimization analyses.

In this thesis, structural optimization study is performed by using three different methods. In the first method, optimization is performed using MSC.NASTRAN Optimization Module, a commercial structural analysis program. In the second method, optimization is performed using the optimization code prepared in MATLAB and MSC.NASTRAN as the solver. As the third method, optimization is performed by using the optimization code prepared in MATLAB and analytical equations as the solver. All three methods provide certain advantages in the solution of optimization problems. Therefore, within the context of the thesis these methods are demonstrated and the interface codes specific to the programs used in this thesis are explained in detail. In order to compare the results obtained by the methods, the verification study has been performed on a cantilever beam with rectangular cross-section. In the verification study, the height and width of the cross-section of the beam are taken as the two design parameters. This way it has been possible to show the design space on the two dimensional graph, and it becomes easier to trace the progress of the optimization methods during each step. In the last section structural optimization of a multi-element wing torque box has been performed by the MSC.NASTRAN optimization module. In this section geometric property optimization has been performed for constant tip loading and variable loading along the wing span. In addition, within the context of shape optimization optimum rib placement problem has also been solved.

The major concern in the design of the multi-storey buildings is the structure to have enough lateral stability to resist wind forces. There are different ways to limit the lateral drift. First method is to use unbraced frame with moment-resisting connections. Second one is to use braced frames with moment-resisting connections. Third one is to use pin-jointed connections instead of moment-resisting one and using bracings. Finally braced frame with both moment-resisting and pin-jointed connections is a solution. There are lots of bracing models and the designer should choose the appropriate one. This thesis investigates optimal lateral bracing systems in steel structures. The method selects appropriate sections for beams, columns and bracings, from a given steel section set, and obtains a design with least weight. After obtaining the best designs in case of weight, cost analysis of all structures are carried out so that the most economical model is found. For this purpose evolution strategies optimization method is used which is a member of the evolutionary algorithms search techniques. First optimum design of steel frames is introduced in the thesis. Then evolution strategies technique is explained. This is followed by some information about design loads and bracing systems are given. It is continued by the cost analysis of the models. Finally numerical examples are presented. Optimum designs of three different structures, comprising twelve different bracing models, are carried out. The calculations are carried out by a computer program (OPTSTEEL) which is recently developed to achieve size optimization design of skeletal structures.

This thesis gives a comprehensive study on the effect of using different structural idealizations on the design, analysis and optimization of thin walled semi-monocoque wing structures in the preliminary design phase. In the design part, wing structures are designed by employing two different structural idealizations that are typically used in the preliminary design phase. In the structural analysis part, finite element analysis of one of the designed wing configurations is performed using six different one and two dimensional element pairs which are typically used to model the sub-elements of semi-monocoque wing structures. The effect of using different finite element types on the analysis results of the wing structure is investigated. During the analysis study, depending on the mesh size used, conclusions are also inferred with regard to the deficiency of certain element types in handling the true external load acting on the wing structure. Finally in the optimization part, wing structure is optimized for minimum weight by using finite element models which have the same six different element pairs used in the analysis phase. The effect of using different one and two dimensional element pairs on the final optimized configurations of the wing structure is investigated, and conclusions are inferred with regard to the sensitivity of the optimized wing configurations with respect to the choice of different element types in the finite element model. Final optimized wing structure configurations are also compared with the simplified method based designs which are also optimized iteratively. Based on the results presented in the thesis, it is concluded that with the simplified methods, preliminary sizing of the wing structures can be performed with enough confidence, as long as the simplified method based designs are also optimized. Results of the simplified method of analysis showed that simplified method is applicable to be used as an analysis tool in performing the preliminary sizing of the wing structure before moving on to more refined finite element based analysis.

The objective of this study is to investigate the use and efficiency of Differential Evolution (DE) method on structural optimization. The solution algorithm developed with DE is computerized into software called SOP2011 using VB.NET. SOP2011 is automated to achieve size optimum design of steel structures consisting of 1-D elements such as trusses and frames subjected to design provisions according to ASD-AISC (2010) and LRFD-AISC (2010). SOP2011 works simultaneously with the structural analysis and design software SAP2000 in order to find the global or near optimum designs for real size truss and frame structures in which the optimization problem is classified as constrained, discrete size optimization. Software interacts with SAP2000 through the Open Application Programming Interface (OAPI), which provides an access to information of SAP2000 inputs and outputs. It is programmed for finding reasonable and optimized results for truss and frame steel structures by choosing appropriate ready sections for structural members considering the minimum weight via DE technique. Based on the comparison of the obtained results with the literature, DE algorithm with penalty function implementation is proved to be an efficient optimization technique amongst several major methods used for discrete constrained size optimization of real size steel structures. Also, it has been shown that by using optimized designs obtained by DE, weight of the structures can be reduced up to 67.9% for steel truss structures and 41.7% for steel frame structures compared to SAP2000 auto design procedure, hence resulting a significant saving of materials, cost, work hours and energy required for the project.

Thesis (M.S.)--Mississippi State University. Department of Mechanical Engineering. / Title from title screen. Includes bibliographical references.

This research includes a preliminary study prior to the commencement of the Ph.D. work and three phases of design, construction and testing of three generations of moment-shaped beams. Each phase of the research brought a better understanding of curved beams which follow the shape of the moment diagram. The moment diagram in this study was for simply supported beams supporting a uniformly distributed load as would be the case in the majority of building designs. The original theory for this research can be described as follows: Moment-shaped beams are the natural outcome of a fundamental understanding of stress paths in a horizontal load bearing member. By following these stress paths we may provide materials where required to most efficiently carry the compression and tension stresses to the supports. Allowing stresses to follow their naturally desired paths reduces regions where stresses cross paths called disturbed regions. The outcome of the final phase of this research was the development of the third generation of curved beams with a camber. These beams, designated as Cambered Curve beams (CCBs), exhibited the same behaviour as the rectangular control beam design using CSA-A23.3 up to the serviceability failure of L/360 (12mm). The CCB moment-shaped beams require 20% less concrete and 40% less reinforcing steel (no shear stirrups) to carry the ultimate load which is only 12% less than that carried by the CSA-designed control beam. Due to a closed system of internal forces, the moment-shaped beams remain intact and are able to sustain self weight, even after total failure. A significant part of this research was to modify and verify a FORTRAN-based finite element analysis program: FINIT-Y. This program was reconstructed to analyse a full size beam, and enabled the researcher to model and correctly predict the maximum load, crack pattern and failure mode. This study found that moment-shaped beams with no shear reinforcement have the same stiffness and load carrying capacity as the CSA-designed rectangular control beam with shear reinforcement up to serviceability failure (L/360). The study also found that moment-shaped beams have significantly lower ductility at the ultimate load.