Title: Long range dependence in time series Author: Alexander Till Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Michaela Prokešová, Ph.D. Abstract: The diploma thesis demonstrates the necessity of a study of long range dependence, introduces fractional Gaussian noise and discusses possible definitions of long memory. It is done by notions of ergodic theory and by second moment characteristics and spectral density. These definitions are confronted with the model of fractional Gaussian noise and with intuitive understanding of long range memory. Relations and connections between these criteria are studied as well. The work is restricted to the study of discrete time processes. 1

Title: Long range dependence in time series Author: Alexander Till Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Michaela Prokešová, Ph.D. Abstract: The diploma thesis demonstrates the necessity of a study of long range dependence, introduces fractional Gaussian noise and discusses possi- ble definitions of long memory. It is done by notions of ergodic theory and by second moment characteristics and spectral density. These definitions are confronted with the model of fractional Gaussian noise and with intuitive un- derstanding of long range memory. Relations and connections between these criteria are studied as well. The work is restricted to the study of discrete time processes. Method for Hurst index estimation for fractional Gaussian noise and it's application on logarithmic returns of shares of selected produ- cers of beer are included in this work. 1

O principal objetivo deste trabalho é apresentar um estudo sobre análise de estrutura tridimensional de edifícios de andares múltiplos considerando a interação de deslocamentos e esforços entre os vários elementos que formam a estrutura, levando-se em consideração a rigidez transversal à flexão das lajes. Isto é realizado através de um modelo que compatibiliza o elemento que discretiza o núcleo com sete graus de liberdade, baseado na teoria da flexo-torção de Vlassov, com o restante da estrutura tridimensional de edifícios de andares múltiplos formada pelos núcleos, pilares, vigas e lajes. Os elementos finitos de placa adotados na discretização do pavimento, responsáveis pela consideração da rigidez transversal das lajes na análise do edifício são o DKT (Discrete Kirchhoff Theory) e DST (Discrete Shear Theory). Para os pilares e os núcleos o equilíbrio de forças é verificado na sua posição deformada, ou como é conhecido da literatura técnica, análise em teoria de 2ª ordem, considerando a não linearidade geométrica. Para o cálculo dos esforços e deslocamentos na estrutura são aplicadas as técnicas de subestruturação em série e paralelo na matriz de rigidez global da estrutura. Elaborou-se um programa de computador para o processo de cálculo, utilizando a linguagem computacional Fortran Power Station 90 e pré e pós processadores em Visual Basic 6.0 para ambiente Windows. Finalmente são apresentados alguns exemplos para comprovar a validade do processo de cálculo utilizado / The main aim of this work is to apresent a study about analysis of three-dimentional structures of multistory buildings considering the interaction of displacements and stresses of the elements of the structures, with the influence of the transverse bending stiffness of slabs. The plate finite elements adopted in floor discretization, responsible for considering the bending stiffness contribution of slabs in the analysis of buildings, are the DKT (Discrete Kirchhoff Theory) and the DST (Discrete Shear Theory). For columns and core walls the forces equilibrium is verified for the columns in their deformed position, which is known in the technical literature as second order analysis, considering the geometric non-linearity. The techniques of serial and parallel analyses of substructures are applied to the global stiffness matrix for the calculus of forces and displacements in the structure. A computer program was developed for the calculation process, using the computer language Fortran Power Station 90 and pre and post-processors in Visual Basic 6.0 for a Windows environment. Finally, some examples are presented to check the validity of the employed calculus process

Este trabalho aborda os conceitos básicos da teoria de segunda ordem das placas elásticas delgadas, utilizando o Método dos Elementos Finitos (introduzido através do Método dos Resíduos Ponderados, na variante de Galerkin). São deduzidas as matrizes de rigidez geométrica, de rigidez secante e de rigidez tangente, relativas ao problema em consideração. É proposta ainda uma conduta notavelmente simplificada, que facilita sobremaneira a construção da matriz de rigidez tangente. / This paper delas with the basic concepts of the secondf order theory of thin elastic plates, through the use of the Finite Element Method 9introcuced through the Weighted Residual Method, in Galerkin\'s approach). The matrices of geometric stiffness, secant stiffness, and tangent stiffness for the problem under consideration are deduced. It is also proposed an outstandingly simplified conduct, which will greatly easen the construction of the tangent stiffness matrix.

Este trabalho aborda os conceitos básicos da teoria de segunda ordem das placas elásticas delgadas, utilizando o Método dos Elementos Finitos (introduzido através do Método dos Resíduos Ponderados, na variante de Galerkin). São deduzidas as matrizes de rigidez geométrica, de rigidez secante e de rigidez tangente, relativas ao problema em consideração. É proposta ainda uma conduta notavelmente simplificada, que facilita sobremaneira a construção da matriz de rigidez tangente. / This paper delas with the basic concepts of the secondf order theory of thin elastic plates, through the use of the Finite Element Method 9introcuced through the Weighted Residual Method, in Galerkin\'s approach). The matrices of geometric stiffness, secant stiffness, and tangent stiffness for the problem under consideration are deduced. It is also proposed an outstandingly simplified conduct, which will greatly easen the construction of the tangent stiffness matrix.

O principal objetivo deste trabalho é apresentar um estudo sobre análise de estrutura tridimensional de edifícios de andares múltiplos considerando a interação de deslocamentos e esforços entre os vários elementos que formam a estrutura, levando-se em consideração a rigidez transversal à flexão das lajes. Isto é realizado através de um modelo que compatibiliza o elemento que discretiza o núcleo com sete graus de liberdade, baseado na teoria da flexo-torção de Vlassov, com o restante da estrutura tridimensional de edifícios de andares múltiplos formada pelos núcleos, pilares, vigas e lajes. Os elementos finitos de placa adotados na discretização do pavimento, responsáveis pela consideração da rigidez transversal das lajes na análise do edifício são o DKT (Discrete Kirchhoff Theory) e DST (Discrete Shear Theory). Para os pilares e os núcleos o equilíbrio de forças é verificado na sua posição deformada, ou como é conhecido da literatura técnica, análise em teoria de 2ª ordem, considerando a não linearidade geométrica. Para o cálculo dos esforços e deslocamentos na estrutura são aplicadas as técnicas de subestruturação em série e paralelo na matriz de rigidez global da estrutura. Elaborou-se um programa de computador para o processo de cálculo, utilizando a linguagem computacional Fortran Power Station 90 e pré e pós processadores em Visual Basic 6.0 para ambiente Windows. Finalmente são apresentados alguns exemplos para comprovar a validade do processo de cálculo utilizado / The main aim of this work is to apresent a study about analysis of three-dimentional structures of multistory buildings considering the interaction of displacements and stresses of the elements of the structures, with the influence of the transverse bending stiffness of slabs. The plate finite elements adopted in floor discretization, responsible for considering the bending stiffness contribution of slabs in the analysis of buildings, are the DKT (Discrete Kirchhoff Theory) and the DST (Discrete Shear Theory). For columns and core walls the forces equilibrium is verified for the columns in their deformed position, which is known in the technical literature as second order analysis, considering the geometric non-linearity. The techniques of serial and parallel analyses of substructures are applied to the global stiffness matrix for the calculus of forces and displacements in the structure. A computer program was developed for the calculation process, using the computer language Fortran Power Station 90 and pre and post-processors in Visual Basic 6.0 for a Windows environment. Finally, some examples are presented to check the validity of the employed calculus process

The aim of this thesis is to undertake simplified design and assessment of cofferdam under vertical surcharge in the form of virtual project. Cofferdam constructed on the sea shore must be able to withstand all loads to enable construction of cut and cover tunnel. As a part of the design it is required to assess ground conditions and it is necessary to review feasibility of the structure on the sea. The construction will be described in construction phases and graphically demonstrated in construction sequence drawing. Because the structure is designed for life time of five years, temperature load on struts is studied in the thesis and further considered in structural analysis. Furthermore, it is required to compare analytical models from GEO5 and PLAXIS. Horizontal frame is analysed separately in Scia Engineer. Structural members – cofferdam wall, waler beam and strut are checked in this thesis. For the design of the cofferdam wall second order theory is considered. All mentioned requirements were accomplished with help of corresponding Eurocodes, books and technical advice. Results of this work are feasible and it was possible to design all members to enable construction of the cut and cover tunnel. The phasing was designed such that deformation of the cofferdam is minimalized and use of machinery is limited to machines on temporary platforms. Comparison of two different analytical models showed that different soil modelling has great effect on internal forces, even though the shape of the bending curve is very similar, values obtained from PLAXIS software are much higher. Assessment of the structural members is done according to Eurocode 3, and horizontal frame is checked also against disproportionate collapse.

This diploma thesis deals with the subject of slenderness bars’ stability assessment, especially in the steel structures. Before the assessment of bars in the frame constructions, we search for the influence of the computational model’s settings on the final result. The initial geometrical imperfections are examined on the model of Euler’s bar. The influence of the rigidity of girders on the poles’ buckling length is examined on the basic frame construction. The buckling lengths are assessed in the comparison with the figures we got from the statistical tables and the computational software. The influence of construction’s initial tilt and its replacement by the system of outer forces is examined on the frame structure. Three-hinged frame structure with variable cross-section member is designed then and the influence of non-linear calculations on the inner forces is studied. In the complex frame assessment, the influence of the number of parts of variable cross-section member on the bars’ buckling length is examined.