Neste trabalho foram desenvolvidas as funções de interpolação com regularidades C1 e C2, utilizando o Método da Partição de Unidade, referentes ao elemento quadrilateral de quatro nós. Estes elementos quadrilaterais Hermitianos de regularidade C1 e C2 foram implementados em uma plataforma própria de elementos finitos, considerando uma estratégia do tipo sub-paramétrica. De forma comparativa com os elementos Lagrangeanos de regularidade C0 e diferentes ordens polinomiais, os elementos de regularidade C1 e C2 foram aplicados na solução de: problemas clássicos de elasticidade plana infinitesimal isotrópica; aproximação das frequências naturais de vibração livre de barras e viga; pro- pagação de onda elástica em barra devido à aplicação de força impulsiva. Os resultados obtidos mostraram que foi possível se obter um maior percentual de frequências naturais aproximadas do espectro discreto, dado um certo nível de erro máximo, com os elementos de regularidade C1 e C2 em comparação com os elementos Lagrangeanos de regularidade C0 de quatro, oito, dezesseis e vinte e cinco nós. Quanto ao problema de propagação de onda elástica devido à aplicação de força impulsiva, as soluções obtidas com os elementos de regularidade C1 e C2 também apresentaram-se satisfatórias em relação à solução ana- lítica e às soluções aproximadas obtidas com os elementos Lagrangeanos de regularidade C0 de quatro e oito nós. Por outro lado, nas simulações dos problemas de elasticidade plana infinitesimal isotrópica, os elementos de regularidade C1 e C2 não apresentaram um comportamento satisfatório. Os erros relativos em normas L2 e de energia da solução aproximada foram maiores do que aqueles obtidos com o elemento Lagrangeano de regularidade C0 de oito nós, por exemplo, e as taxas de convergência em norma de energia obtidas com tais elementos foram inferiores às preditas pelo estimador de erro a priori. / In this work the shape functions with regularity C1 e C2 were developed, by means of the Partition of Unity Method, concerning to the four-node quadrilateral element. These Hermitian quadrilateral elements with regularity C1 e C2 were implemented in an own platform of finite elements, considering the subparametric strategy. Comparatively with the C 0 regularity Lagrangian elements of different polynomial order, C1 and C2 regularity elements were applied in simulations of: classical isotropic infinitesimal plane elasticity problems; approximation of natural frequencies of free vibration for bars and beam; elastic wave propagation in bar caused by forced vibration with impulsive loading applied. The results obtained showed that was possible to get a major number of natural frequencies of free vibration for the discrete spectrum, given a certain level of error, for C1 and C2 regularity elements in comparison with C 0 regularity Lagrangian elements of four, eight, sixteen and twenty-five nodes. Regarding to the elastic wave propagation problem in bar due to the application of impulsive loading, the solution obtained with C1 and C2 regularity elements also presented satisfactory results with relation to the analytical solution and those obtained with C 0 regularity Lagrangian elements with four and eight nodes. On the other hand, for isotropic infinitesimal plane elasticity problems, C1 and C2 regularity elements did not present satisfactory results. Relative errors in L2 and energy norms of approximate solution were greater than those computed for the C 0 Lagrangian element of eight nodes, for example, and convergence rates obtained with the C1 and C2 regularity elements were lower than those predicted by the a priori error estimator.

Neste trabalho foram desenvolvidas as funções de interpolação com regularidades C1 e C2, utilizando o Método da Partição de Unidade, referentes ao elemento quadrilateral de quatro nós. Estes elementos quadrilaterais Hermitianos de regularidade C1 e C2 foram implementados em uma plataforma própria de elementos finitos, considerando uma estratégia do tipo sub-paramétrica. De forma comparativa com os elementos Lagrangeanos de regularidade C0 e diferentes ordens polinomiais, os elementos de regularidade C1 e C2 foram aplicados na solução de: problemas clássicos de elasticidade plana infinitesimal isotrópica; aproximação das frequências naturais de vibração livre de barras e viga; pro- pagação de onda elástica em barra devido à aplicação de força impulsiva. Os resultados obtidos mostraram que foi possível se obter um maior percentual de frequências naturais aproximadas do espectro discreto, dado um certo nível de erro máximo, com os elementos de regularidade C1 e C2 em comparação com os elementos Lagrangeanos de regularidade C0 de quatro, oito, dezesseis e vinte e cinco nós. Quanto ao problema de propagação de onda elástica devido à aplicação de força impulsiva, as soluções obtidas com os elementos de regularidade C1 e C2 também apresentaram-se satisfatórias em relação à solução ana- lítica e às soluções aproximadas obtidas com os elementos Lagrangeanos de regularidade C0 de quatro e oito nós. Por outro lado, nas simulações dos problemas de elasticidade plana infinitesimal isotrópica, os elementos de regularidade C1 e C2 não apresentaram um comportamento satisfatório. Os erros relativos em normas L2 e de energia da solução aproximada foram maiores do que aqueles obtidos com o elemento Lagrangeano de regularidade C0 de oito nós, por exemplo, e as taxas de convergência em norma de energia obtidas com tais elementos foram inferiores às preditas pelo estimador de erro a priori. / In this work the shape functions with regularity C1 e C2 were developed, by means of the Partition of Unity Method, concerning to the four-node quadrilateral element. These Hermitian quadrilateral elements with regularity C1 e C2 were implemented in an own platform of finite elements, considering the subparametric strategy. Comparatively with the C 0 regularity Lagrangian elements of different polynomial order, C1 and C2 regularity elements were applied in simulations of: classical isotropic infinitesimal plane elasticity problems; approximation of natural frequencies of free vibration for bars and beam; elastic wave propagation in bar caused by forced vibration with impulsive loading applied. The results obtained showed that was possible to get a major number of natural frequencies of free vibration for the discrete spectrum, given a certain level of error, for C1 and C2 regularity elements in comparison with C 0 regularity Lagrangian elements of four, eight, sixteen and twenty-five nodes. Regarding to the elastic wave propagation problem in bar due to the application of impulsive loading, the solution obtained with C1 and C2 regularity elements also presented satisfactory results with relation to the analytical solution and those obtained with C 0 regularity Lagrangian elements with four and eight nodes. On the other hand, for isotropic infinitesimal plane elasticity problems, C1 and C2 regularity elements did not present satisfactory results. Relative errors in L2 and energy norms of approximate solution were greater than those computed for the C 0 Lagrangian element of eight nodes, for example, and convergence rates obtained with the C1 and C2 regularity elements were lower than those predicted by the a priori error estimator.

[pt] Neste trabalho aborda-se a geração de malha quadrilateral sobre domínios delimitados por duas, três e quatro curvas de bordo, usando padrões de decomposição de domínio, os quais são aplicados sobre domínios que satisfazem um conjunto de condições chamadas de essenciais que permite a geração de malha sobre eles. No entanto, a metodologia desenvolvida pode ser estendida para ser aplicada sobre outras topologias de domínio. A ideia é decompor um domínio em subdomínios, cada subdomínio é decomposto de forma independente até que todos os subdomínios permitam gerar malha usando diretamente o algoritmo de mapeamento transfinito bilinear. A decomposição é feita pela criação de curvas internas fictícias que delimitarão os subdomínios. Estas curvas podem intersectarse dando lugar a pontos de interseção, os quais são chamados de parâmetros geométricos e podem ser variados para mudar a geometria dos subdomínios com o propósito de melhorar a qualidade da malha gerada. Os subdomínios são delimitados por curvas que terão um número definido de subdivisões, isto será chamado de parâmetros topológicos e de cujos valores dependerá o tipo de decomposição aplicada nos subdomínios. Os padrões de decomposição foram projetados dando lugar aos padrões de geração de malha que têm valores definidos para seus parâmetros geométricos e topológicos. Desta forma é possível conhecer a topologia e o nível de decomposição hierárquica a priori. Os parâmetros topológicos podem ser variados dinamicamente para encontrar a topologia de malha de melhor qualidade sobre um domínio. Foram incluídos exemplos para mostrar a aplicabilidade da metodologia proposta. / [en] In this work, it is discussed quadrilateral mesh generation using patterns of domain decomposition. Mesh generation is treated on domains delimited by two, three and four curves. Patterns of domain decomposition are applied to domains that satisfy a set of conditions called essential conditions. However, the approach developed can be applied to other domain topologies. Mesh generation begins with an initial domain decomposition, each subdomain also is independently decomposed until all the subdomains enable mesh generation using bilinear mapping. The decomposition is done by creating fictitious internal curves that demarcate the subdomains. These curves can intersect giving rise to points of intersection, which are called geometric parameters and can be varied to change the geometry of the subdomains in order to improve the quality of the generated mesh. The subdomains are bounded by curves, which have a defined number of subdivisions, this will be called topological parameters and of whose values depend the type of decomposition applied on subdomains. Patterns of decomposition were designed giving way to patterns of mesh generation that have values set for its geometric and topological parameters, in this way is possible to know the topology and the level of hierarchical decomposition a priori. Topological parameters were dynamically varied to show the possibility of finding various mesh topologies on a domain. Examples are included to show the applicability of the proposed methodology.

Thesis / There is potential for a schism, within the Methodist Church of Southern Africa (MCSA) today, between Fundamentalist and Liberationist Methodists, who struggle to find common identity and vision. A question that needs examination is whether it is possible to develop an authentically, uniting Southern African Methodist Theology within the current Institutional structure of the MCSA. For this to become possible, some key areas of discussion are highlighted in this paper, such as the training of ministers and the MCSA as Institution. This paper attempts to enter into conversation between Fundamental and Liberation Methodism using the Doctrine of Christian Perfection, 'the Grand Depositum' of Methodism, as a point of reference and develop an epistemological framework based on Wesley’s 'quadrilateral' of Scripture, reason, experience and tradition. This paper takes as a standpoint the need for an authentically Southern African Methodist theology, which is both uniting and transformatory, in order for the MCSA to fulfil its vision of “A Christ Healed Africa for the Healing of Nations.” / Systematic theology and Theological Ethics / D. Th. (Systematic Testament)

This study aims to investigate the behaviour of low-order beam and plate elements especially for their application to laminated structures. The merits and dements of the existing elements are brought out and new low-order elements with better interpolation polynomials are proposed. Two new beam elements are proposed for laminated composite beams that yield better representation of twist due to material coupling. Out of the two elements developed, one is based on the conventional formulation and the other on the coupled-field formulation, both capturing material induced coupling. The beam developed using coupled field formulation shows a novel way of obtaining a fully coupled interpolation function for field variables using the complete set of equilibrium equations for the composite beams. The element has shown a superior coarse mesh performance. These elements can practically capture plate behaviour in beam elements for a wide range of plate thickness. The locking problems in conventional 4-node quadrilateral elements, such as shear locking and geometric locking are studied. Various techniques available in literature to remedy these problems are also studied. A suite of QUAD4 with conventional techniques such as. Reduced Integration, Field Consistency, Mixed Interpolation of Tensorial strain Components, Assumed Natural Strain, Discrete Shear Gap, Incompatible modes Q6 and QM6 is developed. An effort is made to combine these techniques to develop new element that yields improved performance. The element is shown to exhibit improved performance for certain cases. Several four-node rectangular elements are developed based on the coupled-field techniques. First two new-coupled elements are formulated that employ Sabir's [101] plane bending formulation with drilling degree of freedom, and the plate bending rotations are generated using equilibrium equations. However, since Sabir's plane bending interpolation polynomials yielded inaccurate performance for composites, it led to development of elements with fully coupled field formulations. Finally, two new 4-node rectangular elements are developed using coupled-field formulations with six and seven dof freedom per node respectively. Here the interpolation polynomials are derived using the complete equilibrium equations. The elements are extensively tested for static deflection, dynamics and buckling of isotropic and laminated plates/beams. The elements show superior coarse mesh convergence. Several problems pertaining to vibration and buckling of composite plates/beams are solved using the elements developed in this work.

Thesis / There is potential for a schism, within the Methodist Church of Southern Africa (MCSA) today, between Fundamentalist and Liberationist Methodists, who struggle to find common identity and vision. A question that needs examination is whether it is possible to develop an authentically, uniting Southern African Methodist Theology within the current Institutional structure of the MCSA. For this to become possible, some key areas of discussion are highlighted in this paper, such as the training of ministers and the MCSA as Institution. This paper attempts to enter into conversation between Fundamental and Liberation Methodism using the Doctrine of Christian Perfection, 'the Grand Depositum' of Methodism, as a point of reference and develop an epistemological framework based on Wesley’s 'quadrilateral' of Scripture, reason, experience and tradition. This paper takes as a standpoint the need for an authentically Southern African Methodist theology, which is both uniting and transformatory, in order for the MCSA to fulfil its vision of “A Christ Healed Africa for the Healing of Nations.” / Systematic theology and Theological Ethics / D. Th. (Systematic Testament)

The assignment of my degree work was a proposal of two variants of the steel structure of a modern art exhibition hall. The ground plan dimensions of the structure are 52,5 x 24 m. The whole structure of the two variants is supported by two quadrilateral truss columns and the upper floor level is at a height of 8 m above the ground. The ceiling structure is set by the truss girders. The proposal of two alternative solutions and the assessment of the main structure support elements forms another part of the work. With a winning option then a solution of the selected details, working out of the detailed drawings of the solved joints and the creation of the workshop documentation of the selected parts is supposed.

Like many denominations in the secularized West, the Canadian Baptists of Ontario and Quebec have been engaged in debates regarding sexuality and marriage over the past decade. As these debates have developed, it has become increasingly clear that at their center are differences in biblical interpretive practice. Yet it is my experience that, by and large, many evangelicals, particularly in the Canadian Baptist context, do not know how to discuss their interpretive practice. In order to work through difficult topics, such as the one mentioned above, Christians need to develop the ability to reflect both on how they are interpreting Scripture and how they see others interpreting Scripture, so that they can coherently and constructively discuss their interpretations with others with whom they disagree. In this dissertation, I utilize a hermeneutic theory, metamodern cultural theory, and a proposed revision of an integrative theological method, the Wesleyan Quadrilateral, to develop a a paradigm for observing and describing differences in biblical interpretive practice. Using the aforementioned debates concerning sexuality and marriage as an illustrative example, the project reveals that metamodern interpretations of scripture are complex and tension-filled, and that amidst this complexity, the prioritization (or lack thereof) of theological reflection sources prompts particular interpretive applications. When they are able to perceive the multivalent nature of interpretation, readers are better equipped through this work to think carefully and critically about how they come to their interpretive conclusions and how those conclusions draw them towards faithful living in Christ via situational application of the biblical text.

Series compensation is extensively applied to the transmission lines to increase the power transfer capability of transmission lines, reduce transmission losses, improve voltage profiles, and improve power oscillation damping and transient stability of power systems. But it modifies the apparent impedance of the transmission lines during fault conditions and might cause the distance protection of transmission lines to encounter directional discrimination issues and reach problems. The non-linear characteristic of metal oxide varistor in series compensation model creates further complexity to the fault analysis and might affects the performance of conventional distance protection scheme. The distance protection issues in the series compensated lines need to be addressed for the reliable and sustainable operation of power system.The directional discrimination issues related to current inversion and voltage inversion phenomenon, and reach problems related to sub-synchronous oscillation phenomenon are addressed in this thesis report. This report aims to analyse the impacts of series compensation on the performance of conventional distance relays, and proposes a new protection solution to mitigate the shortcomings of distance relays in the series compensated lines. The proposed new protection solution includes: new tripping characteristic of quadrilateral distance relays to cope with the steady-state reach problems due to current or voltage inversion, and a new high-pass filtering technique to handle the transient reach problems due to SSO.The proposed new protection algorithm is developed in MATLAB. The performance of new protection algorithm is evaluated by simulating a 500 kV two-source power system with a 200 km series compensated line in EMTDC/ PSCAD (Manitoba Hydro). The proposed new protection solution is found to be beneficial. / Seriekompensation tillämpas i stor utsträckning på överföringsledningarna för att öka överföringsförmågan hos överföringsledningar, minska överföringsförluster, förbättra spänningsprofiler och förbättra effektdämpning och övergående stabilitet hos elsystem. Men det ändrar transmissionslinjernas uppenbara impedans under felförhållanden och kan orsaka att distansskydd för överföringsledningarna stöter på diskrimineringsproblem och uppnår problem. Den icke-linjära egenskapen hos metalloxidvaristor i seriekompensationsmodell skapar ytterligare komplexitet för felanalysen och kan påverka prestandan hos konventionella distansskyddssystem. Distansskydd problemen i seriekompenserade linjer måste lösas för en pålitlig och hållbar drift av elsystemet. De riktningsdiskrimineringsproblem som är relaterade till det aktuella inversions- och spänningsinversionsfenomenet och uppnår problem relaterade till subsynkron oscillationsfenomen tas upp i denna avhandlingsrapport. Denna rapport syftar till att analysera effekterna av seriekompensation för prestanda hos konventionella distansreläer och föreslår en ny skyddslösning för att mildra bristerna i distansreläerna i seriekompenserade linjer. Den föreslagna nya skyddslösningen innefattar: Ny utlösningskaraktäristik för fyrsidig distansreläer för att klara avståndet med stillastående / räckvidden på grund av ström- eller spänningsinversion och en ny högpassfiltreringsteknik för hantering av övergående över- Nå problem på grund av SSO. Den föreslagna nya skyddsalgoritmen har utvecklats i MATLAB. Utförandet av den nya skyddsalgoritmen utvärderas genom simulering av ett 500 kV två-källa kraftverk med en 200 km serie kompenserad linje i EMTDC / PSCAD (Manitoba Hydro). Den föreslagna nya skyddslösningen har visat sig vara fördelaktig.

In computer graphics we can handle unstructured triangular 3D meshes which are not too usable for processing through their irregularity. In these situations it occurs need of conversion that 3D mesh to more suitable representation. Some kind of 3D spline surface can be proper alternative because it institutes regularity in the form of control points grid and that's why it is more suitable for next processing. During conversion, which is described in this thesis, quadrilateral 3D mesh is constructed at first. This mesh has regular structure but mainly the structure corresponds to structure of control points grid of resulting 3D spline surface. Created quadrilateral 3D mesh can be saved and consequently used in specific modeling applications for T-spline surface creation.