Tesi sul tema "Non-linear geometry"
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1
Luo, Ye. "Linear systems on metric graphs and some applications to tropical geometry and non-archimedean geometry". Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/52323.
Abstract (sommario):
The divisor theories on finite graphs and metric graphs were introduced systematically as analogues to the divisor theory on algebraic curves, and all these theories are deeply connected to each other via tropical geometry and non-archimedean geometry. In particular, rational functions, divisors and linear systems on algebraic curves can be specialized to those on finite graphs and metric graphs. Important results and interesting problems, including a graph-theoretic Riemann-Roch theorem, tropical proofs of conventional Brill-Noether theorem and Gieseker-Petri theorem, limit linear series on metrized complexes, and relations among moduli spaces of algebraic curves, non-archimedean analytic curves, and metric graphs are discovered or under intense investigations. The content in this thesis is divided into three main subjects, all of which are based on my research and are essentially related to the divisor theory of linear systems on metric graphs and its application to tropical geometry and non-archimedean geometry. Chapter 1 gives an overview of the background and a general introduction of the main results. Chapter 2 is on the theory of rank-determining sets, which are subsets of a metric graph that can be used for the computation of the rank function. A general criterion is provided for rank-determining sets and certain specific examples of finite rank-determining sets are presented. Chapter 3 is on the subject of a tropical convexity theory on linear systems on metric graphs. In particular, the notion of general reduced divisors is introduced as the main tool used to study this tropical convexity theory. Chapter 4 is on the subject of smoothing of limit linear series of rank one on re_ned metrized complexes. A general criterion for smoothable limit linear series of rank 1 is presented and the relations between limit linear series of rank 1 and possible harmonic morphisms to genus 0 metrized complexes are studied.
2
Li, Siran. "Analysis of several non-linear PDEs in fluid mechanics and differential geometry". Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:20866cbb-e5ab-4a6b-b9dc-88a247d15572.
Abstract (sommario):
In the thesis we investigate two problems on Partial Differential Equations (PDEs) in differential geometry and fluid mechanics. First, we prove the weak L p continuity of the Gauss-Codazzi-Ricci (GCR) equations, which serve as a compatibility condition for the isometric immersions of Riemannian and semi-Riemannian manifolds. Our arguments, based on the generalised compensated compactness theorems established via functional and micro-local analytic methods, are intrinsic and global. Second, we prove the vanishing viscosity limit of an incompressible fluid in three-dimensional smooth, curved domains, with the kinematic and Navier boundary conditions. It is shown that the strong solution of the Navier-Stokes equation in H r+1 (r > 5/2) converges to the strong solution of the Euler equation with the kinematic boundary condition in H r, as the viscosity tends to zero. For the proof, we derive energy estimates using the special geometric structure of the Navier boundary conditions; in particular, the second fundamental form of the fluid boundary and the vorticity thereon play a crucial role. In these projects we emphasise the linkages between the techniques in differential geometry and mathematical hydrodynamics.
3
Le, Gros Brian Neil. "Three-dimensional, non-linear finite element analysis, and elastic modulus optimization of a geometry for a non-metallic femoral stem". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2002. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/MQ65632.pdf.
4
Ody, Michael S. "The (2+1)-dimensional non-linear O(3) sigma model and the classical differential geometry of curves and surfaces". Thesis, University of Kent, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.358169.
5
Zois, Ioannis. "The duality between two-index potentials and the non-linear sigma model in field theory". Thesis, University of Oxford, 1996. http://ora.ox.ac.uk/objects/uuid:c350f73e-5e44-4942-8674-4321f5075b1e.
Abstract (sommario):
We interpret the generalised gauge symmetry introduced in string theory and M-Theory as a special case of Grothendieck's stability equivalence relation in the definition of the 0th K-group and we calculate the Euler number of the elliptic de Rham complex twisted by a flat connection. Then using Polyakov's classical equivalence of flat bundles with non-linear sigma models we define a new topological invariant for foliations using techniques from noncommutative geometry, in particular the Connes' pairing between K-Theory and cyclic cohomology. This new invariant classifies foliations up to Morita equivalence.
6
Cabrera, Carnero Iraida [UNESP]. "Modelos integráveis multicarregados e integrabilidade no plano não comutativo". Universidade Estadual Paulista (UNESP), 2003. http://hdl.handle.net/11449/102515.
Abstract (sommario):
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cabreracarnero_i_dr_ift.pdf: 1015322 bytes, checksum: 915c6683e6c1c022f54ca1d9f5a03904 (MD5)Nesta fase construísmo e estudamos uma nova classe de modelos integráveis (relativístico e não relativístico) em duas dimensões, associados à álgebra afim 'A IND.3 POT.(1)'. Estes modelos apresentam sólitons tipológicos os quais portam duas cargas elétricas U(1) X U(1). O modelo de Toda afim (relativístico) é construído a partir do modelo WZNW mediante a calibração da ação Swznw e corresponde ao primeiro membro de grau negativo q = -1 de uma hierarquia de modelos cKP do tipo dyon. O modelo mais simples não relativístico dentro desta hierarquia corresponde ao grau q = 2 positivo. As soluções de 1-sóliton para ambos modelos foram construídas e relações explícitas entre ambas soluções (assim como entre as cargas conservadas) foram encontradas. Outro modelo integrável com simetrias não abelianas locais SL(2) X U(1) é introduzido. Numa aproximação à integrabilidade em espaços não-comutativos estudamos generalizações não comutativas no plano dos modelos integráveis bidimensionais sine-, sinh-Gordon e U(N) Quiral Principal. Calculando a amplitude de espalhamento à nível de árvore de um processo de produção de partículas provamos que a versão não-comutativa do modelo de sinh-Gordon que se obtém mediante a deformação Moyal da respectiva ação não é integrável. Por outro lado, a incorporação de vínculos adicionais que são obtidos a partir da generalização da condição de curvatura nula, tornam o modelo integrável. O modelo Quiral Principal generalizado a partir da deformação Moyal da ação, preserva a sua integrabilidade, ao contrário dos modelos sinh-Gordon e sine-Gordon.
In this thesis we have constructed and studied a new class of two-dimensional integrable models (relativistic and nonrelativistic), related to the affine algebra 'A IND.3 POT.(1)'. These models admit U(1) X U(1) charged topological solitons. The affine Toda relativistic model is constructed from the gauged WZNW action and corresponds to the first negative grade q = -1 member of a dyonic hierarchy of cKP models. The simplest nonrelativistic model corresponds to the positive grade q = 2 of this hierarchy. The 1-soliton solutions for both models were constructed and explicit relations between them (and the conserved charges as well) were found. Another integrable model with local nonabelian SL(2) X U(1) simetries is introduced. In the context of integrability on noncommutative spaces, we have studied noncommutative generalizations on the plane of the two-dimensional integrable models sine-, sinh-Gordon and U(N) Principal Quiral. By computing for the sinh-Gordon model, the tree-level amplitude of a process of production of particles, we proved that the noncommutative generalization of this model that it is obtained by the Moyal deformation of the corresponding action is not integrable. On the other hand, the addition of extra constraints, obtained by the generalization of the zero-curvature method, renders the integrability of the model. The generalization of the Principal Quiral model by the Moyal deformation of the action preserves the integrability, contrary to the previous case
7
Göteman, Malin. "The Complex World of Superstrings : On Semichiral Sigma Models and N=(4,4) Supersymmetry". Doctoral thesis, Uppsala universitet, Teoretisk fysik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-183407.
Abstract (sommario):
Non-linear sigma models with extended supersymmetry have constrained target space geometries, and can serve as effective tools for investigating and constructing new geometries. Analyzing the geometrical and topological properties of sigma models is necessary to understand the underlying structures of string theory. The most general two-dimensional sigma model with manifest N=(2,2) supersymmetry can be parametrized by chiral, twisted chiral and semichiral superfields. In the research presented in this thesis, N=(4,4) (twisted) supersymmetry is constructed for a semichiral sigma model. It is found that the model can only have additional supersymmetry off-shell if the target space has a dimension larger than four. For four-dimensional target manifolds, supersymmetry can be introduced on-shell, leading to a hyperkähler manifold, or pseudo-supersymmetry can be imposed off-shell, implying a target space which is neutral hyperkähler. Different sigma models and corresponding geometries can be related to each other by T-duality, obtained by gauging isometries of the Lagrangian. The semichiral vector multiplet and the large vector multiplet are needed for gauging isometries mixing semichiral superfields, and chiral and twisted chiral superfields, respectively. We find transformations that close off-shell to a N=(4,4) supersymmetry on the field strengths and gauge potentials of the semichiral vector multiplet, and show that this is not possible for the large vector multiplet. A sigma model parametrized by chiral and twisted chiral superfields can be related to a semichiral sigma model by T-duality. The N=(4,4) supersymmetry transformations of the former model are linear and close off-shell, whereas those of the latter are non-linear and close only on-shell. We show that this discrepancy can be understood from T-duality, and find the origin of the non-linear terms in the transformations.
8
Bredthauer, Andreas. "Tensionless Strings and Supersymmetric Sigma Models : Aspects of the Target Space Geometry". Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-7105.
9
Cabrera, Carnero Iraida. "Modelos integráveis multicarregados e integrabilidade no plano não comutativo /". São Paulo : [s.n.], 2003. http://hdl.handle.net/11449/102515.
Abstract (sommario):
Orientador: José Francisco GomesBanca: Galen Mihaylov Sotkov
Banca: Abraham Hirsz Zimerman
Banca: Paulo Teotônio Sobrinho
Banca: Márcio José Martins
Resumo: Nesta fase construísmo e estudamos uma nova classe de modelos integráveis (relativístico e não relativístico) em duas dimensões, associados à álgebra afim 'A IND.3 POT.(1)'. Estes modelos apresentam sólitons tipológicos os quais portam duas cargas elétricas U(1) X U(1). O modelo de Toda afim (relativístico) é construído a partir do modelo WZNW mediante a calibração da ação Swznw e corresponde ao primeiro membro de grau negativo q = -1 de uma hierarquia de modelos cKP do tipo dyon. O modelo mais simples não relativístico dentro desta hierarquia corresponde ao grau q = 2 positivo. As soluções de 1-sóliton para ambos modelos foram construídas e relações explícitas entre ambas soluções (assim como entre as cargas conservadas) foram encontradas. Outro modelo integrável com simetrias não abelianas locais SL(2) X U(1) é introduzido. Numa aproximação à integrabilidade em espaços não-comutativos estudamos generalizações não comutativas no plano dos modelos integráveis bidimensionais sine-, sinh-Gordon e U(N) Quiral Principal. Calculando a amplitude de espalhamento à nível de árvore de um processo de produção de partículas provamos que a versão não-comutativa do modelo de sinh-Gordon que se obtém mediante a deformação Moyal da respectiva ação não é integrável. Por outro lado, a incorporação de vínculos adicionais que são obtidos a partir da generalização da condição de curvatura nula, tornam o modelo integrável. O modelo Quiral Principal generalizado a partir da deformação Moyal da ação, preserva a sua integrabilidade, ao contrário dos modelos sinh-Gordon e sine-Gordon.
Abstract: In this thesis we have constructed and studied a new class of two-dimensional integrable models (relativistic and nonrelativistic), related to the affine algebra 'A IND.3 POT.(1)'. These models admit U(1) X U(1) charged topological solitons. The affine Toda relativistic model is constructed from the gauged WZNW action and corresponds to the first negative grade q = -1 member of a dyonic hierarchy of cKP models. The simplest nonrelativistic model corresponds to the positive grade q = 2 of this hierarchy. The 1-soliton solutions for both models were constructed and explicit relations between them (and the conserved charges as well) were found. Another integrable model with local nonabelian SL(2) X U(1) simetries is introduced. In the context of integrability on noncommutative spaces, we have studied noncommutative generalizations on the plane of the two-dimensional integrable models sine-, sinh-Gordon and U(N) Principal Quiral. By computing for the sinh-Gordon model, the tree-level amplitude of a process of production of particles, we proved that the noncommutative generalization of this model that it is obtained by the Moyal deformation of the corresponding action is not integrable. On the other hand, the addition of extra constraints, obtained by the generalization of the zero-curvature method, renders the integrability of the model. The generalization of the Principal Quiral model by the Moyal deformation of the action preserves the integrability, contrary to the previous case
Doutor
10
Peñaranda, Luis. "Géométrie algorithmique non linéaire et courbes algébriques planaires". Electronic Thesis or Diss., Nancy 2, 2010. http://www.theses.fr/2010NAN23002.
Abstract (sommario):
Nous abordons dans cette thèse le problème du calcul de la topologie de courbes algébriques planes. Nous présentons un algorithme qui, grâce à l’application d’outils algébriques comme les bases de Gröbner et les représentations rationnelles univariées, ne nécessite pas de traitement particulier de cas dégénérés. Nous avons implanté cet algorithme et démontré son efficacité par un ensemble de comparaisons avec les logiciels similaires. Nous présentons également une analyse de complexité sensible a la sortie de cet algorithme. Nous discutons ensuite des outils nécessaires pour l’implantation d’algorithmes de géométrie non-linéaire dans CGAL, la bibliothèque de référence de la communauté de géométrie algorithmique. Nous présentons un noyau univarié pour CGAL, un ensemble de fonctions nécessaires pour le traitement d’objets courbes définis par des polynômes univariés. Nous avons validé notre approche en la comparant avec les implantations similairesWe tackle in this thesis the problem of computing the topology of plane algebraic curves. We present an algorithm that avoids special treatment of degenerate cases, based on algebraic tools such as Gröbner bases and rational univariate representations. We implemented this algorithm and showed its performance by comparing to simi- lar existing programs. We also present an output-sensitive complexity analysis of this algorithm. We then discuss the tools that are necessary for the implementation of non- linear geometric algorithms in CGAL, the reference library in the computational geom- etry community. We present an univariate algebraic kernel for CGAL, a set of functions aimed to handle curved objects defined by univariate polynomials. We validated our approach by comparing it to other similar implementations
11
Allavarapu, Santosh. "A New Additive Manufacturing (AM) File Format Using Bezier Patches". University of Cincinnati / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1385114646.
12
Moog, Claude. "Inversion, decouplage, poursuite de modele des systemes non lineaires". Nantes, 1987. http://www.theses.fr/1987NANT2030.
Abstract (sommario):
Analyse des systemes non lineaires et leur commande par bouclage dynamique par approches structurelle et algebrique differentielles. Etude de l'inversion des systemes non lineaires a partir de notions algebriques et obtention de facon algorithmique de la structure a l'infini pour une classe generales de systemes non lineaires d'ou l'extension d'une liste d'invariants definie dans le cas de systemes lineaires invariants
13
Ladeia, Cibele Aparecida. "A equação de transferência radiativa condutiva em geometria cilíndrica para o problema do escape do lançamento de foguetes". reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2016. http://hdl.handle.net/10183/152738.
Abstract (sommario):
Nesta contribuição apresentamos uma solução para a equação de transferência radiativa condutiva em geometria cilíndrica. Esta solução é aplicada para simular a radiação e campo de temperatura juntamente com o transporte de energia radiativa e condutiva proveniente do escape liberado em lançamentos de foguetes. Para este fim, discutimos uma abordagem semianalítica reduzindo a equação original, que é contínua nas variáveis angulares, numa equação semelhante ao problema SN da transferência radiativa condutiva. A solução é construída usando um método de composição por transformada de Laplace e o método da decomposição de Adomian. O esquema recursivo ´e apresentado para o sistema de equações de ordenadas duplamente discretas juntamente com as dependências dos parâmetros e suas influências sobre a convergência heurística da solução. A solução obtida, em seguida, permite construir o campo próximo relevante para caracterizar o termo fonte para problemas de dispersão ao ajustar os parâmetros do modelo, tais como, emissividade, refletividade, albedo e outros, em comparação com a observação, que são relevantes para os processos de dispersão de campo distante e podem ser manipulados de forma independente do presente problema. Além do método de solução, também relatamos sobre algumas soluções e simulações numéricas.In this contribution we present a solution for the radiative conductive transfer equation in cylinder geometry. This solution is applied to simulate the radiation and temperature field together with conductive and radiative energy transport originated from the exhaust released in rocket launches. To this end we discuss a semi-analytical approach reducing the original equation, which is continuous in the angular variables, into an equation similar to the SN radiative conductive transfer problem. The solution is constructed using a composite method by Laplace transform and Adomian decomposition method. The recursive scheme is presented for the doubly discrete ordinate equations system together with parameter dependencies and their influence on heuristic convergence of the solution. The obtained solution allows then to construct the relevant near field to characterize the source term for dispersion problems when adjusting the model parameters such as emissivity, reflectivity, albedo and others in comparison to the observation, that are relevant for far field dispersion processes and may be handled independently from the present problem. In addition to the solution method we also report some solutions and numerical simulations.
14
Ferro, Dennis Eduardo Zavaleta [UNESP]. "Some geometric aspects of non-linear sigma models". Universidade Estadual Paulista (UNESP), 2016. http://hdl.handle.net/11449/151647.
Abstract (sommario):
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
We review some relevant examples for String Theory of non-linear sigma models. These are bosonic strings propagating in curved background, the Wess-Zumino-Witten model and superstrings in flat and AdS superspace. The mathematical tools required for the study of these models (e.g. topological quantization, Cartan geometry, Lie superalgebras and geometry on coset spaces) are also described. Throughout the dissertation we have focused on classical aspects of these models such as the construction of the action and its symmetries where conditions for holomorphic symmetry of the bosonic string case were found.
Nesta dissertação estudamos alguns exemplos de modelos sigma não lineares em Teoria de cordas. Estes são a corda bosónica se propagando em espaços curvos, o modelo Wess-Zumino-Witten e supercordas em superespaço plano e AdS. As ferramentas matemáticas que se precisam para o estudo destes modelos (e.g. quantização topológica, geometria de Cartan, super-álgebras de Lie e geometria em espaços coset) também são descritas. Ao longo desta dissertação focamos os aspectos clássicos destes modelos tais como a construção da ação e suas simetrias onde condições para serem estas holomorficas no caso da corda bosónica foram achadas.
15
Ferro, Dennis Eduardo Zavaleta. "Some geometric aspects of non-linear sigma models /". São Paulo, 2016. http://hdl.handle.net/11449/151647.
Abstract (sommario):
Orientador: Andrei MikhailovResumo: We review some relevant examples for String Theory of non-linear sigma models. These are bosonic strings propagating in curved background, the Wess-Zumino-Witten model and superstrings in flat and AdS superspace. The mathematical tools required for the study of these models (e.g. topological quantization, Cartan geometry, Lie superalgebras and geometry on coset spaces) are also described. Throughout the dissertation we have focused on classical aspects of these models such as the construction of the action and its symmetries where conditions for holomorphic symmetry of the bosonic string case were found.
Mestre
16
Persson, Jonas. "Strings as Sigma Models and in the Tensionless Limit". Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-7783.
17
Debaecker, Thibaud. "Geometric and bio-inspired analysis of non-linear image sensors". Paris 6, 2010. http://www.theses.fr/2010PA066717.
Abstract (sommario):
Alors que l'image sous toutes ses formes s'est désormais imposée dans la vie quotidienne de chacun d'entre nous, les capteurs d'images sortant du classique modèle perspectif à point de vue unique se banalisent jusqu'à devenir les pièces maîtresses de nombreux produits de hautes technologies, à destination d'industries comme du grand public. Qu'ils soient bio-inspirés, se rapprochant des rétines artificielles ou à large champs de vue, grâce à des lentilles ou à des miroirs, l'utilisation des images acquises pas ces appareils nécessitent des modèles qui, jusqu'à présent, ont été construits comme des généralisations des modèles pré-existants et considèrent qu'un capteur d'images réalise un mapping d'un monde en trois dimensions vers une image plane, reliant chaque point de l'image par un rayon à son antécédent dans l'espace. Tous ces capteurs souffrent pourtant de résolutions variables telles, que l'approximation du champ de vue du pixel comme un rayon de lumière pose de réels problèmes dans leur utilisation. Cette thèse présente une triple approche pour la caractérisation de ces capteurs, la première inspirée de l'architecture biologique de la rétine, la seconde est un modèle générique de caméra utilisant les Algèbres Géométriques et une méthode qui en permet le calibrage, quelque soit le type de caméra employé, et la troisième montre que considérer ces ouvertures angulaires pour chaque pixel d'un point de vue projectif permet de retrouver certaines caractéristiques du capteur, de s'affranchir des distortions optiques, et enfin d'obtenir des images après remapping, correspondant à celles qui auraient été prises si le capteur avait été parfaitement perspectif
18
Carr, Andrew Newberry. "Geometric Extensions of Neural Processes". BYU ScholarsArchive, 2020. https://scholarsarchive.byu.edu/etd/8394.
Abstract (sommario):
Neural Processes (NPs) are a class of regression models that learn a map from a set of input-output pairs to a distribution over functions. NPs are computationally tractable and provide a number of benefits over traditional nonlinear regression models. Despite these benefits, there are two main domains where NPs fail. This thesis is focused on presenting extensions of the Neural Process to these two areas. The first of these is the extension of Neural Processes graph and network data which we call Graph Neural Processes (GNP). A Graph Neural Process is defined as a Neural Process that operates on graph data. It takes spectral information from the graph Laplacian as inputs and then outputs a distribution over values. We demonstrate Graph Neural Processes in edge value imputation and discuss benefits and drawbacks of the method for other application areas. The second extension of Neural Processes comes in the fundamental training mechanism. NPs are traditionally trained using maximum likelihood, a probabilistic technique. We show that there are desirable classes of problems where NPs fail to learn. We also show that this drawback is solved by using approximations of the Wasserstein distance. We give experimental justification for our method and demonstrate its performance. These Wasserstein Neural Processes (WNPs) maintain the benefits of traditional NPs while being able to approximate new classes of function mappings.
19
RODRIGUES, LARA. "INFLUENCE OF INITIAL GEOMETRIC IMPERFECTIONS ON THE INTERNAL RESONANCES AND NON-LINEAR VIBRATIONS OF THIN-WALLED CYLINDRICAL SHELLS". PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2018. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=35757@1.
Abstract (sommario):
PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
A análise das ressonâncias internas em sistemas estruturais contínuos é uma das principais áreas de pesquisa no campo da dinâmica não linear. A ressonância interna entre dois modos de vibração ocorre quando a proporção de suas frequências naturais é um número inteiro. De particular importância, devido à sua influência na resposta estrutural, é a ressonância interna 1:1, geralmente associada às simetrias do sistema, a ressonância interna 1:2, devida às não linearidades quadráticas e a ressonância 1:3 decorrente de não linearidades cúbicas. A ressonância interna permite a transferência de energia entre os modos de vibração relacionados, levando geralmente a novos fenômenos com profunda influência sobre a estabilidade da resposta dinâmica. As cascas de revolução geralmente exibem ressonâncias internas devido à inerente simetria circunferencial e um denso espectro de frequência em sua faixa de frequências mais baixas. Isso pode levar não apenas a ressonâncias internas do tipo m:n, mas a múltiplas ressonâncias internas. Nesta tese é realizada a análise de múltiplas ressonâncias internas em cascas cilíndricas delgadas, em particular as ressonâncias internas de 1:1:1:1 e 1:1:2:2 são investigadas em detalhes, um tópico pouco explorado na literatura técnica. A investigação de ressonâncias internas em sistemas contínuos geralmente é realizada usando modelos discretos de baixa dimensão. Embora alguns trabalhos anteriores tenham investigado ressonâncias internas do tipo m:n em cascas cilíndricas, muitos resultados não são consistentes, uma vez que os modelos discretos derivados não consideram os acoplamentos modais devido a não linearidades quadráticas e cúbicas. Aqui, usando um procedimento de perturbação, expansões modais consistentes são derivadas para um número arbitrário de modos de interação, levando a modelos de baixa dimensão confiáveis. A precisão desses modelos é corroborada usando o método Karhunen-Loève. Finalmente, é bem sabido que pequenas imperfeições geométricas da ordem da espessura da casca têm uma forte influência na sua resposta não linear. No entanto, sua influência nas ressonâncias internas, instabilidade dinâmica e transferência de energia é desconhecida. Assim, a influência de diferentes tipos de imperfeição modal é devidamente considerada na presente análise. Utilizando os modelos discretos aqui derivados, é apresentada uma análise detalhada das bifurcações, utilizando técnicas de continuação e o critério de estabilidade de Floquet, esclarecendo a importância das ressonâncias internas nas vibrações não lineares e instabilidades de cascas cilíndricas. Os resultados também confirmam que a forma e a magnitude das imperfeições geométricas iniciais têm uma influência profunda nos resultados, permitindo ou impedindo a transferência de energia entre os modos ressonantes considerados.
The analysis of internal resonances in continuous structural systems is one of the main research areas in the field of nonlinear dynamics. Internal resonance between two vibration modes occur when the ratio of their natural frequencies in an integer number. Of particular importance, due to its influence on the structural response, is the 1:1 internal resonance, usually associated with system symmetries, the 1:2 internal resonance, due to quadratic nonlinearities, and the 1:3 resonance arising from cubic nonlinearities. The internal resonance enables the energy transfer between the related vibration modes, leading usually to new phenomena with profound influence on the stability of the dynamic response. Shells of revolution usually exhibit internal resonances due to the inherent circumferential symmetry and a dense frequency spectrum in their lower frequency range. This may lead not only to m:n internal resonances, but also multiple internal resonances. In this thesis, the analysis of multiple internal resonances in slender cylindrical shells is conducted, in particular 1:1:1:1 and 1:1:2:2 internal resonances are investigated in detail, a topic rarely found in the technical literature. The investigation of internal resonances in continuous systems is usually conducted using low dimensional discrete models. Although some previous works have investigated m:n internal resonances in cylindrical shells, many results are not consistent since the derived discrete models do not consider the modal couplings due to quadratic and cubic nonlinearities. Here, using a perturbation procedure, consistent modal expansions are derived for an arbitrary number of interacting modes, leading to reliable low dimensional models. The accuracy of these models is corroborated using the Karhunen-Loève method. Finally, it is well known that small geometric imperfections of the order of the shell thickness has a strong influence on the shell nonlinear response. However, their influence on internal resonances, dynamic instability and energy transfer is largely unknown. Thus, the influence of different types of modal imperfection is properly considered in the present analysis. Using the derived discrete models, a detail bifurcation analysis, using continuation techniques and Floquet stability criterion, is presented, clarifying the importance of internal resonances on the nonlinear vibrations and instabilities of cylindrical shells. The results also confirm that the form and magnitude of initial geometric imperfections has a profound influence on the results enabling or preventing the energy transfer among the considered resonant modes.
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Lindqvist, Björn. "Combined Control and Path Planning for a Micro Aerial Vehicle based on Non-linear MPC with Parametric Geometric Constraints". Thesis, Luleå tekniska universitet, Rymdteknik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-76212.
Abstract (sommario):
Using robots to navigate through un-mapped environments, specially man-made infrastructures, for the purpose of exploration or inspection is a topic that has gathered a lot of interest in the last years. Micro Aerial Vehicles (MAV's) have the mobility and agility to move quickly and access hard-to-reach areas where ground robots would fail, but using MAV's for that purpose comes with its own set of problems since any collision with the environment results in a crash. The control architecture used in a MAV for such a task needs to perform obstacle avoidance and on-line path-planning in an unknown environment with low computation times as to not lose stability. In this thesis a Non-linear Model Predictive Controller (NMPC) for obstacle avoidance and path-planning on an aerial platform will be established. Included are methods for constraining the available state-space, simulations of various obstacle avoidance scenarios for single and multiple MAVs and experimental validation of the proposed control architecture. The validity of the proposed approach is demonstrated through multiple experimental and simulation results. In these approaches, the positioning information of the obstacles and the MAV are provided by a motion-capture system. The thesis will conclude with the demonstration of an experimental validation of a centralized NMPC for collision avoidance of two MAV's.
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Nakauchi, Gene. "Analytical and numerical results for a curvature-driven geometric flow rule". Thesis, Queensland University of Technology, 2019. https://eprints.qut.edu.au/127335/1/Gene_Nakauchi_Thesis.pdf.
Abstract (sommario):
This research studies a particular curvature-driven geometric flow rule in the plane using techniques from differential geometry, computational mathematics, and formal asymptotics. The flow rule is a combination of the well-studied curve shortening flow, which is governed by a parabolic system of partial differential equations, and the Eikonal equation, which is governed by a hyperbolic system. The physical motivations for considering our model include propagating fire fronts and phase separation. The focus is on a variety of mathematical problems related to the flow rule, such as the explicit form of travelling wave solutions, linear stability, self-intersection, singularity formation, and the extinction problem for convex curves.
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Kayikci, Duygu y. "The Behavior of Moment Resisting Steel Frames Under Seismic Excitation with Variation of Geometric Dimensions of Architectural Setbacks". Scholarly Repository, 2011. http://scholarlyrepository.miami.edu/oa_dissertations/583.
Abstract (sommario):
This study investigates seismic response of the Moment-Resisting-Steel Frames (MRSF) with the architectural setbacks. The main objective of the study is to understand the variation of the elastic and inelastic, static and dynamic behavior with changes in the geometric dimensions of the tower portion. A second objective of the study is to determine the adequacy of the analysis procedures of various rigors, specified in current seismic design provision, in predicting those behaviors for MRSF with various size of setback. The analytical study is conducted using a regular and 16 irregular models to capture all possible combinations of configuration of setback in five-story, five-bay MRSFs. An irregular model is developed by gradually changing the horizontal and vertical dimensions of the tower portion of the regular base 2D frame-model. All models were designed for (a) equal global displacement and uniform distribution of inter-story drift under First-Mode (FM) lateral force distribution pattern at first significant yield, and (b) equal period of vibration at the first mode, using Nonlinear Static Seismic analysis procedure. Among the conclusions derived from the research is that the variation of (a) the elastic and inelastic inter-story drift, the ductility demand for the top three stories, and (b) the elastic and inelastic global displacement exhibited a pattern similar to the variation of the FM participation factor at the roof, PF1Φr,1. The square-root-of-sum-of-square (SRSS) distribution provided accurate estimates of elastic story shear and inter-story drift demand as well as the story yield strength and drift.
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Graham, David(David Warwick) 1976. "Forced Brakke flows". Monash University, School of Mathematical Sciences, 2003. http://arrow.monash.edu.au/hdl/1959.1/7774.
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Graham, David (David Warwick) 1976. "Forced Brakke flows". Monash University, School of Mathematical Sciences, 2003. http://arrow.monash.edu.au/hdl/1959.1/5712.
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Manríquez, Peñafiel Ronald. "Local approximation by linear systems and Almost-Riemannian Structures on Lie groups and Continuation method in rolling problem with obstacles". Electronic Thesis or Diss., université Paris-Saclay, 2022. https://theses.hal.science/tel-03716186.
Abstract (sommario):
L'objectif de cette thèse est d'étudier deux sujets en géométrie sub-Riemannienne. D'une part, l'approximation locale d'une structure presque riemannienne aux points singuliers, et d'autre part, le système cinématique d’une variété à 2 dimensions roulant (sans torsion ni glissement) sur le plan euclidien avec des régions interdites. Une structure presque riemannienne de dimension n peut être définie localement par n champs vectoriels satisfaisant la condition de rang de l'algèbre de Lie, jouant le rôle d'un cadre orthonormé. L'ensemble des points où ces champs vectoriels sont colinéaires est appelé l'ensemble singulier Z. Aux points de tangence, c'est-à-dire aux points où l'espace linéaire engendré par champs vectoriels est égale à l'espace tangent de Z, l'approximation nilpotente peut être remplacée par l'approximation solvable. Dans cette thèse, sous des conditions génériques, nous établissons l'ordre d'approximation de la distance originale par d ̃ (la distance induite par l'approximation solvable) et nous prouvons que d ̃ est plus proche que la distance induite par l'approximation nilpotente de la distance originale. En ce qui concerne les structures des systèmes d'approximation, l'algèbre de Lie générée par cette nouvelle famille de champs vectoriels est de dimension finie et solvable (dans le cas générique). De plus, l'approximation solvable est équivalente à un ARS linéaire sur un espace homogène ou un groupe de Lie. D'autre part, les systèmes non-holonomes ont attiré l'attention de nombreux auteurs de différentes disciplines pour leurs applications variées, principalement en robotique. Le problème du corps roulant (sans glissement ni rotation) d'une variété riemannien bidimensionnel sur une autre variété peut être écrit comme un système non-holonomique. De nombreuses méthodes, algorithmes et techniques ont été développés pour le résoudre. Une implémentation numérique de la méthode de continuation pour résoudre le problème dans lequel une surface convexe roule sur le plan euclidien avec des régions interdites (ou obstacles) sans glisser ou tourner est effectuée. Plusieurs exemples sont illustrésThe aim of this thesis is to study two topics in sub-Riemannian geometry. On the one hand, the local approximation of an almost-Riemannian structure at singular points, and on the other hand, the kinematic system of a 2-dimensional manifold rolling (without twisting or slipping) on the Euclidean plane with forbidden regions. A n-dimensional almost-Riemannian structure can be defined locally by n vector fields satisfying the Lie algebra rank condition, playing the role of an orthonormal frame. The set of points where these vector fields are colinear is called the singular set (Z). At tangency points, i.e., points where the linear span of the vector fields is equal to the tangent space of Z, the nilpotent approximation can be replaced by the solvable one. In this thesis, under generic conditions, we state the order of approximation of the original distance by d ̃ (the distance induced by the solvable approximation), and we prove that d ̃ is closer than the distance induced by the nilpotent approximation to the original distance. Regarding the structure of the approximating system, the Lie algebra generated by this new family of vector fields is finite-dimensional and solvable (in the generic case). Moreover, the solvable approximation is equivalent to a linear ARS on a homogeneous space or a Lie group. On the other hand, nonholonomic systems have attracted the attention of many authors from different disciplines for their varied applications, mainly in robotics. The rolling-body problem (without slipping or spinning) of a 2-dimensional Riemannian manifold on another one can be written as a nonholonomic system. Many methods, algorithms, and techniques have been developed to solve it. A numerical implementation of the Continuation Method to solve the problem in which a convex surface rolls on the Euclidean plane with forbidden regions (or obstacles) without slipping or spinning is performed. Several examples are illustrated
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Silva, Wagner Queiroz. "Análise não linear geométrica do acoplamento solo-estrutura através da combinação MEC-MEF". Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/18/18134/tde-10032010-104324/.
Abstract (sommario):
Neste trabalho foi desenvolvida uma formulação alternativa para o acoplamento entre o método dos elementos de contorno (MEC) e o método dos elementos finitos (MEF) para análise não linear geométrica de estruturas reticuladas ligadas a meios contínuos bidimensionais heterogêneos, aplicado a problemas de interação solo-estrutura. O solo foi considerado com comportamento elástico linear e modelado via MEC por meio de uma formulação alternativa à clássica técnica de sub-região permitindo a consideração de múltiplas inclusões mais ou menos rígidas do que o material padrão e de linhas de carga internas aos domínios. Este código foi então acoplado ao programa AcadFrame, baseado no MEF posicional para análise não linear geométrica de pórticos com consideração de cinemática exata. O acoplamento numérico foi realizado por meio de uma formulação algébrica onde a matriz de rigidez do solo e a força de contato são condensadas e somadas à matriz e ao vetor de forças internas da estrutura a cada iteração no processo de Newton-Raphson. Em ambos os programas foi utilizada uma generalização do grau de aproximação dos elementos através dos polinômios de Lagrange, o que permite a utilização de elementos curvos de alta ordem. Foi utilizada ainda a técnica dos mínimos quadrados para reduzir as oscilações de forças de superfície no contato. Os resultados obtidos de forma geral são bastante satisfatórios e comprovam a eficiência da formulação. O trabalho permite a análise de problemas de edificações apoiadas sobre solos estratificados com múltiplas inclusões e linhas de carga. Permite tanto a análise de elementos apoiados diretamente sobre o solo (sapatas, radies) quanto de elementos internos e em qualquer direção, como no caso de estacas verticais ou inclinadas. Pode-se inclusive considerar as estacas passando por diferentes camadas de solo. A aplicação pode ser estendida ainda a outros problemas elásticos, acoplamento entre peças mecânicas e análise de materiais compostos.This work presents an alternative coupling of the boundary element method (BEM) and the finite element method (FEM) to create a computer program for non linear geometric analysis of frames coupled to continuous domains, applied to soil-structure interaction. A linear elastic behavior is considered for the soil, modeled by BEM. An alternative formulation is adopted for the classic sub-region technique, allowing the consideration of multiple inclusions and load lines inside the soil domain. The BEM computational code is coupled to the AcadFrame software, based on positional FEM for non linear geometric analysis of frames, considering exact kinematics. The numerical coupling is made by an algebraic formulation where the soil stiffness matrix and contact forces are condensed and added to the structure matrix and internal forces for each iteration on Newton-Raphson process. On both programs it is adopted a generalization of the element degree assuming the Lagrange polynomials, which allows the use of curved high order elements. It was also implemented the least square method in order to obtains better and smoother results of surface forces in the contact interface. The obtained results are satisfactory and prove the formulation efficiency. The program allows the analysis of buildings supported by layered soils with multiples inclusions and load lines. It considers directly supported elements over the soil (footing foundations, radies) and internal elements in any direction, like vertical and diagonal piles. It can also consider piles going through different layers of the soil. This formulation can be applied to other elastic problems like coupling between mechanic pieces and composite material analysis.
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Tuma, Carlos Cesar Mansur. "Aprendizado de máquina baseado em separabilidade linear em sistema de classificação híbrido-nebuloso aplicado a problemas multiclasse". Universidade Federal de São Carlos, 2009. https://repositorio.ufscar.br/handle/ufscar/407.
Abstract (sommario):
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Previous issue date: 2009-06-29Financiadora de Estudos e Projetos
This master thesis describes an intelligent classifier system applied to multiclass non-linearly separable problems called Slicer. The system adopts a low computacional cost supervised learning strategy (evaluated as ) based on linear separability. During the learning period the system determines a set of hyperplanes associated to oneclass regions (sub-spaces). In classification tasks the classifier system uses the hyperplanes as a set of if-then-else rules to infer the class of the input attribute vector (non classified object). Among other characteristics, the intelligent classifier system is able to: deal with missing attribute values examples; reject noise examples during learning; adjust hyperplane parameters to improve the definition of the one-class regions; and eliminate redundant rules. The fuzzy theory is considered to design a hybrid version with features such as approximate reasoning and parallel inference computation. Different classification methods and benchmarks are considered for evaluation. The classifier system Slicer reaches acceptable results in terms of accuracy, justifying future investigation effort.
Este trabalho de mestrado descreve um sistema classificador inteligente aplicado a problemas multiclasse não-linearmente separáveis chamado Slicer. O sistema adota uma estratégia de aprendizado supervisionado de baixo custo computacional (avaliado em ) baseado em separabilidade linear. Durante o período de aprendizagem o sistema determina um conjunto de hiperplanos associados a regiões de classe única (subespaços). Nas tarefas de classificação o sistema classificador usa os hiperplanos como um conjunto de regras se-entao-senao para inferir a classe do vetor de atributos dado como entrada (objeto a ser classificado). Entre outras caracteristicas, o sistema classificador é capaz de: tratar atributos faltantes; eliminar ruídos durante o aprendizado; ajustar os parâmetros dos hiperplanos para obter melhores regiões de classe única; e eliminar regras redundantes. A teoria nebulosa é considerada para desenvolver uma versão híbrida com características como raciocínio aproximado e simultaneidade no mecanismo de inferência. Diferentes métodos de classificação e domínios são considerados para avaliação. O sistema classificador Slicer alcança resultados aceitáveis em termos de acurácia, justificando investir em futuras investigações.
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Abdi, Arash. "Control of Quad-copter with suspended load". Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/16490/.
Abstract (sommario):
A Quadrotor (QR) is a type of unmanned aerial vehicles which has been absorbed lots of attention recently with many institutes have investigated on many application with this tools include search and rescue, surveillance, supply of food and medicine in emergency sub-problem of load transportation by the control of the cable suspended load or directly control of the QR robustly.
The goal of this thesis is to present a nonlinear control approach and investigate on novel approach. The focus is lies on the quadrotor-load subsystem where the cable tension is not zero, which analogous to modeling a rigid link between the quadrotor and load.
After introducing the basic concept, an introduction is given on geometric mechanics. This differential geometric based approach is used to model and control the system, based on the geometric properties of the system dynamics. It is shown how the configuration spaces and analyzed with the principles of differential geometry. Also the common approach for second approach will be hired for illustrate the configuration of the Quadrotor-load, while both approach avoiding the problem of singularities would occur on local charts.
Next, the geometric properties are utilized to define tracking error functions on these same space. A back-stepping approach is applied to generate a cascade structure with multiple nonlinear geometric controllers, allowing control of several flight modes that are responsible for the control of a) quadrotor attitude b) load attitude c) load position.
Finally, simulation illustrate the stability and ability of the geometric controller. Also Zero-dynamics is derived to compare both performances. The tracking performances of both controllers are discussed for many different experiences.
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Sanches, Rodolfo André Kuche. "Sobre o acoplamento fluido-casca utilizando o método dos elementos finitos". Universidade de São Paulo, 2011. http://www.teses.usp.br/teses/disponiveis/18/18134/tde-17042011-184131/.
Abstract (sommario):
Este trabalho consiste no desenvolvimento de ferramentas computacionais para análise não linear geométrica de interação fluido-casca utilizando o Método dos Elementos Finitos (MEF). O algoritmo para dinâmica dos fluidos é explícito e a integração temporal é baseada em linhas características. O código computacional é capaz de simular as equações de Navier-Stokes para escoamentos compressíveis tanto na descrição Euleriana como na descrição Lagrangeana-Euleriana arbitrária (ALE), na qual é possível prescrever movimentos para a malha do fluido. A estrutura é modelada em descrição Lagrangeana total através de uma formulação de MEF para análise dinâmica não linear geométrica de cascas baseada no teorema da mínima energia potencial total escrito em função das posições nodais e vetores generalizados e não em deslocamentos e rotações. Essa característica evita o uso de aproximações de grandes rotações. Dois modelos de acoplamentos são desenvolvidos. O primeiro modelo, ideal para problemas onde a escala de deslocamentos não é muito grande comparada com as dimensões do domínio do fluido, é baseado na descrição ALE e o acoplamento entre as duas diferentes malhas é feito através do mapeamento das posições locais dos nós do contorno do fluido sobre os elementos de casca e vice-versa, evitando a necessidade de coincidência entre os nós da casca e do fluido. A malha do fluido é adaptada dinamicamente usando um procedimento simples baseado nas posições e velocidades nodais da casca. O segundo modelo de acoplamento, ideal para problemas com grande escala de deslocamentos tais como estruturas infláveis, considera a casca imersa na malha do fluido e consiste em um procedimento robusto baseado em curvas de nível da função distância assinalada do contorno, o qual integra o algoritmo Lagrangeano de casca com o Fluido em descrição Euleriana, sem necessidade de movimentação da malha do fluido, onde a representação computacional do fluido se resume a uma malha não estruturada maior ou igual ao domínio inicial do fluido e a interface fluido-casca dentro da malha do fluido é identificada por meio de curvas de nível da função distância assinalada do contorno. Ambos os modelos são testados através de exemplos numéricos mostrando robustez e eficiência. Finalmente, como uma sugestão para o futuro desenvolvimento desta pesquisa, iniciaram-se estudos relativos a funções B-splines. O uso desse tipo de funções deverá resolver problemas de estabilidade relativos a oscilações espúrias devidas ao uso de polinômios de Lagrange para a representação de descontinuidades.This work consists of the development of computational tools for nonlinear geometric fluid-shell interaction analysis using the Finite Element Method (FEM). The fluid solver is explicit and its time integration based on characteristics. The computational code is able to simulate the Navier-Stokes equations for compressible flows written in the Eulerian description as well as in the arbitrary Lagrangian-Eulerian (ALE) description, enabling movements prescription for the fluid mesh. The structure is modeled in a total Lagrangian description, using a FEM formulation to deal with geometrical nonlinear dynamics of shells based on the minimum potential energy theorem written regarding nodal positions and generalized unconstrained vectors, not displacements and rotations, avoiding the use of large rotation approximations. Two partitioned coupling models are developed. The first model, ideal for simulations where the displacements scale is not very large compared to the fluid domain, is based on the ALE description and the coupling between the two different meshes is done by mapping the fluid boundary nodes local positions over the shell elements and vice-versa, avoiding the need for matching fluid and shell nodes. The fluid mesh is adapted using a simple approach based on shell nodal positions and velocities. The second model, ideal for problems with large scales of displacements such as inflatable structures, is based on immersed boundary and consists of a robust level-set based approach that integrates the Lagrangian shell finite and the Eulerian finite element high speed fluid flow solver, with no need for mesh adaptation, where the fluid representation relies on a fixed unstructured mesh larger or equal to the initial fluid domain and the fluid-shell interface inside the fluid mesh is tracked with level sets of a boundary signed distance function. Both models are tested with numerical examples, showing efficiency and robustness. Finally, as a suggestion for future development of this research, we started studies relatives to B-Spline functions. The use of this kind of functions should solve stability problems related to spurious oscillations due to the use of Lagrange polynomials for representing discontinuities.
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Maia, Wanderson Fernando. "Sobre a estabilidade de cantoneiras de aço formadas a frio submetidas à compressão". Universidade de São Paulo, 2008. http://www.teses.usp.br/teses/disponiveis/18/18134/tde-16052008-084426/.
Abstract (sommario):
Aparentemente, a análise estrutural de uma cantoneira simples submetida à compressão constitui um problema elementar e, portanto, já largamente conhecido. Entretanto, as cantoneiras formadas a frio, em geral com paredes delgadas (elevadas relações largura/espessura), apresentam dois modos críticos de instabilidade: (i) modo global de flexão, no caso de barras longas, e um modo coincidente local-chapa/global de flexo-torção, que é crítico para barras de menor comprimento. Embora existam procedimentos simplificados de cálculo, recomendados pelas normas, a consideração do modo de flexo-torção é controversa entre pesquisadores. Alguns trabalhos recentes indicam que é conservador considerar o modo de flexo-torção no cálculo da força normal resistente, enquanto outros trabalhos apontam para a necessidade dessa abordagem. Nesse trabalho é investigada a resposta estrutural de cantoneiras simples e enrijecida submetidas à compressão centrada e excêntrica, por meio de análise experimental e de análise numérica não-linear via elementos finitos, sendo avaliado o efeito das imperfeições geométricas iniciais na força normal resistente; também são avaliados os resultados provenientes dos procedimentos normativos: (i) o clássico método das larguras efetivas e (ii) o método da resistência direta (MRD), em que as cantoneiras não são relacionadas como perfis pré-qualificados. Os resultados da análise experimental e da análise numérica não-linear com imperfeições geométricas iniciais indicam a necessidade da consideração do modo de flexo-torção.Apparently, the structural analysis of a simple angle under compression is an elementary problem, therefore, already largely known. However, cold-formed steel angles, mostly with slender legs, present two critical buckling modes: (i) global-flexural mode, in cases of high length members, (ii) and a coincident local-plate/global-torsional-flexural mode, which is critical for short length members. Although simplified design procedures exist, recommended by specifications, the consideration of the torsional-flexural mode is controversial among researchers. A few recent papers indicate that considering the torsional-flexural mode is conservative, while other papers point to the necessity of this approach. This work investigates the structural response of simple and lipped angles under concentrically and eccentrically compression, by means of tests and nonlinear finite element analysis, being evaluated the effect of initial geometric imperfections; also evaluating the results from design procedures: (i) the classic effective width method and (ii) the direct strength method (DSM), where the angles are not pre-qualified shapes. The results of the experimental and nonlinear numerical analysis with initial imperfections indicate the necessity of considering the torsional-flexural mode.
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Jan, Taimoor. "Active fault tolerant control for general aircraft using NLGA". Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018.
Abstract (sommario):
The aerospace applications are considered among one of most complex. The non-linear dynamics and coupling within aircraft systems remains a challenging research area for long time till date. The faults and failures are ordinary in all electrical/mechanical sub-systems. The probability of occurrence can be debatable but it is impossible to assume fault free systems. The faults in input actuators in aircraft can be fatal and highly undesirable. There is a need to make aircraft remain safe/operational and stable in case of such undesirable event. This goal can only be achieved using fault tolerant controls FTC, and in this case active fault tolerant control system AFTCS methodology is considered and investigated. The fault detection and diagnosis FDD can provide the basis of AFTCS. The accurate and effective FDD is explored using Non-linear Geometric Approach (NLGA) for non-linear dynamics of aircraft. In addition, the criticality of descent/landing phases is not unknown since accidents are more prone to happen during these phases. The backstepping (BS) control scheme is proposed as a non-linear method to achieve glide slope control system. The proposed control scheme provided sound tracking performance. The FDD module in combination with BS based control system, provided AFTCS which is capable of stabilizing the aircraft and achieving the desired performance in both scenarios, i.e. faulty/faultless. Minor performance degradation is present but comfort/workload of pilot remains similar to faultless system since aircraft recovers nominal condition promptly, post-fault occurrence. The robustness analysis is satisfactory.
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Chodraui, Gustavo Monteiro de Barros. "Análise teórica e experimental de perfis de aço formados a frio submetidos à compressão". Universidade de São Paulo, 2006. http://www.teses.usp.br/teses/disponiveis/18/18134/tde-31082006-152727/.
Abstract (sommario):
Os perfis de aço formados a frio apresentam, em geral, maior esbeltez local (relação largura-espessura dos elementos) em relação aos clássicos perfis laminados, acentuando a instabilidade local. Além disso, em se tratando de seções abertas com paredes muito delgadas, a rigidez à torção resulta muito pequena, o que torna os modos globais de torção e flexo-torção muitas vezes dominantes em relação aos modos de flexão. Outro modo de instabilidade que pode se manifestar é o modo distorcional, característico nos perfis com enrijecedores de borda. Com relação à análise do modo global, as normas para cálculo de perfis formados a frio têm adotado as mesmas curvas de resistência à compressão desenvolvidas para os perfis laminados e soldados, como a curva do SSRC (Structural Stability Research Council), adotada pela NAS (North American Specification), e as curvas européias, adotadas pela norma brasileira. Embora alguns estudos indiquem que as citadas curvas sejam aceitáveis para os perfis formados a frio, há também referências explícitas quanto à necessidade de um maior aprofundamento na investigação sobre o comportamento estrutural destes perfis, uma vez que apresentam particularidades quanto às tensões residuais, imperfeições geométricas e interação entre modos de instabilidade. Nesse trabalho é apresentada uma análise experimental em perfis usualmente empregados no Brasil (perfis U, U enrijecidos e cantoneiras simples e duplas), e uma estratégia de análise numérica não-linear, considerando os efeitos das imperfeições geométricas globais e localizadas (de chapa e distorcional), bem como das tensões residuais, de modo a se obter teoricamente um valor confiável da força normal de compressão resistente da barra. Os resultados permitiram constatar a viabilidade do emprego das atuais curvas de resistência à compressão para os perfis formados a frio. Complementando, foi analisada a aplicação do método da resistência direta (MRD) a todos os perfis estudados, confirmando bons resultados. Especial atenção foi dada ao estudo da estabilidade elástica de cantoneiras, com foco principal na coincidência entre o modo local-chapa e o modo global-torsional, o que tem gerado controvérsias na aplicação dos métodos de cálculo. Além disso, como as cantoneiras não são pré-qualificadas para aplicação do MRD, foram analisadas várias opções para emprego do método, onde pode-se concluir que desconsiderar a torção na análise do modo global conduz a resultados contra a segurançaCold-formed steel members present, in general, higher local slenderness than classical hot- rolled ones, which make them more prone to local buckling. Besides, thin-walled open sections have small torsional stiffness, and hence global torsional and flexural-torsional instability modes are many times more critical than global flexural ones. Also, distortional mode can happen in sections with lips (edge stiffener). Concerning on global buckling for members under compression, curves used in cold-formed steel design are based on hot-rolled and welded members. For example, the SSRC (Structural Stability Research Council) buckling curve, adopted by NAS (North American Specification), and Eurocode buckling curves, adopted by brazilian codes. Although some papers indicate these curves are acceptable for cold-formed steel members, others claim for a deeper analysis on their unique structural behavior, specially on residual stress, geometric imperfections and coupled buckling modes. It is presented in this thesis an experimental analysis of sections usually used in Brazil (simple and lipped channels, and also single and built-up angles). Moreover, it is developed a strategy for numerical non-linear analysis, considering the effects of global and local (also distortional) geometric imperfections and residual stress as well, in order to obtain a trustable theoretical value for the axial member stength. Results show the viability of the current buckling curves for cold-formed steel members. Finally, direct strength method (DSM) was analysed for all studied members, showing good results. Special attention to angles elastic stability, focusing on the coincidence between local-plate and global-torsional mode, which still causes confusion in design methods. Also, due to the fact angles are not pre- qualified sections for using DSM, many options on its application were studied, where it was concluded that negleting torsion in global analysis leeds to unconservative results
33
ASSIS, Lilian Pureza de. "Otimização de estruturas reticuladas planas com comportamento geometricamente não linear". Universidade Federal de Goiás, 2006. http://repositorio.bc.ufg.br/tede/handle/tde/678.
Abstract (sommario):
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Previous issue date: 2006-10-20The aim of this work is to present a formulation and corresponding computational implementation for sizing optimization of plane frames and cable-stayed columns considering geometric non liner behavior. The structural analysis is based on the finite element method using the updated lagrangian approach for plane frame and cable elements, which are represented by plane truss elements. The non linear system is solved by the Newton-Raphson method coupled to load increment strategies such as the arch length method and the generalized displacement parameter method, which allow the algorithm to transpose any critical point that happen to appear along the equilibrium path. In the optimization process the design variables are the heights of the crosssection of the frame elements, the objective function represents the volume of the structure and the constraints impose limits to displacements and critical load. Lateral constraints impose limits to the design variables. The finite difference method is used in the sensitivity analysis of the displacement and critical load constraints. The optimization process is carried out using three different optimization strategies: the sequential quadratic programming algorithm; the interior points algorithm; and the branch and bound method. Some numerical experiments are carried out so as to test the analysis and the sensitivity strategies. Numerical experiments are presented to show the validity of the implementation presented in this dissertation.
O objetivo deste trabalho é a otimização de dimensões de pórticos planos e de colunas estaiadas planas pela minimização do volume da estrutura, considerando os efeitos da não-linearidade geométrica em seu comportamento. A formulação utiliza, para análise das estruturas, elementos finitos de pórtico e de treliça planos e referencial lagrangeano atualizado. O método de Newton-Raphson foi utilizado como estratégia para solução do sistema de equações não lineares. Foram acopladas estratégias especiais para ultrapassagem de pontos críticos que possam existir ao longo da trajetória de equilíbrio, tais como o comprimento de arco cilíndrico e o controle dos deslocamentos generalizados. Na otimização, as variáveis de projeto são as alturas das seções transversais dos elementos, a função objetivo é o volume do material e as restrições dizem respeito a limitações impostas a deslocamentos e à carga limite, além de limitações impostas aos valores das variáveis. A sensibilidade da função objetivo foi obtida por diferenciação direta e a sensibilidade das restrições pelo método das diferenças finitas. Foram utilizados o algoritmo de programação quadrática seqüencial, PQS, o algoritmo de pontos interiores, PI, e o algoritmo de Branch and Bound, B&B. São apresentados exemplos de validação das estratégias de análise não linear e da análise de sensibilidade, além dos exemplos de validação da formulação empregada para a otimização resolvidos pelos métodos implementados.
34
Rodrigues, Flávio. "Comportamento estrutural de vigas de aço com abertura na alma". Universidade do Estado do Rio de Janeiro, 2007. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=421.
Abstract (sommario):
Limitações de altura são frequentemente impostas à edificações de múltiplos pavimentos por regulamentos de zoneamento urbano, aspectos econômicos e considerações estéticas. Um pé-direito alto é normalmente requerido para se permitir a passagem de tubulações e dutos de grande diâmetro sob vigas de aço, conduzindo muitas vezes à alturas inaceitáveis entre pavimentos de edificações. Várias são as soluções possíveis para se resolver tal inconveniência, dentre elas pode-se citar: Vigas com inércia variável, stub girders , treliças mistas e vigas misuladas. Outra solução frequentemente utilizada é a abertura de furos na alma das vigas d e aço para a passagem das tubulações de serviço. A presente dissertação tem por objetivo avaliar e descrever o comportamento estrutural de vigas de aço com aberturas de diferentes tamanhos e formas na alma. Outro propósito deste trabalho de pesquisa é a avaliação dos parâmetros que influenciam diretamente a capacidade de resistência das vigas com diferentes tipos de abertura na alma, tais como: Tipo de furo, localização do furo ao longo do vão, altura do furo em relação à altura do perfil, esbeltez da alma, localização da carga solicitante ao longo do vão, entre outros. Também é objetivo deste trabalho, a avaliação dos diferentes mecanismos de ruína para as vigas com aberturas na alma e as causas que conduziram o colapso das mesmas. Finalmente, apresenta-se um estudo da eficácia de enrijecedores longitudinais nos locais de abertura da alma das vigas de aço. A metodologia empregada para tal estudo baseou-se em uma análise paramétrica com o auxílio do método numérico dos elementos finitos.Height limitations are frequent in multi-storey buildings due to zoning regulations, economic requirements and esthetical considerations . In order to provide the passage of large pipes and ducts beneath steel beams, huge spaces are normally required, leading many times to unacceptable heights between storeys. There are many possible solutions to solve these problems, such as: Tapered beams, stub girders, composite trusses and haunched beams. Another frequent solution is the opening of holes in the web beam steel to enable the passage of the services. This dissertation has the objective of evaluating and describing the structural behavior of steel beams with web openings of different shapes and sizes. Another aim of this research work is the evaluation of the parameters that directly influence the load carry capacity of the beams with different web openings, such as: Holesh ape, the location of the opening throughout the span, the height hole to height profile ratio, the web slenderness and the location of the load point throughout the span. The evaluation of the different failure mechanisms of steel beams with web openings and the reasons that conducted the collapse of them are also focused on the present work. Finally, a study of the efficiency of the use of longitudinal stiffeners at web openings locations is also presented. The methodology employed for such study was based on a parametric analysis based on the finite elements method.
35
"Deformations with non-linear constraints". 2013. http://library.cuhk.edu.hk/record=b5549277.
Abstract (sommario):
於參數化和特徵模型的變形中保持幾何特徵是CAD建模中一項新的挑戰。這篇論文提出了一個以限制為基礎去進行變形的系統。此系統結合了自由曲面和特徵模型建模的好處，而且容許更自由的工程設計。本方法可分為三個主要步驟。以常用的變形技術去改變一個模型的形狀，包括自由變形及軸向變形，然後參數特徵會根據用戶的要求去分拆為一系列基本的限制，最後目標特徵將會以逐步增量的優化技術去重建。
這篇論文提出了一個逐步增量的方法為優化中提供導引。這個優化是於維持所有提供的限制下盡量減少變形後模型的改變。另外，於一組的限制中以一個基准為參考，能使本系統更有效的運行。最後，我們也會展示一些使用本系統以限制為基礎去進行變形的結果。
To retain geometric features in the deformation of a parametric and feature-based model is a new challenge for CAD modeling. This thesis presents a constraints based deformation framework. This framework combines the advantage of free-form modeling with feature based modeling, and allows engineering design to be performed in a free-form manner.
The proposed method can be divided into three major steps. An object is deformed by common deformation techniques such as FFD and axial deformation. Parametric features are divided into systems of primitive constraints based on user specification. The targeting features are reconstructed by the use of incremental optimization technique.
An incremental constrained deformation is introduced. It is used to provide hints for the optimization. The optimization is to minimize the changes in the deformed model subjected to all the provided constraints. For a structural constraint specified with a group of constraints, it would be better to use a reference datum for all its component constraints. We show numerous results of constraints retained models using our framework.
Detailed summary in vernacular field only.
Detailed summary in vernacular field only.
Detailed summary in vernacular field only.
Tang, Wing Shing.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2013.
Includes bibliographical references (leaves 84-86).
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Abstracts also in Chinese.
Chapter 1 --- INTRODUCTION --- p.3
Chapter 1.1 --- Aims and Objectives --- p.4
Chapter 1.2 --- Report Organization --- p.5
Chapter 2 --- BACKGROUND AND LITERATURE REVIEW --- p.7
Chapter 2.1 --- Mesh Editing Techniques --- p.7
Chapter 2.1.1 --- Mesh Deformation Techniques --- p.7
Chapter 2.1.2 --- Detail Preserving Techniques --- p.9
Chapter 2.2 --- Optimization Techniques --- p.11
Chapter 2.2.1 --- Optimization Techniques --- p.11
Chapter 2.2.2 --- Linear Programming --- p.12
Chapter 2.2.2.1 --- Simplex Method --- p.12
Chapter 2.2.2.2 --- Interior Point Method --- p.12
Chapter 2.2.2.2.1 --- Primal-Dual Interior Point Method --- p.13
Chapter 2.2.3 --- Nonlinear Programming --- p.14
Chapter 2.2.3.1 --- Sequential Quadratic Programming --- p.14
Chapter 2.2.3.2 --- Reduced Gradient Methods --- p.14
Chapter 2.2.3.3 --- Interior Point Methods --- p.15
Chapter 2.2.4 --- Optimization Solver --- p.15
Chapter 2.2.4.1 --- KNITRO --- p.16
Chapter 3 --- SPECIFICATION OF CONSTRAINTS --- p.18
Chapter 3.1 --- Constraints --- p.18
Chapter 3.1.1 --- Constraints with Reference Points --- p.22
Chapter 3.1.2 --- Constraints with Reference Variables --- p.24
Chapter 3.1.3 --- Reference Vector Constraints --- p.26
Chapter 3.1.4 --- Constraints with Reference Datum --- p.27
Chapter 3.1.4.1 --- Planer Constraint with References --- p.28
Chapter 3.1.4.2 --- Collinear Constraint with References --- p.29
Chapter 3.1.4.3 --- Circular Constraint with References --- p.30
Chapter 3.2 --- Redundant Constraints --- p.31
Chapter 4 --- CONSTRAINED OPTIMZATION --- p.32
Chapter 4.1 --- Objective Function --- p.32
Chapter 4.2 --- Incremental Constrained Deformation --- p.39
Chapter 4.3 --- The Scaling Problem --- p.43
Chapter 5 --- CASE STUDIES --- p.44
Chapter 5.1 --- Maintain Individual Engineering Features --- p.44
Chapter 5.2 --- Maintain Pattern between Engineering Features --- p.49
Chapter 5.3 --- Maintain Relationship between Engineering Features --- p.51
Chapter 5.4 --- Implementation Issue --- p.66
Chapter 6 --- TESTS AND RESULTS --- p.68
Chapter 6.1 --- Constraints with References --- p.68
Chapter 6.2 --- Level Of Detail --- p.71
Chapter 6.3 --- Incremental Method --- p.73
Chapter 6.4 --- Comparison --- p.76
Chapter 7 --- FURTHER WORK AND CONCLUSIONS --- p.81
Chapter 7.1 --- Recommendation for Further Work --- p.81
Chapter 7.2 --- Conclusions --- p.82
REFERENCES --- p.84
36
Berberich, Eric [Verfasser]. "Robust and efficient software for problems in 2.5-dimensional non-linear geometry : algorithms and implementations / vorgelegt von Eric Berberich". 2008. http://d-nb.info/996728066/34.
37
(7847843), Rahul Deshmukh. "Influence of geometry and placement configuration on side forces in compression springs". Thesis, 2019.
Abstract (sommario):
A leading cause of premature failure and excessive wear and tear in mechanical components that rely on compression springs for their operation is the development of unwanted side forces when the spring is compressed.
These side forces are usually around 10% - 20% of the magnitude of the axial load and point in different directions in the plane perpendicular to the axis of the spring.
The magnitude and direction of the resultant of side forces varies very non-linearly and unpredictably even though the axial force behavior of the spring is very consistent and predictable.
Since these side forces have to be resisted by the housing components that hold the spring in place, it is difficult to design these components for optimal operation.
The hypothesis of this study is that side forces are highly sensitive to small changes in spring geometry and its placement configuration in the housing.
Several experiments are conducted to measure the axial and side forces in barrel springs and two different types of finite element models are developed and calibrated to model the spring behavior.
Spring geometry and placement are parameterized using several control variables and an approach based on design of experiments is used to identify the critical parameters that control the behavior of side-forces.
The models resulted in deeper insight into the development of side forces as the spring is progressively loaded and how its contact interactions with the housing lead to changes in the side force.
It was found that side-forces are indeed sensitive to variations in spring geometry and placement.
These sensitivities are quantified to enable designers to and manufacturers of such springs to gain more control of side force variations between different spring specimens.
38
Marzia, José António Assunção. "Influence of the yield criterion in the formability prediction on parts with complex geometry". Master's thesis, 2020. http://hdl.handle.net/10316/93932.
Abstract (sommario):
Dissertação de Mestrado Integrado em Engenharia Mecânica apresentada à Faculdade de Ciências e TecnologiaA conformação de chapas metálicas é uma tecnologia de produção indispensável na indústria automóvel. A produção de componentes metálicos com esta tecnologia envolve o planeamento do processo, que requer ferramentas complexas e dispendiosas. A conceção dessas ferramentas deve considerar os limites de conformabilidade das chapas metálicas. Os códigos de análise por elementos finitos, como o AutoForm®, são utilizados na indústria para apoiar a conceção das ferramentas, já que permitem prever defeitos, como rugas e a localização da deformação. Infelizmente, em alguns casos surgem defeitos nos componentes metálicos, seja no try-out das ferramentas ou na produção, que não são previstos pelos modelos de elementos finitos. O objetivo principal deste trabalho é compreender os fatores que podem contribuir para melhorar a previsão de defeitos de conformação em componentes automóveis estampados.Neste trabalho foram considerados três casos de estudo, um guarda-lamas e dois portões interiores. São utilizados dois aços galvanizados da mesma classe, DX54D e DX56D, para produzir o guarda-lamas e os portões interiores, respetivamente. Para o guarda-lamas e um dos portões interiores, o estudo focou-se na análise da influência do valor da tensão equibiaxial na previsão da conformabilidade, com base nos critérios de plasticidade de Hill'48 e BBC 2005. Para o outro portão interior, foi realizada uma análise minuciosa da cinemática do processo de conformação, para analisar os fatores que contribuem para a ocorrência de problemas esporádicos na produção. Neste contexto, foram exploradas as opções de controle das ferramentas, assim como o gerador de materiais do AutoForm® R8, o que exigiu a realização de alguns ensaios experimentais para caracterizar o comportamento mecânico do material. Assim, foi possível utilizar o critério de plasticidade de Vegter 2017, para este caso de estudo.Para todos os casos de estudo, a análise de conformabilidade foi realizada com a curva limite de estampagem linear e não-linear. Com base em resultados anteriores, sabe-se que o critério de plasticidade de Hill'48 sobrestima o valor da tensão equibiaxial, para esta classe de material. Os resultados mostram que o valor da tensão equibiaxial tem impacto nas previsões de conformabilidade e pode até mesmo alterar as regiões críticas para a ocorrência de defeitos. Nesse contexto, o uso da curva limite de estampagem não-linear é muito importante, uma vez que trajetórias de deformação próximas da deformação plana seguidas de estado equibiaxial, ou vice-versa, apresentam maior exaustão de conformabilidade. Com base nas previsões de conformabilidade, é possível estimar um valor para a tensão equibiaxial de 0.9 vezes o valor previsto pelo critério de Hill'48, o que corrobora estudos anteriores. Nesse contexto, o critério de plasticidade de Vegter 2017 pode ser considerado uma abordagem interessante para descrever o comportamento plástico do material, uma vez que a identificação dos seus parâmetros requer apenas a realização de três ensaios de tração uniaxial. Finalmente, além de uma descrição precisa do comportamento plástico do material, a previsão de defeitos requer a descrição adequada da cinemática do processo de conformação.
Sheet metal forming is an indispensable manufacturing technology in the automotive industry. The production of metallic components using this technology involves the planning of the process that requires complex and expensive tooling. The development of these tools has to consider the formability limits of the metal sheets. Finite element analysis codes, such as AutoForm®, are used throughout the industry to support the development of the tools, since they enable the prediction of defects, such as wrinkling and thinning. Unfortunately, in some cases defects arise in the metallic components, either in the tools try-out or in the production, which were not predicted by the finite element model. The main objective of this work is to understand the factors that can contribute to improving the prediction of forming defects for deep drawn automotive components. Three case studies were considered in this work, a fender and two inner liftgates. Two galvanized steels of the same class, DX54D and DX56D, are used to produce the fender and the inner liftgates, respectively. For the fender and one of the inner liftgates, the study focused on the analysis of the influence of the equibiaxial stress value in the prediction of the formability, considering the Hill’48 and the BBC 2005 yield criteria. For the other inner liftgate, a thorough analysis of the kinematics of the forming process was performed to understand the factors that contribute for the occurrence of sporadic problems in production. In this context, the control options for the tools were explored as well as the material generator of AutoForm® R8, which required performing some experimental tests to characterize the mechanical behavior of the material. This enabled the use of the Vegter 2017 yield criterion, for this case study. For all case studies, the formability analysis was performed with the linear and the non-linear forming limit curve. For this material class, it is known that the Hill’48 yield criteria overestimates the equibiaxial stress value. The results show that the equibiaxial stress value has impact on the formability predictions and it can even change the critical locations of defects. In this context, the use of the non-linear forming limit curve is very important, since strain paths close to plane strain followed by equibiaxial state or vice versa show higher exhaustion in formability. Based on the formability predictions, the equibiaxial stress value is estimated to be around 0.9 times the value predicted by the Hill’48 criterion, corroborating previous studies. In this context, the Vegter 2017 yield criterion can be considered an interesting approach to describe the plastic behavior of the material, since its parameters identification only requires performing three uniaxial tensile tests. Finally, besides an accurate description of the plastic behavior of the material, the prediction of defects requires the proper description of the kinematics of the forming process.
39
Weischedel, Clarisse. "A discrete geometric view on shear-deformable shell models". Doctoral thesis, 2012. http://hdl.handle.net/11858/00-1735-0000-000D-F06B-C.
40
Krishnam, Raju N. R. B. "Nonlinear Structural Analysis Using Integrated Force Method". Thesis, 1999. https://etd.iisc.ac.in/handle/2005/1618.
41
Krishnam, Raju N. R. B. "Nonlinear Structural Analysis Using Integrated Force Method". Thesis, 1999. http://etd.iisc.ernet.in/handle/2005/1618.
42
Bukhari, Abdulwahab Abdullatif. "Optimization of production allocation under price uncertainty : relating price model assumptions to decisions". Thesis, 2011. http://hdl.handle.net/2152/ETD-UT-2011-08-3780.
Abstract (sommario):
Allocating production volumes across a portfolio of producing assets is a complex optimization problem. Each producing asset possesses different technical attributes (e.g. crude type), facility constraints, and costs. In addition, there are corporate objectives and constraints (e.g. contract delivery requirements). While complex, such a problem can be specified and solved using conventional deterministic optimization methods. However, there is often uncertainty in many of the inputs, and in these cases the appropriate approach is neither obvious nor straightforward. One of the major uncertainties in the oil and gas industry is the commodity price assumption(s). This paper investigates this problem in three major sections: (1) We specify an integrated stochastic optimization model that solves for the optimal production allocation for a portfolio of producing assets when there is uncertainty in commodity prices, (2) We then compare the solutions that result when different price models are used, and (3) We perform a value of information analysis to estimate the value of more accurate price models. The results show that the optimum production allocation is a function of the price model assumptions. However, the differences between models are minor, and thus the value of choosing the “correct” price model, or similarly of estimating a more accurate model, is small. This work falls in the emerging research area of decision-oriented assessments of information value.text