Dissertations / Theses on the topic 'Higher order beam element'
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Garbin, Turpaud Fernando, and Pachas Ángel Alfredo Lévano. "Higher-order non-local finite element bending analysis of functionally graded." Bachelor's thesis, Universidad Peruana de Ciencias Aplicadas (UPC), 2019. http://hdl.handle.net/10757/626024.
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La teoría de vigas de Timoshenko TBT y una teoría de alto orden IFSDT son formuladas utilizando las ecuaciones constitutivas no locales de Eringen. Se utilizaron ecuaciones constitutivas en 3D en el modelo IFSDT. Se utilizó una variación del material con el uso de materiales funcionalmente graduados a lo largo del peralte de una viga de sección rectangular. El principio de trabajos virtuales utilizado y ejemplos numéricos fueron presentados para comparar ambas teorías de vigas.Timoshenko Beam Theory (TBT) and an Improved First Shear Deformation Theory (IFSDT) are reformulated using Eringen’s non-local constitutive equations. The use of 3D constitutive equation is presented in IFSDT. A material variation is made by the introduction of FGM power law in the elasticity modulus through the height of a rectangular section beam. The virtual work statement and numerical results are presented in order to compare both beam theories.
Tesis
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MAIARU', MARIANNA. "Multiscale approaches for the failure analysis of fiber-reinforced composite structures using the 1D CUF." Doctoral thesis, Politecnico di Torino, 2014. http://hdl.handle.net/11583/2571353.
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Composites provide significant advantages in performance, efficiency and costs; thanks to
these features, their application is increasing in many engineering fields, such as aerospace,
naval and mechanical engineering. Although the adoption of composites is rising, there
are still open issues to be investigated, in particular, understanding their failure mechanism has a prominent role in enhancing component designs. Numerous methodologies are available to compute
accurate stress/strain fields for laminated structures, multi-scale approaches are required
when micro- and macro-scales are accounted for. Despite the increasing development in
computer hardware, the computational effort of these methods is still prohibitive for extensive applications, especially when a high number of layers is considered. Then, the
reduction of the computational time and cost required to perform failure analysis is still
a challenging task.
This work proposes two multiscale approaches for the failure analysis of fiber-reinforced composites.
A concurrent multiscale approach ("Component-Wise") and a hierarchical method are developed based on the
1D Carrera Unified Formulation (CUF). 1D higher order elements are very powerful tools for multiscale analysis
since they provide accurate stress and strain fields with very low computational costs.
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Ayad, Mohammad. "Homogenization-based, higher-gradient dynamical response of micro-structured media." Electronic Thesis or Diss., Université de Lorraine, 2020. http://www.theses.fr/2020LORR0062.
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Une approche dynamique discrète (DDM) est proposée dans le contexte de la mécanique des poutres pour calculer les caractéristiques de dispersion des structures périodiques. Cette démarche permet de calculer les caractéristiques de dispersion de milieux périodiques unidimensionnels et bidimensionnels. Il est montré qu’un développement d'ordre supérieur suffisamment élevé des forces et des moments d’éléments structuraux est nécessaire pour décrire avec précision les modes de propagation d’ordre supérieur. Ces résultats montrent dans l’ensemble que les calculs des caractéristiques de dispersion de systèmes structurels périodiques peuvent être abordés avec une bonne précision par la dynamique des éléments discrets. Les comportements non classiques peuvent être capturés non seulement par une expansion d'ordre supérieur mais aussi par des formulations à gradient supérieur. Nous calculons ainsi les paramètres constitutifs macroscopiques jusqu'au deuxième gradient du déplacement en utilisant deux formulations différentes, soit selon une méthode d'homogénéisation dynamique à gradient supérieur (DHGE) prenant en compte les effets de micro-inertie, ou alternativement selon le principe de Hamilton. Nous analysons ensuite la sensibilité des termes constitutifs du second gradient aux paramètres microstructuraux pour des matériaux composites à microstructure périodique de type laminés. En plus, on montre que les modèles du deuxième gradient formulés à partir de l'énergie interne totale en tenant compte des termes de gradient d'ordre supérieur donnent la meilleure description du propagation d’onde à travers ces milieux. On analyse les contributions d'ordre supérieur et de micro-inertie sur le comportement mécanique de structures composites en utilisant une méthode d'homogénéisation dynamique d'ordre supérieur qui intègre les effets de micro-inertie. Nous calculons la réponse effective statique longitudinale à gradient d’ordre supérieur, en quantifiant la différence relative par rapport à la formulation classique de type Cauchy qui repose sur le premier gradient du déplacement. Nous analysons ensuite les propriétés de propagation d’ondes longitudinales en termes de fréquence propre de composites, en tenant compte de la contribution de la micro-inertie. La longueur interne joue un rôle crucial dans les contributions de micro-inertie avec un effet substantiel pour les faibles valeurs de longueur interne, et qui correspond à une large gamme de matériaux utilisés en ingénierie des structures. La méthode d’homogénéisation développée montre un effet de taille important pour les modules élastiques homogénéisés d’ordre supérieur. Par conséquent, nous développons une formulation indépendante de la taille qui est basée sur des termes de correction liée aux moment quadratique. Dans ce contexte, on analyse l’influence des termes de correction sur le comportement statique et dynamique de composites à inclusionA discrete dynamic approach (DDM) is developed in the context of beam mechanics to calculate the dispersion characteristics of periodic structures. Subsequently, based on this dynamical beam formulation, we calculate the dispersion characteristics of one-dimensional and two-dimensional periodic media. A sufficiently high order development of the forces and moments of the structural elements is necessary to accurately describe the propagation modes of higher order. These results show that the calculations of the dispersion characteristics of structural systems can be approached with good accuracy by the dynamics of the discrete elements. Besides, non-classical behaviors can be captured not only by higher order expansion but also by higher gradient formulations. To that scope, we develop a higher gradient dynamic homogenization method with micro-inertia effects. Using this formulation, we compute the macroscopic constitutive parameters up to the second gradient, using two distinct approaches, namely Hamilton’s principle and a total internal energy formulation. We analyze the sensitivity of the second gradient constitutive terms on the inner material and geometric parameters for the case of composite materials made of a periodic, layered microstructure. Moreover, we show that the formulations based on the total internal energy taking into account higher order gradient terms give the best description of wave propagation through the composite. We analyze the higher order and micro-inertia contributions on the mechanical behavior of composite structures by calculating the effective static and dynamic properties of composite beams using a higher order dynamic homogenization method. We compute the effective longitudinal static response with higher order gradient, by quantifying the relative difference compared to the classical formulation of Cauchy type, which is based on the first gradient of displacement. We then analyze the propagation properties of longitudinal waves in terms of the natural frequency of composite structural elements, taking into account the contribution of micro-inertia. The internal length plays a crucial role in the contributions of micro-inertia, which is particularly significant for low internal length values, therefore for a wide range of materials used in structural engineering. The developed method shows an important size effect for the higher gradients, and to remove these effects correction terms have been incorporated which are related to the quadratic moment of inertia. We analyze in this context the influence of the correction terms on the static and dynamic behavior of composites with a central inclusion
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Oskooei, Saeid G. "A higher order finite element for sandwich plate analysis." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape17/PQDD_0014/MQ34105.pdf.
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El-Esber, Lina. "Hierarchal higher order finite element modeling of periodic structures." Thesis, McGill University, 2005. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=82483.
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Periodic structures play an important role in engineering since they allow the manipulation of the electromagnetic properties of certain materials. To design such structures and investigate their different properties, it is essential to use simulation techniques. Among the various methods that have been used traditionally, the finite element method offers great advantages. In this thesis, a three dimensional finite element method is used to obtain the band diagrams of periodic structures; hierarchal higher-order elements are employed, thereby opening up the possibility of goal oriented h-p adaptivity. The computed dispersion curves for doubly-periodic and triply-periodic metallic structures are presented and compared to previously published curves. The results confirm the accuracy of the finite element formulation developed in this thesis and its implementation. Further, the triply-periodic results support the case for using higher-order, less dense meshes rather than lower-order, more highly refined meshes; the doubly-periodic results are inconclusive.
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Wagner, Carlee F. "Improving shock-capturing robustness for higher-order finite element solvers." Thesis, Massachusetts Institute of Technology, 2015. http://hdl.handle.net/1721.1/101498.
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Thesis: S.M., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2015.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 81-91).
Simulation of high speed flows where shock waves play a significant role is still an area of development in computational fluid dynamics. Numerical simulation of discontinuities such as shock waves often suffer from nonphysical oscillations which can pollute the solution accuracy. Grid adaptation, along with shock-capturing methods such as artificial viscosity, can be used to resolve the shock by targeting the key flow features for grid refinement. This is a powerful tool, but cannot proceed without first converging on an initially coarse, unrefined mesh. These coarse meshes suffer the most from nonphysical oscillations, and many algorithms abort the solve process when detecting nonphysical values. In order to improve the robustness of grid adaptation on initially coarse meshes, this thesis presents methods to converge solutions in the presence of nonphysical oscillations. A high order discontinuous Galerkin (DG) framework is used to discretize Burgers' equation and the Euler equations. Dissipation-based globalization methods are investigated using both a pre-defined continuation schedule and a variable continuation schedule based on homotopy methods, and Burgers' equation is used as a test bed for comparing these continuation methods. For the Euler equations, a set of surrogate variables based on the primitive variables (density, velocity, and temperature) are developed to allow the convergence of solutions with nonphysical oscillations. The surrogate variables are applied to a flow with a strong shock feature, with and without continuation methods, to demonstrate their robustness in comparison to the primitive variables using physicality checks and pseudo-time continuation.
by Carlee F. Wagner.
S.M.
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Underwood, Tyler Carroll. "Performance Comparison of Higher-Order Euler Solvers by the Conservation Element and Solution Element Method." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1399017583.
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Li, Ming-Sang. "Higher order laminated composite plate analysis by hybrid finite element method." Thesis, Massachusetts Institute of Technology, 1989. http://hdl.handle.net/1721.1/40145.
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Bonhaus, Daryl Lawrence. "A Higher Order Accurate Finite Element Method for Viscous Compressible Flows." Diss., Virginia Tech, 1998. http://hdl.handle.net/10919/29458.
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The Streamline Upwind/Petrov-Galerkin (SU/PG) method is applied to higher-order
finite-element discretizations of the Euler equations in one dimension and the Navier-Stokes
equations in two dimensions. The unknown flow quantities are discretized on
meshes of triangular elements using triangular Bezier patches. The nonlinear residual
equations are solved using an approximate Newton method with a pseudotime term. The
resulting linear system is solved using the Generalized Minimum Residual algorithm with
block diagonal preconditioning.
The exact solutions of Ringleb flow and Couette flow are used to quantitatively
establish the spatial convergence rate of each discretization. Examples of inviscid flows
including subsonic flow past a parabolic bump on a wall and subsonic and transonic flows
past a NACA 0012 airfoil and laminar flows including flow past a a flat plate and flow past
a NACA 0012 airfoil are included to qualitatively evaluate the accuracy of the discretiza-tions.
The scheme achieves higher order accuracy without modification. Based on the test
cases presented, significant improvement of the solution can be expected using the higher-order
schemes with little or no increase in computational requirements. The nonlinear sys-tem
also converges at a higher rate as the order of accuracy is increased for the same num-ber
of degrees of freedom; however, the linear system becomes more difficult to solve.
Several avenues of future research based on the results of the study are identified, includ-ing
improvement of the SU/PG formulation, development of more general grid generation
strategies for higher order elements, the addition of a turbulence model to extend the
method to high Reynolds number flows, and extension of the method to three-dimensional
flows. An appendix is included in which the method is applied to inviscid flows in three
dimensions. The three-dimensional results are preliminary but consistent with the findings
based on the two-dimensional scheme.Ph. D.
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Bilyeu, David L. "A HIGHER-ORDER CONSERVATION ELEMENT SOLUTION ELEMENT METHOD FOR SOLVING HYPERBOLIC DIFFERENTIAL EQUATIONS ON UNSTRUCTURED MESHES." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1396877409.
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Couchman, Benjamin Luke Streatfield. "On the convergence of higher-order finite element methods to weak solutions." Thesis, Massachusetts Institute of Technology, 2018. http://hdl.handle.net/1721.1/115685.
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Thesis: S.M., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2018.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 77-79).
The ability to handle discontinuities appropriately is essential when solving nonlinear hyperbolic partial differential equations (PDEs). Discrete solutions to the PDE must converge to weak solutions in order for the discontinuity propagation speed to be correct. As shown by the Lax-Wendroff theorem, one method to guarantee that convergence, if it occurs, will be to a weak solution is to use a discretely conservative scheme. However, discrete conservation is not a strict requirement for convergence to a weak solution. This suggests a hierarchy of discretizations, where discretely conservative schemes are a subset of the larger class of methods that converge to the weak solution. We show here that a range of finite element methods converge to the weak solution without using discrete conservation arguments. The effect of using quadrature rules to approximate integrals is also considered. In addition, we show that solutions using non-conservation working variables also converge to weak solutions.
by Benjamin Luke Streatfield Couchman.
S.M.
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鍾偉昌 and Wai-cheong Chung. "Geometrically nonlinear analysis of plates using higher order finite elements." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1986. http://hub.hku.hk/bib/B31207601.
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Chung, Wai-cheong. "Geometrically nonlinear analysis of plates using higher order finite elements /." [Hong Kong : University of Hong Kong], 1986. http://sunzi.lib.hku.hk/hkuto/record.jsp?B12225022.
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Chrusch, Peter P. "Conventional and differential scanning optical microscopy using higher-order Gaussian-Hermite beam patterns /." Online version of thesis, 1990. http://hdl.handle.net/1850/10897.
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Zhang, Pei. "Beam position diagnostics with higher order modes in third harmonic superconducting accelerating cavities." Thesis, University of Manchester, 2013. https://www.research.manchester.ac.uk/portal/en/theses/beam-position-diagnostics-with-higher-order-modes-in-third-harmonic-superconducting-accelerating-cavities(587aa24b-8adc-4bc6-8f5c-475aa0028d06).html.
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Higher order modes (HOM) are electromagnetic resonant fields. They can be excited by an electron beam entering an accelerating cavity, and constitute a component of the wakefield. This wakefield has the potential to dilute the beam quality and, in the worst case, result in a beam-break-up instability. It is therefore important to ensure that these fields are well suppressed by extracting energy through special couplers. In addition, the effect of the transverse wakefield can be reduced by aligning the beam on the cavity axis. This is due to their strength depending on the transverse offset of the excitation beam. For suitably small offsets the dominant components of the transverse wakefield are dipole modes, with a linear dependence on the transverse offset of the excitation bunch. This fact enables the transverse beam position inside the cavity to be determined by measuring the dipole modes extracted from the couplers, similar to a cavity beam position monitor (BPM), but requires no additional vacuum instrumentation.At the FLASH facility in DESY, 1.3 GHz (known as TESLA) and 3.9 GHz (third harmonic) cavities are installed. Wakefields in 3.9 GHz cavities are significantly larger than in the 1.3 GHz cavities. It is therefore important to mitigate the adverse effects of HOMs to the beam by aligning the beam on the electric axis of the cavities. This alignment requires an accurate beam position diagnostics inside the 3.9 GHz cavities. It is this aspect that is focused on in this thesis. Although the principle of beam diagnostics with HOM has been demonstrated on 1.3 GHz cavities, the realization in 3.9 GHz cavities is considerably more challenging. This is due to the dense HOM spectrum and the relatively strong coupling of most HOMs amongst the four cavities in the third harmonic cryo-module. A comprehensive series of simulations and HOM spectra measurements have been performed in order to study the modal band structure of the 3.9 GHz cavities. The dependencies of various dipole modes on the offset of the excitation beam were subsequently studied using a spectrum analyzer. Various data analysis methods were used: modal identification, direct linear regression, singular value decomposition and k-means clustering. These studies lead to three modal options promising for beam position diagnostics, upon which a set of test electronics has been built. The experiments with these electronics suggest a resolution of 50 micron accuracy in predicting local beam position in the cavity and a global resolution of 20 micron over the complete module. This constitutes the first demonstration of HOM-based beam diagnostics in a third harmonic 3.9 GHz superconducting cavity module. These studies have finalized the design of the online HOM-BPM for 3.9 GHz cavities at FLASH.
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Alon, Yair. "Analysis of thick composite plates using higher order three dimensional finite elements." Thesis, Monterey, California : Naval Postgraduate School, 1990. http://handle.dtic.mil/100.2/ADA243188.
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Thesis (M.S. in Aeronautical Engineering and Aeronautics and Astronautics Engineers Degree)--Naval Postgraduate School, December 1990.Thesis Advisor(s): Kolar, Ramesh. Second Reader: Lindsey, G. H. "December 1990." Description based on title screen as viewed on March 30, 2010. DTIC Descriptor(s): Thickness, stability, composite materials, laminates, theory, elastic properties, orientation(direction), composite structures, three dimensional, solutions(general), integration, plates, anisotropy, isotropism, convergence, thinness, behavior, nonlinear analysis, static tests, formulas(mathematics), lagrangian functions, fibers DTIC Identifier(s): Laminates, plates, structural response, composite structures, finite element analysis, nonlinear analysis, stress strain relations, theses, displacement, buckling, interpolation. Author(s) subject terms: Finite element, nonlinear analysis, plate bending thick plates, laminated composites, buckling, constant arc length three dimensional element Includes bibliographical references (p. 87-88). Also available in print.
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Namarathne, Dinithi L. "Measuring intensity dependent optical nonlineartities without sample damage using higher order vortex beams." Thesis, Queensland University of Technology, 2019. https://eprints.qut.edu.au/129569/9/Dinithi_Namarathne_Thesis.pdf.
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This study developed a beam shaping based method to avoid nonlinear sample damage in high intense pulse laser applications. This is achieved by developing a complete theoretical and experimental framework for Z-scan experiments to utilise higher order vortex beams instead of common Gaussian beam. An image processing based extension was introduced to Z-scan experiments, which can be utilised to achieve results of different Z-scan modes from a single experimental dataset efficiently. The results of this study will have a positive impact on utilising different beam profiles to achieve profile specific advantages in nonlinear applications.
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Dubcová, Lenka. "Novel self-adaptive higher-order finite elements methods for Maxwell's equations of electromagnetics." To access this resource online via ProQuest Dissertations and Theses @ UTEP, 2008. http://0-proquest.umi.com.lib.utep.edu/login?COPT=REJTPTU0YmImSU5UPTAmVkVSPTI=&clientId=2515.
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Pipilis, Konstantinos Georgiou. "Higher order moving finite element methods for systems described by partial differential-algebraic equations." Thesis, Imperial College London, 1990. http://hdl.handle.net/10044/1/7510.
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Lamichhane, Bishnu P. "Higher order mortar finite elements with dual Lagrange multiplier spaces and applications." [S.l. : s.n.], 2006. http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-26215.
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Quattrochi, Douglas J. (Douglas John). "Hypersonic heat transfer and anisotropic visualization with a higher order discontinuous Galerkin finite element method." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/35567.
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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2006.Includes bibliographical references (leaves 83-89).
Higher order discretizations of the Navier-Stokes equations promise greater accuracy than conventional computational aerodynamics methods. In particular, the discontinuous Galerkin (DG) finite element method has O(hP+l) design accuracy and allows for subcell resolution of shocks. This work furthers the DG finite element method in two ways. First, it demonstrates the results of DG when used to predict heat transfer to a cylinder in a hypersonic flow. The strong shock is captured with a Laplacian artificial viscosity term. On average, the results are in agreement with an existing hypersonic benchmark. Second, this work improves the visualization of the higher order polynomial solutions generated by DG with an adaptive display algorithm. The new algorithm results in more efficient displays of higher order solutions, including the hypersonic flow solutions generated here.
by Douglas J. Quattrochi.
S.M.
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Marais, Neilen. "Higher order hierarchal curvilinear triangular vector elements for the finite element method in computational electromagnetics." Thesis, Stellenbosch : Stellenbosch University, 2003. http://hdl.handle.net/10019.1/53447.
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Thesis (MScEng)--Stellenbosch University, 2003.ENGLISH ABSTRACT: The Finite Element Method (FEM) as applied to Computational Electromagnetics (CEM), can be used to solve a large class of Electromagnetics problems with high accuracy, and good computational efficiency. Computational efficiency can be improved by using element basis functions of higher order. If, however, the chosen element type is not able to accurately discretise the computational domain, the converse might be true. This paper investigates the application of elements with curved sides, and higher order basis functions, to computational domains with curved boundaries. It is shown that these elements greatly improve the computational efficiency of the FEM applied to such domains, as compared to using elements with straight sides, and/or low order bases.
AFRIKAANSE OPSOMMING: Die Eindige Element Metode (EEM) kan breedvoerig op Numeriese Elektromagnetika toegepas word, met uitstekende akkuraatheid en 'n hoë doeltreffendheids vlak. Numeriese doeltreffendheid kan verbeter word deur van hoër orde element basisfunksies gebruik te maak. Indien die element egter nie die numeriese domein effektief kan diskretiseer nie, mag die omgekeerde geld. Hierdie tesis ondersoek die toepassing van elemente met geboë sye, en hoër orde basisfunksies, op numeriese domeine met geboë grense. Daar word getoon dat sulke elemente 'n noemenswaardinge verbetering in die numeriese doeltreffendheid van die EEM meebring, vergeleke met reguit- en/of laer-orde elemente.
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Fortin, Jose Donato. "Consequences of the application of a higher order beam theory to the steady-state deformation and free vibrations of a moving beam /." The Ohio State University, 1988. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487586889189672.
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Gersbacher, Christoph [Verfasser], and Dietmar [Akademischer Betreuer] Kröner. "Higher-order discontinuous finite element methods and dynamic model adaptation for hyperbolic systems of conservation laws." Freiburg : Universität, 2017. http://d-nb.info/1136263853/34.
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Ayed, Alshammari Marji. "DESIGN OF HIGHER-ORDER ALL OPTICAL BINARY DELTA-SIGMA MODULATOR USING RING LASER." OpenSIUC, 2018. https://opensiuc.lib.siu.edu/dissertations/1619.
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The aim of this research is to investigate the performance of a bi-stable device using a single active element and to design a higher order all optical binary delta-sigma modulator (BΔΣM). A Delta sigma modulator has two important components that require enhancement to achieve robust modulation. The first component is the integrator which accumulates the error and at the same time leaks it. Here, the integrator is a single ring laser consisting of a semiconductor optical amplifier (SOA) and a filter to allow the light frequency of interest into the ring. The other component is the bi-stable device (called Schmitt trigger) that switches either ON (1) or OFF (0). There are different novel approaches to developing a bi-stable circuit. First, the coupled two ring lasers where each ring suppresses each other. Second, a novel idea that considered as a bi-stable device with single active element to achieve reduced power and reduce cost. This type of circuit is merged ring lasers with using single SOA. This system is modeled and its bistability hysteretic characteristics is investigated. The first bi-stable device is used to construct an all optical BΔΣM with 1st, 2nd and 3rd -order approaches. It performs better when the SOA bulk device is replaced by multi-quantum well (MQW) SOA.
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Aghabarati, Ali. "Multilevel and algebraic multigrid methods for the higher order finite element analysis of time harmonic Maxwell's equations." Thesis, McGill University, 2014. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=121485.
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The Finite Element Method (FEM) applied to wave scattering and quasi-static vector field problems in the frequency domain leads to sparse, complex-symmetric, linear systems of equations. For large problems with complicated geometries, most of the computer time and memory used by FEM goes to solving the matrix equation. Krylov subspace methods are widely used iterative methods for solving large sparse systems. They depend heavily on preconditioning to accelerate convergence. However, application of conventional preconditioners to the "curl-curl" operator which arises in vector electromagnetics does not result in a satisfactory performance and specialized preconditioning techniques are required. This thesis presents effective Multilevel and Algebraic Multigrid (AMG) preconditioning techniques for p-adaptive FEM analysis. In p-adaption, finite elements of different polynomial orders are present in the mesh and the system matrix can be structured into blocks corresponding to the orders of the basis functions. The new preconditioners are based on a p-type multilevel Schwarz (pMUS) approximate inversion of the block structured system. A V-cycle multilevel correction starts by applying Gauss-Seidel to the highest block level, then the next level down, and so on. On the other side of the V, Gauss-Seidel iterations are applied in the reverse order. At the bottom of the cycle is the lowest order system, which is usually solved exactly with a direct solver. The proposed alternative is to use Auxiliary Space Preconditioning (ASP) at the lowest level and continue the V-cycle downwards, first into a set of auxiliary, node-based spaces, then through a series of progressively smaller matrices generated by an Algebraic Multigrid (AMG). The algebraic coarsening approach is especially useful for problems with fine geometric details, requiring a very large mesh in which the bulk of the elements remain at low order. In addition, for wave problems, a "shifted Laplace" technique is applied, in which part of the ASP/AMG algorithm uses a perturbed, complex frequency. A significant convergence acceleration is achieved. The performance of Krylov algorithms is further enhanced during p-adaption by incorporation of a deflation technique. This projects out from the preconditioned system the eigenvectors corresponding to the smallest eigenvalues. The construction of the deflation subspace is based on efficient estimation of the eigenvectors from information obtained when solving the first problem in a p-adaptive sequence. Extensive numerical experiments have been performed and results are presented for both wave and quasi-static problems. The test cases considered are complicated to solve and the numerical results show the robustness and efficiency of the new preconditioners. Deflated Krylov methods preconditioned with the current Multilevel/ASP/AMG approach are always considerably faster than the reference methods and speedups of up to 10 are achieved for some test problems.La méthode des éléments finis (FEM) appliquée à la dispersion des ondes et aux problèmes de champ de vecteurs quasi-statique dans le domaine fréquentiel mène à des systèmes d'équations linéaires rares, symétriques-complexes. Pour de grands problèmes ayant des géométries complexes, la plupart du temps et de la mémoire d'ordinateur utilisé par FEM va à la résolution de l'équation de la matrice. Les méthodes itératives de Krylov sont celles largement utilisées dans la résolution de grands systèmes creux. Elles dépendent fortement des préconditionnement qui accélèrent la convergence. Toutefois, l'application de préconditionnements conventionnels à l'opérateur "rot-rot" qui surgit en électromagnétisme vectoriel n'aboutit pas à des résultats satisfaisants et des techniques de préconditionnement spécialisés sont exigées.Cette thèse présente des techniques de préconditionnement efficaces multiniveau et multigrilles algébrique (AMG) pour l'analyse p-adaptative FEM. Dans la p-adaptation, des éléments finis de différents ordres polynomiaux sont présents dans le maillage et la matrice du système peut être structurée en blocs correspondant aux ordres des fonctions de base. Les nouveaux préconditionneurs sont basés sur un type d'inversion approximative à multiniveau p Schwarz (pMUS) du système structuré de bloc. Une correction à niveaux multiples en cycle V débute par l'application de Gauss-Seidel au niveau du bloc le plus élevé, suivi par le niveau inférieur, et ainsi de suite. De l'autre côté du V, des itérations de Gauss-Seidel sont appliquées en ordre inverse. Au bas du cycle se trouve le système d'ordre le plus bas, qui est habituellement résolu exactement avec un solveur direct. L'alternative proposée est d'utiliser l'espace auxiliaire de préconditionnement (ASP) au niveau le plus bas et de poursuivre le cycle en V vers le bas, d'abord en un ensemble d'auxiliaires, basé sur les espacements de nœuds, à travers une série de plus en plus petites de matrices générées par un multigrille algébrique (AMG). L'approche de grossissement algébrique est particulièrement utile aux problèmes ayant de fins détails géométriques, nécessitant une très grande maille dans laquelle la majeure partie des éléments restent à un niveau plus bas.En outre, pour des problèmes d'onde, la technique "décalé Laplace" est appliquée, dans laquelle une partie de l'algorithme ASP/AMG utilise une fréquence complexe perturbée. Une accélération de la convergence significative est atteinte. La performance des algorithmes de Krylov est davantage renforcée au cours du p-adaptation par l'incorporation d'une technique de déflation. Cette saillie fait dépasser hors du système préconditionné, les vecteurs propres correspondants aux plus petites valeurs propres. La construction du sous-espace de déflation est basée sur une estimation efficace des vecteurs propres à partir d'informations obtenues lors de la résolution du premier problème dans une séquence p-adaptatif. Des expériences numériques approfondies ont été effectuées et les résultats sont présentés à la fois aux problèmes d'onde et quasi-statiques. Les cas de test sont considérés comme compliqués à résoudre et les résultats numériques montrent la robustesse et l'efficacité des nouveaux préconditionnements. Les méthodes de Krylov de déflation préconditionnés par l'approche multiniveaux/ASP/AMG actuelle sont toujours considérablement plus rapides que les méthodes de référence et des accélérations allant jusqu'à 10 sont atteintes pour certains problèmes de test.
27
Barter, Garrett E. (Garrett Ehud) 1979. "Shock capturing with PDE-based artificial viscosity for an adaptive, higher-order discontinuous Galerkin finite element method." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/44931.
Full textAbstract:
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2008.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Includes bibliographical references (p. 135-143).
The accurate simulation of supersonic and hypersonic flows is well suited to higher-order (p > 1), adaptive computational fluid dynamics (CFD). Since these cases involve flow velocities greater than the speed of sound, an appropriate shock capturing for higher-order, adaptive methods is necessary. Artificial viscosity can be combined with a higher-order discontinuous Galerkin finite element discretization to resolve a shock layer within a single cell. However, when a nonsmooth artificial viscosity model is employed with an otherwise higher-order approximation, element-to-element variations induce oscillations in state gradients and pollute the downstream flow. To alleviate these difficulties, this work proposes a new, higher-order, state based artificial viscosity with an associated governing partial differential equation (PDE). In the governing PDE, the shock sensor acts as a forcing term, driving the artificial viscosity to a non-zero value where it is necessary. The decay rate of the higher-order solution modes and edge-based jumps are both shown to be reliable shock indicators. This new approach leads to a smooth, higher-order representation of the artificial viscosity that evolves in time with the solution. For applications involving the Navier-Stokes equations, an artificial dissipation operator that preserves total enthalpy is introduced. The combination of higher-order, PDE-based artificial viscosity and enthalpy-preserving dissipation operator is shown to overcome the disadvantages of the non-smooth artificial viscosity. The PDE-based artificial viscosity can be used in conjunction with an automated grid adaptation framework that minimizes the error of an output functional. Higher-order solutions are shown to reach strict engineering tolerances with fewer degrees of freedom.
(cont.) The benefit in computational efficiency for higher-order solutions is less dramatic in the vicinity of the shock where errors scale with O(h/p). This includes the near-field pressure signals necessary for sonic boom prediction. When applied to heat transfer prediction on unstructured meshes in hypersonic flows, the PDE-based artificial viscosity is less susceptible to errors introduced by poor shock-grid alignment. Surface heating can also drive the output-based grid adaptation framework to arrive at the same heat transfer distribution as a well-designed structured mesh.
by Garrett Ehud Barter.
Ph.D.
28
Stöcker, Christina. "Level set methods for higher order evolution laws." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2008. http://nbn-resolving.de/urn:nbn:de:bsz:14-ds-1205350171405-81971.
Full textAbstract:
A numerical treatment of non-linear higher-order geometric evolution equations with the level set and the finite element method is presented. The isotropic, weak anisotropic and strong anisotropic situation is discussed. Most of the equations considered in this work arise from the field of thin film growth. A short introduction to the subject is given. Four different models are discussed: mean curvature flow, surface diffusion, a kinetic model, which combines the effects of mean curvature flow and surface diffusion and includes a further kinetic component, and an adatom model, which incorporates in addition free adatoms. As an introduction to the numerical schemes, first the isotropic and weak anisotropic situation is considered. Then strong anisotropies (non-convex anisotropies) are used to simulate the phenomena of faceting and coarsening. The experimentally observed effect of corner and edge roundings is reached in the simulation through the regularization of the strong anisotropy with a higher-order curvature term. The curvature regularization leads to an increase by two in the order of the equations, which results in highly non-linear equations of up to 6th order. For the numerical solution, the equations are transformed into systems of second order equations, which are solved with a Schur complement approach. The adatom model constitutes a diffusion equation on a moving surface. An operator splitting approach is used for the numerical solution. In difference to other works, which restrict to the isotropic situation, also the anisotropic situation is discussed and solved numerically. Furthermore, a treatment of geometric evolution equations on implicitly given curved surfaces with the level set method is given. In particular, the numerical solution of surface diffusion on curved surfaces is presented. The equations are discretized in space by standard linear finite elements. For the time discretization a semi-implicit discretization scheme is employed. The derivation of the numerical schemes is presented in detail, and numerous computational results are given for the 2D and 3D situation. To keep computational costs low, the finite element grid is adaptively refined near the moving curves and surfaces resp. A redistancing algorithm based on a local Hopf-Lax formula is used. The algorithm has been extended by the authors to the 3D case. A detailed description of the algorithm in 3D is presented in this workIn der Arbeit geht es um die numerische Behandlung nicht-linearer geometrischer Evolutionsgleichungen höherer Ordnung mit Levelset- und Finite-Elemente-Verfahren. Der isotrope, schwach anisotrope und stark anisotrope Fall wird diskutiert. Die meisten in dieser Arbeit betrachteten Gleichungen entstammen dem Gebiet des Dünnschicht-Wachstums. Eine kurze Einführung in dieses Gebiet wird gegeben. Es werden vier verschiedene Modelle diskutiert: mittlerer Krümmungsfluss, Oberflächendiffusion, ein kinetisches Modell, welches die Effekte des mittleren Krümmungsflusses und der Oberflächendiffusion kombiniert und zusätzlich eine kinetische Komponente beinhaltet, und ein Adatom-Modell, welches außerdem freie Adatome berücksichtigt. Als Einführung in die numerischen Schemata, wird zuerst der isotrope und schwach anisotrope Fall betrachtet. Anschließend werden starke Anisotropien (nicht-konvexe Anisotropien) benutzt, um Facettierungs- und Vergröberungsphänomene zu simulieren. Der in Experimenten beobachtete Effekt der Ecken- und Kanten-Abrundung wird in der Simulation durch die Regularisierung der starken Anisotropie durch einen Krümmungsterm höherer Ordnung erreicht. Die Krümmungsregularisierung führt zu einer Erhöhung der Ordnung der Gleichung um zwei, was hochgradig nicht-lineare Gleichungen von bis zu sechster Ordnung ergibt. Für die numerische Lösung werden die Gleichungen auf Systeme zweiter Ordnungsgleichungen transformiert, welche mit einem Schurkomplement-Ansatz gelöst werden. Das Adatom-Modell bildet eine Diffusionsgleichung auf einer bewegten Fläche. Zur numerischen Lösung wird ein Operatorsplitting-Ansatz verwendet. Im Unterschied zu anderen Arbeiten, die sich auf den isotropen Fall beschränken, wird auch der anisotrope Fall diskutiert und numerisch gelöst. Außerdem werden geometrische Evolutionsgleichungen auf implizit gegebenen gekrümmten Flächen mit Levelset-Verfahren behandelt. Insbesondere wird die numerische Lösung von Oberflächendiffusion auf gekrümmten Flächen dargestellt. Die Gleichungen werden im Ort mit linearen Standard-Finiten-Elementen diskretisiert. Als Zeitdiskretisierung wird ein semi-implizites Diskretisierungsschema verwendet. Die Herleitung der numerischen Schemata wird detailliert dargestellt, und zahlreiche numerische Ergebnisse für den 2D und 3D Fall sind gegeben. Um den Rechenaufwand gering zu halten, wird das Finite-Elemente-Gitter adaptiv an den bewegten Kurven bzw. den bewegten Flächen verfeinert. Es wird ein Redistancing-Algorithmus basierend auf einer lokalen Hopf-Lax Formel benutzt. Der Algorithmus wurde von den Autoren auf den 3D Fall erweitert. In dieser Arbeit wird der Algorithmus für den 3D Fall detailliert beschrieben
29
Stöcker, Christina. "Level set methods for higher order evolution laws." Doctoral thesis, Forschungszentrum caesar, 2007. https://tud.qucosa.de/id/qucosa%3A24054.
Full textAbstract:
A numerical treatment of non-linear higher-order geometric evolution equations with the level set and the finite element method is presented. The isotropic, weak anisotropic and strong anisotropic situation is discussed. Most of the equations considered in this work arise from the field of thin film growth. A short introduction to the subject is given. Four different models are discussed: mean curvature flow, surface diffusion, a kinetic model, which combines the effects of mean curvature flow and surface diffusion and includes a further kinetic component, and an adatom model, which incorporates in addition free adatoms. As an introduction to the numerical schemes, first the isotropic and weak anisotropic situation is considered. Then strong anisotropies (non-convex anisotropies) are used to simulate the phenomena of faceting and coarsening. The experimentally observed effect of corner and edge roundings is reached in the simulation through the regularization of the strong anisotropy with a higher-order curvature term. The curvature regularization leads to an increase by two in the order of the equations, which results in highly non-linear equations of up to 6th order. For the numerical solution, the equations are transformed into systems of second order equations, which are solved with a Schur complement approach. The adatom model constitutes a diffusion equation on a moving surface. An operator splitting approach is used for the numerical solution. In difference to other works, which restrict to the isotropic situation, also the anisotropic situation is discussed and solved numerically. Furthermore, a treatment of geometric evolution equations on implicitly given curved surfaces with the level set method is given. In particular, the numerical solution of surface diffusion on curved surfaces is presented. The equations are discretized in space by standard linear finite elements. For the time discretization a semi-implicit discretization scheme is employed. The derivation of the numerical schemes is presented in detail, and numerous computational results are given for the 2D and 3D situation. To keep computational costs low, the finite element grid is adaptively refined near the moving curves and surfaces resp. A redistancing algorithm based on a local Hopf-Lax formula is used. The algorithm has been extended by the authors to the 3D case. A detailed description of the algorithm in 3D is presented in this work.In der Arbeit geht es um die numerische Behandlung nicht-linearer geometrischer Evolutionsgleichungen höherer Ordnung mit Levelset- und Finite-Elemente-Verfahren. Der isotrope, schwach anisotrope und stark anisotrope Fall wird diskutiert. Die meisten in dieser Arbeit betrachteten Gleichungen entstammen dem Gebiet des Dünnschicht-Wachstums. Eine kurze Einführung in dieses Gebiet wird gegeben. Es werden vier verschiedene Modelle diskutiert: mittlerer Krümmungsfluss, Oberflächendiffusion, ein kinetisches Modell, welches die Effekte des mittleren Krümmungsflusses und der Oberflächendiffusion kombiniert und zusätzlich eine kinetische Komponente beinhaltet, und ein Adatom-Modell, welches außerdem freie Adatome berücksichtigt. Als Einführung in die numerischen Schemata, wird zuerst der isotrope und schwach anisotrope Fall betrachtet. Anschließend werden starke Anisotropien (nicht-konvexe Anisotropien) benutzt, um Facettierungs- und Vergröberungsphänomene zu simulieren. Der in Experimenten beobachtete Effekt der Ecken- und Kanten-Abrundung wird in der Simulation durch die Regularisierung der starken Anisotropie durch einen Krümmungsterm höherer Ordnung erreicht. Die Krümmungsregularisierung führt zu einer Erhöhung der Ordnung der Gleichung um zwei, was hochgradig nicht-lineare Gleichungen von bis zu sechster Ordnung ergibt. Für die numerische Lösung werden die Gleichungen auf Systeme zweiter Ordnungsgleichungen transformiert, welche mit einem Schurkomplement-Ansatz gelöst werden. Das Adatom-Modell bildet eine Diffusionsgleichung auf einer bewegten Fläche. Zur numerischen Lösung wird ein Operatorsplitting-Ansatz verwendet. Im Unterschied zu anderen Arbeiten, die sich auf den isotropen Fall beschränken, wird auch der anisotrope Fall diskutiert und numerisch gelöst. Außerdem werden geometrische Evolutionsgleichungen auf implizit gegebenen gekrümmten Flächen mit Levelset-Verfahren behandelt. Insbesondere wird die numerische Lösung von Oberflächendiffusion auf gekrümmten Flächen dargestellt. Die Gleichungen werden im Ort mit linearen Standard-Finiten-Elementen diskretisiert. Als Zeitdiskretisierung wird ein semi-implizites Diskretisierungsschema verwendet. Die Herleitung der numerischen Schemata wird detailliert dargestellt, und zahlreiche numerische Ergebnisse für den 2D und 3D Fall sind gegeben. Um den Rechenaufwand gering zu halten, wird das Finite-Elemente-Gitter adaptiv an den bewegten Kurven bzw. den bewegten Flächen verfeinert. Es wird ein Redistancing-Algorithmus basierend auf einer lokalen Hopf-Lax Formel benutzt. Der Algorithmus wurde von den Autoren auf den 3D Fall erweitert. In dieser Arbeit wird der Algorithmus für den 3D Fall detailliert beschrieben.
30
Lu, Yunkai. "Random Vibration Analysis of Higher-Order Nonlinear Beams and Composite Plates with Applications of ARMA Models." Diss., Virginia Tech, 2008. http://hdl.handle.net/10919/29128.
Full textAbstract:
In this work, the random vibration of higher-order nonlinear beams and composite plates subjected to stochastic loading is studied. The fourth-order nonlinear beam equation is examined to study the effect of rotary inertia and shear deformation on the root mean square values of displacement response. A new linearly coupled equivalent linearization method is proposed and compared with the widely used traditional equivalent linearization method. The new method is proven to yield closer predictions to the numerical simulation results of the nonlinear beam vibration. A systematical investigation of the nonlinear random vibration of composite plates is conducted in which effects of nonlinearity, choices of different plate theories (the first order shear deformation plate theory and the classical plate theory), and temperature gradient on the plate statistical transverse response are addressed. Attention is paid to calculate the R.M.S. values of stress components since they directly affect the fatigue life of the structure. A statistical data reconstruction technique named ARMA modeling and its applications in random vibration data analysis are discussed. The model is applied to the simulation data of nonlinear beams. It is shown that good estimations of both the nonlinear frequencies and the power spectral densities are given by the technique.Ph. D.
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VARELLO, ALBERTO. "Advanced higher-order one-dimensional models for fluid-structure interaction analysis." Doctoral thesis, Politecnico di Torino, 2013. http://hdl.handle.net/11583/2517517.
Full textAbstract:
The aim of this work is the development of a refined reduced order model suitable for numerical applications in solid and fluid mechanics with a remarkable reduction in computational cost. Nowadays, numerical reduced order models are widely exploited in many areas, such as aerospace, mechanical and biomechanical engineering for structural analysis, fluid dynamic analysis and coupled (aeroelastic) fluid-structure interaction analysis.
One-dimensional (1D) structural models, commonly known as beams, are for instance used in many applications to analyze the structural behavior of slender bodies, such as columns, arches, blades, aircraft wings, bridges, skyscrapers, rotor and wind turbine blades. One-dimensional structural elements are simpler and computationally more efficient than 2D (plate/shell) and 3D (solid) elements. This feature makes beam theories still very attractive for the static, dynamic response, free vibration and aeroelastic analyses, despite the approximations which they introduce in the simulation.
Recently, 1D models are intensively exploited for the simulation of the human cardiovascular system under either physiological or pathological conditions. As it is easily comprehensible, fluid flows in pipes, channel, capillaries or even arteries are particularly suitable for the application of one-dimensional models also to fluid dynamics. Typically, one-dimensional models for fluid dynamics and fluid-structure interaction (FSI) problems are again remarkably more efficient than three-dimensional methods in terms of computational cost.
A key point for reduced order models is the capability in simulating in an accurate way the investigated physical problem. For instance, in last decades the growing use of advanced composite and sandwich materials in thin-walled beam-like structures has revealed that 1D theories have to be refined in order to predict the behavior of such complex structures with high fidelity. For this purpose, a higher-order one-dimensional method is introduced in this work and its capabilities are highlighted and discussed. The present work is subdivided into three fundamental parts corresponding to the physical fields the proposed refined model is applied to.
Firstly, a structural part presents the formulation of a displacement-based higher-order one-dimensional model for the analysis of beam-like structures. Classical beam theories (Euler-Bernoulli and Timoshenko) have intrinsic limitations which preclude their applications for the analysis of a wide class of engineering problems. The Carrera Unified Formulation (CUF) is employed to introduce a hierarchical modeling with a variable order of expansion for the displacement unknowns over the beam cross-section. The finite element method (FEM) is used to handle arbitrary geometries and loading conditions. The influence of higher-order effects over the cross-section deformation, not detectable by classical and low-order beam theories, on the static, free vibration and time-dependent response of several structures with arbitrary cross-section geometries and made of arbitrary materials is remarked through the numerical results presented.
Secondly, an aeroelastic part describes the extension of the refined structural model to the static aeroelastic analysis of lifting surfaces made of metallic and composite materials. A coupled aeroelastic computational model based on the Vortex Lattice aerodynamic Method and the finite element method (FEM) is formulated. A refined aeroelastic approach is also presented by replacing the Vortex Lattice aerodynamic Method with the more powerful 3D Panel Method. Comparison with results obtained by existing plate/shell aeroelastic models shows that the present 1D model could result less expensive from the computational point of view with respect to shell cases with same accuracy. The effect of the cross-section deformation on the aeroelastic static response and on the critical wing divergence velocity is evaluated for different wing configurations. The beneficial effects of aeroelastic tailoring in the case of wings made of composite anisotropic materials are also confirmed by using the present model.
Finally, a third part concerning the use of the refined one-dimensional CUF model for fluid dynamic problems is presented. The basic partial differential equations (PDEs) of fluid mechanics (Navier-Stokes and Stokes equations) are faced and 1D refined models with variable velocity-pressure accuracy are presented on the basis of the one-dimensional Carrera Unified Formulation and the finite element method. The application of these higher-order models to describe the three-dimensional fluid flow evolution on a computational domain is formulated for the Stokes problem. The present approach reveals its capabilities in predicting accurately, with a reduced computational cost with respect to more consuming two-dimensional or three-dimensional methods, nonclassical and complex fluid flows. Moreover, the numerical results show the promising potentiality of such an approach to the future extension of fluid-structure CUF-CUF models, i.e. the coupling of CUF models used for both structural and fluid dynamic analyses.
32
Simon, Kristin [Verfasser]. "Higher order stabilized surface finite element methods for diffusion-convection-reaction equations on surfaces with and without boundary / Kristin Simon." Magdeburg : Universitätsbibliothek, 2017. http://d-nb.info/1147834520/34.
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33
Yi, Fan, and n/a. "Optimal Algorithmic Techniques of LASIK Procedures." Griffith University. School of Engineering, 2006. http://www4.gu.edu.au:8080/adt-root/public/adt-QGU20070216.152339.
Full textAbstract:
Clinical wavefront-guided corneal ablation has been now the most technologically advanced method to reduce the dependence of glasses and contact lenses. It has the potential not only to eliminate spherocylindrical errors but also to reduce higher-order aberrations (HOA). Recent statistics show that more than 96% of the patients who received laser in situ keratomileusis (LASIK) treatment reported their satisfaction about the improvement on vision, six months after the surgery. However, there are still patients complaining that their vision performance did not achieve the expectation or was even worse than before surgery. The reasons causing the unexpected post-surgical outcome include undercorrection, overcorrection, induced HOA, and other postoperative diseases, most of which are caused by inaccurate ablation besides other pathological factors. Therefore, to find out the method to optimize the LASIK procedures and provide a higher surgical precision has become increasingly important. A proper method to calculate ablation profile and an effective way to control the laser beam size and shape are key aspects in this research to resolve the problem. Here in this Master of Philosophy degree thesis, the author has performed a meticulous study on the existing methods of ablation profile calculation and investigated the efficiency of wavefront only ablation by a computer simulation applying real patient data. Finally, the concept of a refractive surgery system with dynamical beam shaping function is sketched, which can theoretically overcome the disadvantages of traditional procedures with a finite laser beam size.
34
Yi, Fan. "Optimal Algorithmic Techniques of LASIK Procedures." Thesis, Griffith University, 2006. http://hdl.handle.net/10072/368097.
Full textAbstract:
Clinical wavefront-guided corneal ablation has been now the most technologically advanced method to reduce the dependence of glasses and contact lenses. It has the potential not only to eliminate spherocylindrical errors but also to reduce higher-order aberrations (HOA). Recent statistics show that more than 96% of the patients who received laser in situ keratomileusis (LASIK) treatment reported their satisfaction about the improvement on vision, six months after the surgery. However, there are still patients complaining that their vision performance did not achieve the expectation or was even worse than before surgery. The reasons causing the unexpected post-surgical outcome include undercorrection, overcorrection, induced HOA, and other postoperative diseases, most of which are caused by inaccurate ablation besides other pathological factors. Therefore, to find out the method to optimize the LASIK procedures and provide a higher surgical precision has become increasingly important. A proper method to calculate ablation profile and an effective way to control the laser beam size and shape are key aspects in this research to resolve the problem. Here in this Master of Philosophy degree thesis, the author has performed a meticulous study on the existing methods of ablation profile calculation and investigated the efficiency of wavefront only ablation by a computer simulation applying real patient data. Finally, the concept of a refractive surgery system with dynamical beam shaping function is sketched, which can theoretically overcome the disadvantages of traditional procedures with a finite laser beam size.Thesis (Masters)
Master of Philosophy (MPhil)
School of Engineering
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Liebenstein, Stefan [Verfasser], Paul [Akademischer Betreuer] Steinmann, and Michael [Gutachter] Zaiser. "From Beam to Higher-Order Continuum Modelling of the Mechanical Properties of Cellular Solids / Stefan Liebenstein ; Gutachter: Michael Zaiser ; Betreuer: Paul Steinmann." Erlangen : Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 2018. http://d-nb.info/1172503338/34.
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36
Barrera, Cruz Jorge Luis. "A Hierarchical Interface-enriched Finite Element Method for the Simulation of Problems with Complex Morphologies." The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1430838711.
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Wang, Yaqi. "hp-mesh adaptation for 1-D multigroup neutron diffusion problems." Texas A&M University, 2006. http://hdl.handle.net/1969.1/4707.
Full textAbstract:
In this work, we propose, implement and test two fully automated mesh adaptation methods
for 1-D multigroup eigenproblems. The first method is the standard hp-adaptive refinement
strategy and the second technique is a goal-oriented hp-adaptive refinement strategy. The
hp-strategies deliver optimal guaranteed solutions obtained with exponential convergence rates
with respect to the number of unknowns. The goal-oriented method combines the standard
hp-adaptation technique with a goal-oriented adaptivity based on the simultaneous solution of an
adjoint problem in order to compute quantities of interest, such as reaction rates in a sub-domain
or point-wise fluxes or currents. These algorithms are tested for various multigroup 1-D
diffusion problems and the numerical results confirm the optimal, exponential convergence rates
predicted theoretically.
38
Bangemann, Tim Richard. "Nonlinear finite element treatment of bifurcation in the post-buckling analysis of thin elastic plates and shells." Thesis, Brunel University, 1995. http://bura.brunel.ac.uk/handle/2438/6362.
Full textAbstract:
The geometrically nonlinear constant moment triangle based on the von Karman theory of thin plates is first described. This finite element, which is believed to be the simplest possible element to pass the totality of the von Karman patch test, is employed throughout the present work. It possesses the special characteristic of providing a tangent stiffness matrix which is accurate and without approximation. The stability of equilibrium of discrete conservative systems is discussed. The criteria which identify the critical points (limit and bifurcation), and the method of determination of the stability coefficients are presented in a simple matrix formulation which is suitable for computation. An alternative formulation which makes direct use of higher order directional derivatives of the total potential energy is also presented. Continuation along the stable equilibrium solution path is achieved by using a recently developed Newton method specially modified so that stable points are points of attraction. In conjunction with this solution technique, a branch switching method is introduced which directly computes any intersecting branches. Bifurcational buckling often exhibits huge structural changes and it is believed that the computation of the required switch procedure is performed here, and for the first time, in a satisfactory manner. Hence, both limit and bifurcation points can be treated without difficulty and with continuation into the post buckling regime. In this way, the ability to compute the stable equilibrium path throughout the load-deformation history is accomplished. Two numerical examples which exhibit bifurcational buckling are treated in detail and provide numerical evidence as to the ability of the employed techniques to handle even the most complex problems. Although only relatively coarse finite element meshes are used it is evident that the technique provides a powerful tool for any kind of thin elastic plate and shell problem. The thesis concludes with a proposal for an algorithm to automate the computation of the unknown parameter in the branch switching method.
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Martini, Till. "The Matrix Element Method at next-to-leading order QCD using the example of single top-quark production at the LHC." Doctoral thesis, Humboldt-Universität zu Berlin, 2018. http://dx.doi.org/10.18452/19288.
Full textAbstract:
Hochenergiephysikanalysen zielen darauf ab, das Standardmodell—die gemeinhin akzeptierte Theorie—zu testen. Für überzeugende Schlüsse, sind Analysemethoden nötig, welche einen eindeutigen Vergleich zwischen Daten und Theorie ermöglichen und zuverlässige Abschätzung der Unsicherheiten erlauben.
Die Matrixelement-Methode (MEM) ist eine Maximum-Likelihood-Methode, welche speziell auf Signalsuche und Parameterschätzung an Beschleunigern zugeschnitten ist. Die MEM hat sich durch optimale Nutzung vorhandener Information und sauberer statistischer Interpretation der Ergebnisse als vorteilhaft erwiesen.
Sie hat jedoch einen großen Nachteil: In der Originalformulierung ist die Berechnung der Likelihood intrinsisch auf die erste störungstheoretische Ordnung in der Kopplung limitiert. Höhere Ordnungskorrekturen verbessern die Genauigkeit theoretischer Vorhersagen und erlauben eindeutige feldtheoretische Interpretation der gewonnen Informationen.
In dieser Arbeit wird erstmalig die MEM unter Einbezug der Korrekturen der nächstführenden Ordnung (NLO) der QCD-Kopplung durch Definition von Ereignisgewichten für die Berechnung der Likelihood präsentiert. Diese Gewichte ermöglichen auch die Erzeugung ungewichteter Ereignisse, welche dem in NLO-Genauigkeit berechneten Wirkungsquerschnitt folgen.
Der Methode wird anhand von Top-Quark-Ereignissen veranschaulicht.
Die Top-Quark-Masse wird aus den erzeugten Ereignissen mithilfe der MEM in NLO-Genauigkeit bestimmt. Die erhaltenen Schätzer stimmen mit den Eingabewerten aus der Ereigniserzeugung überein. Wiederholung der Massenbestimmung aus denselben Ereignissen, ohne NLO-Korrekturen in den Vorhersagen, führt zu verfälschten Schätzern. Diese Verschiebungen werden nicht durch abgeschätzte theoretische Unsicherheiten berücksichtigt, was die Abschätzung der theoretischen Unsicherheiten der Analyse in führender Ordnung unzuverlässig macht.
Die Resultate unterstreichen die Wichtigkeit der Berücksichtigung von NLO-Korrekturen in der MEM.Analyses in high energy physics aim to put the Standard Model—the commonly accepted theory—to test. For convincing conclusions, analysis methods are needed which offer an unambiguous comparison between data and theory while allowing reliable estimates of uncertainties. The Matrix Element Method (MEM) is a Maximum Likelihood method which is especially tailored for signal searches and parameter estimation at colliders. The MEM has proven to be beneficial due to optimal use of the available information and a clean statistical interpretation of the results. But it has a big drawback: In its original formulation, the likelihood calculation is intrinsically limited to the leading perturbative order in the coupling. Higher-order corrections improve the accuracy of theoretical predictions and allow for unambiguous field-theoretical interpretation of the extracted information. In this work, the MEM incorporating corrections of next-to-leading order (NLO) in QCD by defining event weights suited for the likelihood calculation is presented for the first time. These weights also enable the generation of unweighted events following the cross section calculated at NLO accuracy. The method is demonstrated for top-quark events. The top-quark mass is determined with the MEM at NLO accuracy from the generated events. The extracted estimators are in agreement with the input values from the event generation. Repeating the mass determinations from the same events, without NLO corrections in the predictions, results in biased estimators. These shifts may not be accounted for by estimated theoretical uncertainties rendering the estimation of the theoretical uncertainties unreliable in the leading-order analysis. The results emphasise the importance of the inclusion of NLO corrections into the MEM.
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Diercks, David Robert. "Measurement of Lattice Strain and Relaxation Effects in Strained Silicon Using X-ray Diffraction and Convergent Beam Electron Diffraction." Thesis, University of North Texas, 2007. https://digital.library.unt.edu/ark:/67531/metadc3978/.
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The semiconductor industry has decreased silicon-based device feature sizes dramatically over the last two decades for improved performance. However, current technology has approached the limit of achievable enhancement via this method. Therefore, other techniques, including introducing stress into the silicon structure, are being used to further advance device performance. While these methods produce successful results, there is not a proven reliable method for stress and strain measurements on the nanometer scale characteristic of these devices. The ability to correlate local strain values with processing parameters and device performance would allow for more rapid improvements and better process control. In this research, x-ray diffraction and convergent beam electron diffraction have been utilized to quantify the strain behavior of simple and complex strained silicon-based systems. While the stress relaxation caused by thinning of the strained structures to electron transparency complicates these measurements, it has been quantified and shows reasonable agreement with expected values. The relaxation values have been incorporated into the strain determination from relative shifts in the higher order Laue zone lines visible in convergent beam electron diffraction patterns. The local strain values determined using three incident electron beam directions with different degrees of tilt relative to the device structure have been compared and exhibit excellent agreement.
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Kolchuzhin, Vladimir. "Methods and Tools for Parametric Modeling and Simulation of Microsystems based on Finite Element Methods and Order Reduction Technologies." Doctoral thesis, Universitätsbibliothek Chemnitz, 2010. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-201000550.
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In der vorliegenden Arbeit wird die Entwicklung eines effizienten Verfahrens zur parametrischen Finite Elemente Simulation von Mikrosystemen und zum Export dieser Modelle in Elektronik- und Systemsimulationswerkzeuge vorgestellt. Parametrische FE-Modelle beschreiben den Einfluss von geometrischen Abmessungen, Schwankungen von Materialeigenschaften und veränderten Umgebungsbedingungen auf das Funktionsverhalten von Sensoren und Aktuatoren. Parametrische FE-Modelle werden für die Auswahl geeigneter Formelemente und deren Dimensionierung während des Entwurfsprozesses in der Mikrosystemtechnik benötigt. Weiterhin ermöglichen parametrische Modelle Sensitivitätsanalysen zur Bewertung des Einflusses von Toleranzen und Prozessschwankungen auf die Qualität von Fertigungsprozessen. In Gegensatz zu üblichen Sample- und Fitverfahren wird in dieser Arbeit eine Methode entwickelt, welche die Taylorkoeffizienten höherer Ordnung zur Beschreibung des Einflusses von Designparametern direkt aus der Finite-Elemente- Formulierung, durch Ableitungen der Systemmatrizen, ermittelt. Durch Ordnungsreduktionsverfahren werden die parametrischen FE-Modelle in verschiedene Beschreibungssprachen für einen nachfolgenden Elektronik- und Schaltungsentwurf überführt. Dadurch wird es möglich, neben dem Sensor- und Aktuatorentwurf auch das Zusammenwirken von Mikrosystemen mit elektronischen Schaltungen in einer einheitlichen Simulationsumgebung zu analysieren und zu optimierenThe thesis deals with advanced parametric modeling technologies based on differentiation of the finite element equations which account for parameter variations in a single FE run. The key idea of the new approach is to compute not only the governing system matrices of the FE problem but also high order partial derivatives with regard to design parameters by means of automatic differentiation. As result, Taylor vectors of the system’s response can be expanded in the vicinity of the initial position capturing dimensions and physical parameter. A novel approaches for the parametric MEMS simulation have been investigated for mechanical, electrostatic and fluidic domains in order to improve the computational efficiency. Objective of reduced order modeling is to construct a simplified model which approximates the original system with reasonable accuracy for system level design of MEMS. The modal superposition technique is most suitable for system with flexible mechanical components because the deformation state of any flexible system can be accurately described by a linear combination of its lowest eigenvectors. The developed simulation approach using parametric FE analyses to extract basis functions have been applied for parametric reduced order modeling. The successful implementation of a derivatives based technique for parameterization of macromodel by the example of microbeam and for exporting this macromodel into MATLAB/Similink to simulate dynamical behavior has been reported
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Li, Li [Verfasser], Thomas [Akademischer Betreuer] [Gutachter] Eibert, and Romanus [Gutachter] Dyczij-Edlinger. "Singularity Cancellation Transformations and Hierarchical Higher Order Basis Functions for the Hybrid Finite Element Boundary Integral Technique / Li Li. Betreuer: Thomas Eibert. Gutachter: Romanus Dyczij-Edlinger ; Thomas Eibert." München : Universitätsbibliothek der TU München, 2016. http://d-nb.info/1104368218/34.
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Zdunek, Agnieszka Izabela. "Prediction of natural frequencies of turbine blades for turbocharger application : an investigation of the finite element method, mathematical modelling and frequency survey methods applied to turbocharger blade vibration in order to predict natural frequencies of turbocharger blades." Thesis, University of Bradford, 2014. http://hdl.handle.net/10454/7328.
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Methods of determining natural frequencies of the D76D88, B76D88, A86E93, C86G90, C86L90 and C125L89 turbine wheel designs for various environmental conditions were investigated by application of Finite Element Analysis and beam theory. Modelling and simulation methods were developed ; the first method composed of 15 finite element simulations ; the second composed of 15 finite element simulations and a set of experimental frequency survey results; the third composed of 5 simulations , an incorporated mathematical model and a set of experimental frequency survey results. Each of these methods was designed to allow prediction of resonant frequency changes across a range of exhaust gas temperature and shaft rotational speed. For the new modelling and simulation methods, an analysis template and a plotting tool were developed using Microsoft Excel and MATLAB software. A graph showing a frequency-temperature-speed variations and a Campbell Diagram that incorporates material stiffening and softening effects across a range of rotational speeds was designed, and applied to the D76D88, B76D88, A86E93, C86G90, C86L90 and C125L89 turbine wheel designs. New design methodologies for turbine wheels were formulated and validated, showing a good agreement with a range of data points from frequency survey, strain-gauge telemetry and laser tip-timing test results. The results from the new design method were compared with existing single compensation factor methodology, and showed a great improvement in accuracy of prediction of modal vibration. A new nomenclature for the mode shapes of a turbocharger’s blade was proposed, designed and demonstrated to allow direct identification of associated mode shape. It is concluded that Finite Element Analysis combined with the frequency survey is capable of predicting changes in turbine natural frequencies and, when incorporated into the existing turbine design methodology, resulted in a major improvement in the accuracy of the predictions of vibration frequency.
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Nguyen, Thuy Thi My. "Development of a second-order inelastic analysis method accounted for construction stage effects on the behaviour of prestressed steel structures." Thesis, Queensland University of Technology, 2018. https://eprints.qut.edu.au/117967/8/Thi_Nguyen_Thesis.pdf.
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This research developed a new method to investigate the construction stage effects on the behavior of pre-stressed steel structures. Any changes of structural geometry and/or material properties are properly accounted and evaluated stage-by-stage during the whole construction. Therefore, the structural responses are properly predicted. Any instability and excessive deflection of structural members or the possibility of structural collapse during construction can be avoided.
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Schwebke, Kai G. [Verfasser], Stefan M. [Akademischer Betreuer] Holzer, and Norbert [Akademischer Betreuer] Gebbeken. "On Implementing a Higher Order Generalized Finite Element Method / Kai G. Schwebke. Universität der Bundeswehr München, Fakultät für Bauingenieur- und Vermessungswesen. Gutachter: Stefan Holzer ; Norbert Gebbeken. Betreuer: Stefan Holzer." Neubiberg : Universitätsbibliothek der Universität der Bundeswehr München, 2008. http://d-nb.info/1065677510/34.
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Unnikrishnan, Vinu Unnithan. "Multiscale analysis of nanocomposite and nanofibrous structures." [College Station, Tex. : Texas A&M University, 2007. http://hdl.handle.net/1969.1/ETD-TAMU-1469.
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Sato, Fernando Massami. "Numerical experiments with stable versions of the Generalized Finite Element Method." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/18/18134/tde-16102017-101710/.
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The Generalized Finite Element Method (GFEM) is essentially a partition of unity based method (PUM) that explores the Partition of Unity (PoU) concept to match a set of functions chosen to efficiently approximate the solution locally. Despite its well-known advantages, the method may present some drawbacks. For instance, increasing the approximation space through enrichment functions may introduce linear dependences in the solving system of equations, as well as the appearance of blending elements. To address the drawbacks pointed out above, some improved versions of the GFEM were developed. The Stable GFEM (SGFEM) is a first version hereby considered in which the GFEM enrichment functions are modified. The Higher Order SGFEM proposes an additional modification for generating the shape functions attached to the enriched patch. This research aims to present and numerically test these new versions recently proposed for the GFEM. In addition to highlighting its main features, some aspects about the numerical integration when using the higher order SGFEM, in particular are also addressed. Hence, a splitting rule of the quadrilateral element area, guided by the PoU definition itself is described in detail. The examples chosen for the numerical experiments consist of 2-D panels that present favorable geometries to explore the advantages of each method. Essentially, singular functions with good properties to approximate the solution near corner points and polynomial functions for approximating smooth solutions are examined. Moreover, a comparison among the conventional FEM and the methods herein described is made taking into consideration the scaled condition number and rates of convergence of the relative errors on displacements. Finally, the numerical experiments show that the Higher Order SGFEM is the more robust and reliable among the versions of the GFEM tested.O Método dos Elementos Finitos Generalizados (MEFG) é essencialmente baseado no método da partição da unidade, que explora o conceito de partição da unidade para compatibilizar um conjunto de funções escolhidas para localmente aproximar de forma eficiente a solução. Apesar de suas vantagens bem conhecidas, o método pode apresentar algumas desvantagens. Por exemplo, o aumento do espaço de aproximação por meio das funções de enriquecimento pode introduzir dependências lineares no sistema de equações resolvente, assim como o aparecimento de elementos de mistura. Para contornar as desvantagens apontadas acima, algumas versões aprimoradas do MEFG foram desenvolvidas. O MEFG Estável é uma primeira versão aqui considerada na qual as funções de enriquecimento do MEFG são modificadas. O MEFG Estável de ordem superior propõe uma modificação adicional para a geração das funções de forma atreladas ao espaço enriquecido. Esta pesquisa visa apresentar e testar numericamente essas novas versões do MEFG recentemente propostas. Além de destacar suas principais características, alguns aspectos sobre a integração numérica quando usado o MEFG Estável de ordem superior, em particular, são também abordados. Por exemplo, detalha-se uma regra de divisão da área do elemento quadrilateral, guiada pela própria definição de sua partição da unidade. Os exemplos escolhidos para os experimentos numéricos consistem em chapas com geometrias favoráveis para explorar as vantagens de cada método. Essencialmente, examinam-se funções singulares com boas propriedades de aproximar a solução nas vizinhanças de vértices de cantos, bem como funções polinomiais para aproximar soluções suaves. Ademais, uma comparação entre o MEF convencional e os métodos aqui descritos é feita levando-se em consideração o número de condição do sistema escalonado e as razões de convergência do erro relativo em deslocamento. Finalmente, os experimentos numéricos mostram que o MEFG Estável de ordem superior é a mais robusta e confiável entre as versões do MEFG testadas.
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Schönherr, Marek. "Improving predictions for collider observables by consistently combining fixed order calculations with resummed results in perturbation theory." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-83876.
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With the constantly increasing precision of experimental data acquired at the current collider experiments Tevatron and LHC the theoretical uncertainty on the prediction of multiparticle final states has to decrease accordingly in order to have meaningful tests of the underlying theories such as the Standard Model. A pure leading order calculation, defined in the perturbative expansion of said theory in the interaction constant, represents the classical limit to such a quantum field theory and was already found to be insufficient at past collider experiments, e.g. LEP or Hera. Such a leading order calculation can be systematically improved in various limits. If the typical scales of a process are large and the respective coupling constants are small, the inclusion of fixed-order higher-order corrections then yields quickly converging predictions with much reduced uncertainties. In certain regions of the phase space, still well within the perturbative regime of the underlying theory, a clear hierarchy of the inherent scales, however, leads to large logarithms occurring at every order in perturbation theory. In many cases these logarithms are universal and can be resummed to all orders leading to precise predictions in these limits. Multiparticle final states now exhibit both small and large scales, necessitating a description using both resummed and fixed-order results. This thesis presents the consistent combination of two such resummation schemes with fixed-order results. The main objective therefor is to identify and properly treat terms that are present in both formulations in a process and observable independent manner.
In the first part the resummation scheme introduced by Yennie, Frautschi and Suura (YFS), resumming large logarithms associated with the emission of soft photons in massive Qed, is combined with fixed-order next-to-leading matrix elements. The implementation of a universal algorithm is detailed and results are studied for various precision observables in e.g. Drell-Yan production or semileptonic B meson decays. The results obtained for radiative tau and muon decays are also compared to experimental data.
In the second part the resummation scheme introduced by Dokshitzer, Gribov, Lipatov, Altarelli and Parisi (DGLAP), resumming large logarithms associated with the emission of collinear partons applicable to both Qcd and Qed, is combined with fixed-order next-to-leading matrix elements. While the focus rests on its application to Qcd corrections, this combination is discussed in detail and the implementation is presented. The resulting predictions are evaluated and compared to experimental data for a multitude of processes in four different collider environments. This formulation has been further extended to accommodate real emission corrections to beyond next-to-leading order radiation otherwise described only by the DGLAP resummation. Its results are also carefully evaluated and compared to a wide range of experimental data.
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GUARNERA, DANIELE. "Refined one-dimensional models applied to biostructures and fluids." Doctoral thesis, Politecnico di Torino, 2019. http://hdl.handle.net/11583/2729363.
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GARCIA, DE MIGUEL ALBERTO. "Hierarchical component-wise models for enhanced stress analysis and health monitoring of composites structures." Doctoral thesis, Politecnico di Torino, 2019. http://hdl.handle.net/11583/2729658.
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