Rozprawy doktorskie: „Finite Element Element Method”

1

Starkloff, Hans-Jörg. "Stochastic finite element method with simple random elements". Universitätsbibliothek Chemnitz, 2008. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200800596.

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We propose a variant of the stochastic finite element method, where the random elements occuring in the problem formulation are approximated by simple random elements, i.e. random elements with only a finite number of possible values.

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Rabadi, Kairas. "PERFORMANCE OF INTERFACE ELEMENTS IN THE FINITE ELEMENT METHOD". Master's thesis, University of Central Florida, 2004. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/2188.

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The objective of this research is to assess the performance of interface elements in the finite element method. Interface elements are implemented in the finite element codes such as MSC.NASTRAN, which is used in this study. Interface elements in MSC.NASTRAN provide a tool to transition between a shell-meshed region to another shell-meshed region as well as from a shell-meshed region to a solid-meshed region. Often, in practice shell elements are layered on shell elements or on solid elements without the use of interface elements. This is potentially inaccurate arising in mismatched degrees of freedom. In the case of a shell-to-shell interface, we consider the case in which the two regions have mismatched nodes along the boundary. Interface elements are used to connect these mismatched nodes. The interface elements are especially useful in global/local analysis, where a region with a dense mesh interfaces to a region with a less dense mesh. Interface elements are used to help avoid using special transition elements between two meshed regions. This is desirable since the transition elements can be severely distorted and cause poor results. Accurate results are obtained in shell-shell and shell-solid combinations. The most interesting result is that not using interface elements can lead to severe inaccuracies. This difficulty is illustrated by computing the stress concentration of a sharp elliptical hole.
M.S.M.E.
Department of Mechanical, Materials and Aerospace Engineering;
Engineering and Computer Science
Mechanical Engineering

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Adams, Leila. "Finite element method using vector finite elements applied to eddy current problems". Master's thesis, University of Cape Town, 2011. http://hdl.handle.net/11427/9992.

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Vector fields found in electromagnetics are fundamentally different to vector fields found in other research areas such as structural mechanics. Electromagnetic vector fields possess different physical behaviour patterns and different properties in comparison to the other vector fields and therein lies the necessity of the development of a finite element which would be able to cater for these differences . The vector finite element was then developed and used within the finite element method specifically for the approximation of electromagnetic problems. This dissertation investigates the partial differential equation that governs eddy current behaviour. A finite element algorithm is coded and used to solve this partial differential equation and produce vector field simulations for fundamental eddy current problems.

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Kang, David Sung-Soo. "Hybrid stress finite element method". Thesis, Massachusetts Institute of Technology, 1986. http://hdl.handle.net/1721.1/14973.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1986.
MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERO
Bibliography: leaves 257-264.
by David Sung-Soo Kang.
Ph.D.

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5

Tseng, Gordon Bae-Ji. "Investigation of tetrahedron elements using automatic meshing in finite element analysis /". Online version of thesis, 1992. http://hdl.handle.net/1850/10699.

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Lu, Chuan. "Generalized finite element method for electromagnetic analysis". Diss., Connect to online resource - MSU authorized users, 2008.

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Thesis (Ph. D.)--Michigan State University. Electrical and Computer Engineering, 2008.
Title from PDF t.p. (viewed on Apr. 8, 2009) Includes bibliographical references (p. 148-153). Also issued in print.

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7

Irfanoglu, Bulent. "Boundary Element-finite Element Acoustic Analysis Of Coupled Domains". Phd thesis, METU, 2004. http://etd.lib.metu.edu.tr/upload/12605360/index.pdf.

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This thesis studies interactions between coupled acoustic domain(s) and enclosing rigid or elastic boundary. Boundary element-finite element (BE-FE) sound-structure interaction models are developed by coupling frequency domain BE acoustic and FE structural models using linear inviscid acoustic and elasticity theories. Flexibility in analyses is provided by discontinuous triangular and quadrilateral elements in the BE method (BEM), and a rectangular plate and a triangular shell element in the FE method (FEM). An analytical formulation is developed for an extended fundamental sound-structure interaction problem that involves locally reacting sound absorptive treatment on interior elastic boundary. This new formulation is built upon existing analytical solutions for a configuration known as the cavity-backed-plate problem. Results from developed analytical formulation are compared against those from independent BE-FE analyses. Analytical and BE-FE analysis results for a selection of cavity-plate(s) interaction cases are given. Single- and multi-domain BE analyses of cavity-Helmholtz resonator interaction are provided as an alternative to modal method of acoustoelasticity. A discrete-form of the existing BE acoustic particle velocity formulation is presented and demonstrated on a basic case study. Both the existing and the discretized BE acoustic particle velocity formulations could be utilized in acoustic studies. A selection of case studies involving fundamental configurations are studied both analytically and computationally (by BE or BE-FE methods). These studies could provide a basis for benchmark case development in the field of acoustics.

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Sevilla, Cárdenas Rubén. "NURBS-Enhanced Finite Element Method (NEFEM)". Doctoral thesis, Universitat Politècnica de Catalunya, 2009. http://hdl.handle.net/10803/5857.

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Aquesta tesi proposa una millora del clàssic mètode dels elements finits (finite element method, FEM) per a un tractament eficient de dominis amb contorns corbs: el denominat NURBS-enhanced finite element method (NEFEM). Aquesta millora permet descriure de manera exacta la geometría mitjançant la seva representació del contorn CAD amb non-uniform rational B-splines (NURBS), mentre que la solució s'aproxima amb la interpolació polinòmica estàndard. Per tant, en la major part del domini, la interpolació i la integració numèrica són estàndard, retenint les propietats de convergència clàssiques del FEM i facilitant l'acoblament amb els elements interiors. Només es requereixen estratègies específiques per realitzar la interpolació i la integració numèrica en elements afectats per la descripció del contorn mitjançant NURBS.

La implementació i aplicació de NEFEM a problemes que requereixen una descripció acurada del contorn són, també, objectius prioritaris d'aquesta tesi. Per exemple, la solució numèrica de les equacions de Maxwell és molt sensible a la descripció geomètrica. Es presenta l'aplicació de NEFEM a problemes d'scattering d'ones electromagnètiques amb una formulació de Galerkin discontinu. S'investiga l'habilitat de NEFEM per obtenir solucions precises amb malles grolleres i aproximacions d'alt ordre, i s'exploren les possibilitats de les anomenades malles NEFEM, amb elements que contenen singularitats dintre d'una cara o aresta d'un element. Utilitzant NEFEM, la mida de la malla no està controlada per la complexitat de la geometria. Això implica una dràstica diferència en la mida dels elements i, per tant, suposa un gran estalvi tant des del punt de vista de requeriments de memòria com de cost computacional. Per tant, NEFEM és una eina poderosa per la simulació de problemes tridimensionals a gran escala amb geometries complexes. D'altra banda, la simulació de problemes d'scattering d'ones electromagnètiques requereix mecanismes per aconseguir una absorció eficient de les ones scattered. En aquesta tesi es discuteixen, optimitzen i comparen dues tècniques en el context de mètodes de Galerkin discontinu amb aproximacions d'alt ordre.

La resolució numèrica de les equacions d'Euler de la dinàmica de gasos és també molt sensible a la representació geomètrica. Quan es considera una formulació de Galerkin discontinu i elements isoparamètrics lineals, una producció espúria d'entropia pot evitar la convergència cap a la solució correcta. Amb NEFEM, l'acurada imposició de la condició de contorn en contorns impenetrables proporciona resultats precisos inclús amb una aproximació lineal de la solució. A més, la representació exacta del contorn permet una imposició adequada de les condicions de contorn amb malles grolleres i graus d'interpolació alts. Una propietat atractiva de la implementació proposada és que moltes de les rutines usuals en un codi d'elements finits poden ser aprofitades, per exemple rutines per realitzar el càlcul de les matrius elementals, assemblatge, etc. Només és necessari implementar noves rutines per calcular les quadratures numèriques en elements corbs i emmagatzemar el valor de les funciones de forma en els punts d'integració. S'han proposat vàries tècniques d'elements finits corbs a la literatura. En aquesta tesi, es compara NEFEM amb altres tècniques populars d'elements finits corbs (isoparamètics, cartesians i p-FEM), des de tres punts de vista diferents: aspectes teòrics, implementació i eficiència numèrica. En els exemples numèrics, NEFEM és, com a mínim, un ordre de magnitud més precís comparat amb altres tècniques. A més, per una precisió desitjada NEFEM és també més eficient: necessita un 50% dels graus de llibertat que fan servir els elements isoparamètrics o p-FEM per aconseguir la mateixa precisió. Per tant, l'ús de NEFEM és altament recomanable en presència de contorns corbs i/o quan el contorn té detalls geomètrics complexes.
This thesis proposes an improvement of the classical finite element method (FEM) for an efficient treatment of curved boundaries: the NURBSenhanced FEM (NEFEM). It is able to exactly represent the geometry by means of the usual CAD boundary representation with non-uniform rational Bsplines (NURBS), while the solution is approximated with a standard piecewise polynomial interpolation. Therefore, in the vast majority of the domain, interpolation and numerical integration are standard, preserving the classical finite element (FE) convergence properties, and allowing a seamless coupling with standard FEs on the domain interior. Specifically designed polynomial interpolation and numerical integration are designed only for those elements affected by the NURBS boundary representation.

The implementation and application of NEFEM to problems demanding an accurate boundary representation are also primary goals of this thesis. For instance, the numerical solution of Maxwell's equations is highly sensitive to geometry description. The application of NEFEM to electromagnetic scattering problems using a discontinuous Galerkin formulation is presented. The ability of NEFEM to compute an accurate solution with coarse meshes and high-order approximations is investigated, and the possibilities of NEFEM meshes, with elements containing edge or corner singularities, are explored. With NEFEM, the mesh size is no longer subsidiary to geometry complexity, and depends only on the accuracy requirements on the solution, whereas standard FEs require mesh refinement to properly capture the geometry. This implies a drastic difference in mesh size that results in drastic memory savings, and also important savings in computational cost. Thus, NEFEM is a powerful tool for large-scale scattering simulations with complex geometries in three dimensions. Another key issue in the numerical solution of electromagnetic scattering problems is using a mechanism to perform the absorption of outgoing waves. Two perfectly matched layers are discussed, optimized and compared in a high-order discontinuous Galerkin framework.

The numerical solution of Euler equations of gas dynamics is also very sensitive to geometry description. Using a discontinuous Galerkin formulation and linear isoparametric elements, a spurious entropy production may prevent convergence to the correct solution. With NEFEM, the exact imposition of the solid wall boundary condition provides accurate results even with a linear approximation of the solution. Furthermore, the exact boundary representation allows using coarse meshes, but ensuring the proper implementation of the solid wall boundary condition. An attractive feature of the proposed implementation is that the usual routines of a standard FE code can be directly used, namely routines for the computation of elemental matrices and vectors, assembly, etc. It is only necessary to implement new routines for the computation of numerical quadratures in curved elements and to store the value of shape functions at integration points.

Several curved FE techniques have been proposed in the literature. In this thesis, NEFEM is compared with some popular curved FE techniques (namely isoparametric FEs, cartesian FEs and p-FEM), from three different perspectives: theoretical aspects, implementation and performance. In every example shown, NEFEM is at least one order of magnitude more accurate compared to other techniques. Moreover, for a desired accuracy NEFEM is also computationally more efficient. In some examples, NEFEM needs only 50% of the number of degrees of freedom required by isoparametric FEs or p-FEM. Thus, the use of NEFEM is strongly recommended in the presence of curved boundaries and/or when the boundary of the domain has complex geometric details.

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9

Valivarthi, Mohan Varma, i Hema Chandra Babu Muthyala. "A Finite Element Time Relaxation Method". Thesis, Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-17728.

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In our project we discuss a finite element time-relaxation method for high Reynolds number flows. The key idea consists of using local projections on polynomials defined on macro element of each pair of two elements sharing a face. We give the formulation for the scalar convection–diffusion equation and a numerical illustration.

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Zarco, Mark Albert. "Solution fo soil-structure interaction problems by coupled boundary element-finite element method /". This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-06062008-164808/.

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梁耀華 i Yew-wah Leung. "Finite element solution on microcomputers". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1989. http://hub.hku.hk/bib/B31209300.

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Leung, Yew-wah. "Finite element solution on microcomputers /". [Hong Kong] : University of Hong Kong, 1989. http://sunzi.lib.hku.hk/hkuto/record.jsp?B12754948.

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Dietzsch, Julian. "Implementierung gemischter Finite-Element-Formulierungen für polykonvexe Verzerrungsenergiefunktionen elastischer Kontinua". Master's thesis, Universitätsbibliothek Chemnitz, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-217381.

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In der vorliegenden Arbeit wird ein gemischtes Element gegen Locking-Effekte untersucht. Dazu wird ein Fünf-Feld-Hu-Washizu-Funktional (CoFEM-Element) für lineare und quadratische Hexaeder-Elemente unter einer hyperelastischen, isotropen, polykonvexen sowie einer transversal-isotropen Materialformulierung implementiert. Die resultierenden nichtlinearen Gleichungen werden mithilfe eines Mehrebenen-NEWTON-RAPHSON-Verfahren unter Beachtung einer konsistenten Linearisierung gelöst. Als repräsentatives Beispiel der numerischen Untersuchungen dient der einseitig eingespannte Cook-Balken mit einer quadratischen Druckverteilung am Rand. Zur Beurteilung des CoFEM-Elements wird das räumliche Konvergenzverhalten für unterschiedliche Polynomgrade und für verschiedene Netze unter Beachtung der algorithmischen Effizienz untersucht
This paper presents a mixed finite element formulation of Hu-Washizu type (CoFEM) designed to reduce locking effects with respect to a linear and quadratic approximation in space. We consider a hyperelastic, isotropic, polyconvex material formulation as well as transverse isotropy. The resulting nonlinear algebraic equations are solved with a multilevel NEWTON-RAPHSON method. As a numerical example serves a cook-like cantilever beam with a quadratic distribution of in-plane load on the Neumann boundary. We analyze the spatial convergence with respect to the polynomial degree of the underlying Lagrange polynomials and with respect to the level of mesh refinement in terms of algorithmic efficiency

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Vu, Thu Hang. "Enhancing the scaled boundary finite element method". University of Western Australia. School of Civil and Resource Engineering, 2006. http://theses.library.uwa.edu.au/adt-WU2006.0068.

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[Truncated abstract] The scaled boundary finite element method is a novel computational method developed by Wolf and Song which reduces partial differential equations to a set of ordinary linear differential equations. The method, which is semi-analytical, is suitable for solving linear elliptic, parabolic and hyperbolic partial differential equations. The method has proved to be very efficient in solving various types of problems, including problems of potential flow and diffusion. The method out performs the finite element method when solving unbounded domain problems and problems involving stress singularities and discontinuities. The scaled boundary finite element method involves solution of a quadratic eigenproblem, the computational expense of which increases rapidly as the number of degrees of freedom increases. Consequently, to a greater extent than the finite element method, it is desirable to obtain solutions at a specified level of accuracy while using the minimum number of degrees of freedom necessary. In previous work, no systematic study had been performed so far into the use of elements of higher order, and no consideration made of p adaptivity. . . The primal problem is solved normally using the basic scaled boundary finite element method. The dual problem is solved by the new technique using the fundamental solution. A guaranteed upper error bound based on the Cauchy-Schwarz inequality is derived. A iv goal-oriented p-hierarchical adaptive procedure is proposed and implemented efficiently in the scaled boundary finite element method.

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Bravo, Victor. "Finite element simulation of flow in twin screw extruder mixing elements". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0005/NQ42727.pdf.

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Esterhuizen, Jacob J. B. "The evaluation of embankment stresses by coupled boundary element - finite element method". Thesis, Virginia Tech, 1993. http://hdl.handle.net/10919/42954.

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Numerical methods and specifically the finite element method have improved significantly since their introduction in the 60's. These advances were mainly in: 1) introducing higher-order elements, 2) developing effective solution schemes, 3) developing sophisticated means of modeling the constitutive behavior of geotechnical materials, and 4) introducing iteration techniques to model material non-linearity. This thesis, on the other hand, deals with the topic of modeling the boundary conditions of the finite element problem. Typically, the boundary conditions will be approximated by specifying displacement constraints. such as restraining the bottom boundary of the finite element mesh against displacements in the horizontal and vertical directions (x- and y-directions). Where bedrock or dense residual soils underlie the soft foundation soil at a relatively shallow depth, this is a good assumption. However. when soft soil is encountered for large depths, the assumption of zero movement constraints for a mesh boundary at a shallower depth than the actual bedrock will result in a serious underestimation of stresses and displacements. By coupling boundary elements to the finite elements and using them to model the infinite extent of the foundation soil, a more realistic answer is obtained. Employing the coupled boundary element - finite element method, four cases were analyzed and the results compared to values of the pure finite element method. The results show that the coupled method indeed yielded higher stress- and displacement-values, indicating that the pure finite element method underestimates stresses and displacements when modeling very deep soils.

Master of Science

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Suada, Muhamad Giri. "A finite element method for delamination initiation and growth using interface elements". Thesis, Imperial College London, 1997. http://hdl.handle.net/10044/1/11923.

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Xiao, Dong Wen. "Efficiency analysis on element decomposition method for stochastic finite element analysis". Thesis, University of Macau, 2000. http://umaclib3.umac.mo/record=b1636334.

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Olivier, Albertus Hendrik. "Object-oriented finite element framework". Thesis, Stellenbosch : Stellenbosch University, 2002. http://hdl.handle.net/10019.1/52971.

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Thesis (MScEng)--Stellenbosch University, 2002.
ENGLISH ABSTRACT: The role of the computer has changed from a calculation tool to a tool that supports human thinking. In this thesis fundamental aspects of the Finite Element method are mapped to an object model with a well defined structure which provides for local and distributed analysis work. To achieve this the following was investigated: • An object-oriented framework for the Finite Element analysis method • An associated graphical user interface that enables the user to create and modify Finite Element models in an effective way • Requirements for the sharing of analysis information in a communication network Proposed solutions are implemented in a pilot application which indicates their potential.
AFRIKAANSE OPSOMMING: Die rol van die rekenaar het verander vanaf 'n gereedskapstuk wat berekening doen na 'n gereedskapstuk wat menslike denke ondersteun. In hierdie tesis word die fundamentele aspekte van die Eindige Element metode oorgedra na 'n objek model met 'n goed gedefinieerde struktuur wat lokale en verspreide analisering werk ondersteun. Om dit te bereik is die volgende ondesoek: • 'n Objek orienteerde raamwerk vir die Eindige Element metode • 'n Geassosieerde grafiese raamwerk wat die gebruiker in staat stelom objekte te skep en te verander • Vereistes vir die deel van analise inligting in 'n kommunikasie netwerk Die voorgestelde oplossing is geimplimenteer in 'n loodsimplementering wat die voordele van die benadering uitlig.

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Zarco, Mark Albert. "Solution of soil-structure interaction problems by coupled boundary element-finite element method". Diss., Virginia Tech, 1993. http://hdl.handle.net/10919/38298.

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Thompson, Ronald H. "Plane frame element addition to the MESS finite element program". Thesis, Virginia Polytechnic Institute and State University, 1985. http://hdl.handle.net/10919/80052.

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A plane frame element based on linear, elastic theory is developed and implemented into the MESS finite element program. Post-processed results include nodal displacements, end reactions, maximum tensile and average shear stress, and a deformed geometry plot. The element is tested for accuracy relative to simple beam theory and by comparison with results generated using another finite element program. In both cases agreement to within 6 significant figures was achieved. Because the intended use is educational, a survey of its benefit as a design aid in undergraduate instruction is included. These benefits are based on test cases from senior design class projects. Results generated using analysis techniques presently available are contrasted with those using the plane frame element. Students' work that was examined contained mistakes resulting from large amounts of hand calculations. Conversely, results generated using the finite element method proved to be easily obtained and to have a higher degree of accuracy. A recommendation for further improvements in program capability is provided at the end of the study.
Master of Science

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Heinrich, Bernd, i Beate Jung. "The Fourier-finite-element method with Nitsche-mortaring". Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200601493.

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The paper deals with a combination of the Fourier-finite-element method with the Nitsche-finite-element method (as a mortar method). The approach is applied to the Dirichlet problem of the Poisson equation in three-dimensional axisymmetric domains $\widehat\Omega$ with non-axisymmetric data. The approximating Fourier method yields a splitting of the 3D-problem into 2D-problems. For solving the 2D-problems on the meridian plane $\Omega_a$, the Nitsche-finite-element method with non-matching meshes is applied. Some important properties of the approximation scheme are derived and the rate of convergence in some $H^1$-like norm is proved to be of the type ${\mathcal O}(h+N^{-1})$ ($h$: mesh size on $\Omega_a$, $N$: length of the Fourier sum) in case of a regular solution of the boundary value problem. Finally, some numerical results are presented.

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Müller, Björn. "Parallel Finite Element Method with FEAP 8.2". Darmstadt TU, Fachgebiet Numerische Berechnungsverfahren im Maschinenbau, 2009. http://tuprints.ulb.tu-darmstadt.de/1336/.

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Zhang, Lin. "Generalized finite element method for multiscale analysis". Diss., Texas A&M University, 2003. http://hdl.handle.net/1969.1/1141.

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This dissertation describes a new version of the Generalized Finite Element Method (GFEM), which is well suited for problems set in domains with a large number of internal features (e.g. voids, inclusions, etc.), which are practically impossible to solve using the standard FEM. The main idea is to employ the mesh-based handbook functions which are solutions of boundary value problems in domains extracted from vertex patches of the employed mesh and are pasted into the global approximation by the Partition of Unity Method (PUM). It is shown that the p-version of the Generalized FEM using mesh-based handbook functions is capable of achieving very high accuracy. It is also analyzed that the effect of the main factors affecting the accuracy of the method namely: (a) The data and the buffer included in the handbook domains, and (b) The accuracy of the numerical construction of the handbook functions. The robustness of the method is illustrated by several model problems defined in domains with a large number of closely spaced voids and/or inclusions with various shapes, including the heat conduction problem defined on domains with porous media and/or a real composite material.

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Davidsson, Johan. "Sobolev Spaces and the Finite Element Method". Thesis, Örebro universitet, Institutionen för naturvetenskap och teknik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:oru:diva-67470.

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In this essay we present the Sobolev spaces and some basic properties of them. The Sobolev spaces serve as a theoretical framework for studying solutions to partial differential equations. The finite element method is presented which is a numerical method for solving partial differential equations.

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Pack, Peter Michael Walter. "The finite element method in underwater acoustics". Thesis, University of Southampton, 1986. https://eprints.soton.ac.uk/52298/.

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A Finite Element Method (FEM) is developed to calculate rotationally symmetric acoustic propagation over short range intervals (0-5 km) in shallow oceans (0-200 m deep) at low frequencies (0-50 Hz). The method allows full two-way wave propagation in range dependent environments and includes coupling to a full elastic seabed. Numerical results from a computer program are presented for propagation upslope, downslope, over seamounts and across trenches in the seabed. The seabed is modelled as a pressure release surface, a fluid halfspace and an elastic, solid halfspace and the implications of each type of model are discussed. The halfspaces, being represented by a new set of infinite elements, are modelled without truncation. The results are presented primarily as plots of transmission loss against range for a fixed depth receiver. Subsidiary results show the effect of depth averaging the receiver location, and extract mode amplitude data to reveal the strength of mode coupling and backscatter in different environments.

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Liu, Yunshan. "P-adaptive hybrid/mixed finite element method /". The Ohio State University, 1998. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487950153602937.

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Gundu, Krishna Mohan. "hp-Finite Element Method for Photonics Applications". Diss., The University of Arizona, 2008. http://hdl.handle.net/10150/195940.

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A hp-finite element method is implemented to numerically study the modes of waveguides with two dimensional cross-section and to compute electromagnetic scattering from three dimensional objects. A method to control the chromatic dispersion properties of photonic crystal fibers using the selective hole filling technique is proposed. The method is based on a single hole-size fiber geometry, and uses an appropriate index-matching liquid to modify the effective size of the filled holes. The dependence of dispersion properties of the fiber on the design parameters such as the refractive index of the liquid, lattice constant and hole diameter are studied numerically. It is shown that very small dispersion values between 0±0.5ps/nm-km can be achieved over a bandwidth of 430-510nm in the communication wavelength region of 1300-1900nm. Three such designs are proposed with air hole diameters in the range 1.5-2.0μm. A novel multi-core fiber design strategy for obtaining a at in-phase supermode that optimizes utilization of the active medium inversion in the multiple cores is proposed. The spatially at supermode is achieved by engineering the fiber so that the total mutual coupling between neighboring active cores is equal. Different designs suitable for different fabrication processes such as stack-and-draw and drilling are proposed. An important improvement over previous methods is the design simplicity and better tolerance to perturbations. The optimal implementation of perfectly matched layer (PML) in terms of minimizing the computational overhead it introduces is studied. In one dimension it is shown that PML implementation with a single cell and a high order finite element produces minimal overhead. Estimates of optimal cell size and optimal finite element degree are given. Based on the single cell implementation of PML in three dimensions, field enhancement in metallic bowties is computed.

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Perry, William H. "Finite element analysis of polymer flows". Ohio : Ohio University, 1985. http://www.ohiolink.edu/etd/view.cgi?ohiou1184072781.

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30

Ayers, Christopher Lee. "Concurrent processing of finite element calculations". Thesis, Georgia Institute of Technology, 1989. http://hdl.handle.net/1853/13072.

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31

Fithen, Robert Miller. "Adaptive finite element simulation of incompressible viscous flow". Diss., This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-06062008-170423/.

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32

Wang, Sili. "An ABAQUS Implementation of the Cell-based Smoothed Finite Element Method Using Quadrilateral Elements". University of Cincinnati / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1416233762.

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33

Cenanovic, Mirza. "Finite element methods for surface problems". Doctoral thesis, Tekniska Högskolan, Högskolan i Jönköping, JTH, Produktutveckling, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:hj:diva-35369.

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The purpose of this thesis is to further develop numerical methods for solving surface problems by utilizing tangential calculus and the trace finite element method. Direct computation on the surface is possible by the use of tangential calculus, in contrast to the classical approach of mapping 2D parametric surfaces to 3D surfaces by means of differential geometry operators. Using tangential calculus, the problem formulation is only dependent on the position and normal vectors of the 3D surface. Tangential calculus thus enables a clean, simple and inexpensive formulation and implementation of finite element methods for surface problems. Meshing techniques are greatly simplified from the end-user perspective by utilizing an unfitted finite element method called the Trace Finite Element Method, in which the basic idea is to embed the surface in a higher dimensional mesh and use the shape functions of this background mesh for the discretization of the partial differential equation. This method makes it possible to model surfaces implicitly and solve surface problems without the need for expensive meshing/re-meshing techniques especially for moving surfaces or surfaces embedded in 3D solids, so called embedded interface problems. Using these two approaches, numerical methods for solving three surface problems are proposed: 1) minimal surface problems, in which the form that minimizes the mean curvature was computed by iterative update of a level-set function discretized using TraceFEM and driven by advection, for which the velocity field was given by the mean curvature flow, 2) elastic membrane problems discretized using linear and higher order TraceFEM, which makes it straightforward to embed complex geometries of membrane models into an elastic bulk for reinforcement and 3) stabilized, accurate vertex normal and mean curvature estimation with local refinement on triangulated surfaces. In this thesis the basics of the two main approaches are presented, some aspects such as stabilization and surface reconstruction are further developed, evaluated and numerically analyzed, details on implementations are provided and the current state of work is presented.

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Synn, Sang-Youp. "Practical domain decomposition approaches for parallel finite element analysis". Diss., Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/17032.

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35

Wong, S.-W. "Element-by-element methods in transient analysis". Thesis, University of Manchester, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.383902.

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Al-Zkeri, Ibrahim Abdullah. "Finite element modeling of hard turning". Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1181928433.

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37

Wanstreet, Pinar. "Finite element analysis of slope stability". Morgantown, W. Va. : [West Virginia University Libraries], 2007. https://eidr.wvu.edu/etd/documentdata.eTD?documentid=5480.

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Thesis (M.S.)--West Virginia University, 2007.
Title from document title page. Document formatted into pages; contains xii, 86 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 80-82).

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38

Cheng, Xiao Liang. "Some research on mixed finite element methods". HKBU Institutional Repository, 1995. http://repository.hkbu.edu.hk/etd_ra/48.

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39

Yilmaz, Asim Egemen. "Finite Element Modeling Of Electromagnetic Scattering Problems Via Hexahedral Edge Elements". Phd thesis, METU, 2007. http://etd.lib.metu.edu.tr/upload/12608587/index.pdf.

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In this thesis, quadratic hexahedral edge elements have been applied to the three dimensional for open region electromagnetic scattering problems. For this purpose, a semi-automatic all-hexahedral mesh generation algorithm is developed and implemented. Material properties inside the elements and along the edges are also determined and prescribed during the mesh generation phase in order to be used in the solution phase. Based on the condition number quality metric, the generated mesh is optimized by means of the Particle Swarm Optimization (PSO) technique. A framework implementing hierarchical hexahedral edge elements is implemented to investigate the performance of linear and quadratic hexahedral edge elements. Perfectly Matched Layers (PMLs), which are implemented by using a complex coordinate transformation, have been used for mesh truncation in the software. Sparse storage and relevant efficient matrix ordering are used for the representation of the system of equations. Both direct and indirect sparse matrix solution methods are implemented and used. Performance of quadratic hexahedral edge elements is deeply investigated over the radar cross-sections of several curved or flat objects with or without patches. Instead of the de-facto standard of 0.1 wavelength linear element size, 0.3-0.4 wavelength quadratic element size was observed to be a new potential criterion for electromagnetic scattering and radiation problems.

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40

Burstow, Mark C. "A combined boundary element and finite element method for elasto-plastic fracture analysis". Thesis, University of Sheffield, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.387269.

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Hinks, Thomas. "The application of the finite element method and the boundary element method to fatigue and fracture". Thesis, Cranfield University, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.302734.

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42

Samvin, David. "Finite Element Methods for Interface Problems". Licentiate thesis, Jönköping University, JTH, Industriell produktutveckling, produktion och design, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:hj:diva-54570.

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This thesis focuses on computationally efficient methods for flow in fractured porous media. Two approaches are presented where the interface is embedded on the underlying finite element mesh. The methods allow for representation of the interface geometry from the underlying discretization and with discontinuities across the interface. However, embedding interfaces raises stability concerns in which we alleviate using stabilization terms. The aim of this thesis is to present the basics of the two main approaches and to provide brief details on the mathematics involved.
Denna avhandling fokuserar på effektiva beräkningsmetoder för flöde i porösa media med sprickor. Två tillvägagångssätt presenteras där sprickan tillåts skära det underliggande finita elementnätet. Sprickans inverkan på flödet tas om hand med hjälp av den underliggande diskretiseringen som tillåter diskontinuiteter. Med andra ord kan flöden modelleras med olika egenskaper; på var sida av sprickan, samt längs sprickan. Metoden tar även hand om instabilitet som uppstår dels på grund av godtyckliga skärningar av bakgrundselementen och dels på grund av olika materialegenskaper. Syftet med denna avhandling är att presentera grunderna för dessa metoder och ge grundläggande matematiska förklaringar.

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43

Kalyanpur, Rohan. "Evaluation of finite element error estimation techniques". Thesis, Georgia Institute of Technology, 1999. http://hdl.handle.net/1853/20288.

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44

Noelting, Swen Erik 1960. "FINITE ELEMENT ANALYSIS OF SHELL STRUCTURES". Thesis, The University of Arizona, 1986. http://hdl.handle.net/10150/275502.

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45

Unosson, Mattias. "On failure modelling in finite element analysis : material imperfections and element erosion". Doctoral thesis, Linköping : Linköpings universitet, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-4679.

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46

Ahlbert, Gabriella. "Method Evaluation of Global-Local Finite Element Analysis". Thesis, Linköpings universitet, Hållfasthetslära, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-78103.

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When doing finite element analysis upon the structure of Saab’s aeroplanes a coarse global model of mainly shell elements is used to determine the load distribution for sizing the structure. At some parts of the aeroplane it is however desirable to implement a more detailed analysis. These areas are usually modelled with solid elements; the problem of connecting the fine local solid elements to the coarse global model will shell elements then arises. This master thesis is preformed to investigate possible Global-Local methods to use for the structural analysis on Gripen. First a literature study of current methods on the market is made, thereafter a few methods are implemented on a generic test structure and later on also tested on a real detail of Gripen VU. The methods tested in this thesis are Mesh refinement in HyperWorks, RBE3 in HyperWorks, Glue in MSC Patran/Nastran and DMIG in MSC Nastran. The software is however not evaluated in this thesis, and a further investigation is recommended to find the most fitting software for this purpose. All analysis are performed with linear assumptions. Mesh refinement is an integrated technique where the elements are gradually decreasing in size. Per definition, this technique cannot handle gaps, but it has almost identical results to the fine reference model. RBE3 is a type of rigid body elements with zero stiffness, and is used as an interface element. RBE3 is possible to use to connect both Shell-To-Shell and Shell-To-Solid, and can handle offsets and gaps in the boundary between the global and local model. Glue is a contact definition and is also available in other software under other names. The global respectively the local model is defined as contact bodies and a contact table is used to control the coupling. Glue works for both Shell-To-Shell and Shell-To-Solid couplings, but has problem dealing with offsets and gaps in the boundary between the global and local model. DMIG is a superelement technique where the global model is divided into smaller sub-models which are mathematically connected. DMIG is only possible to use when the nodes on the boundary on the local model have the same position as the nodes at the boundary of the global model. Thus, it is not possible to only use DMIG as a Global-Local method, but can advantageously be combined with other methods. The results indicate that the preferable method to use for Global-Local analysis is RBE3. To decrease the size of the files and demand of computational power, RBE3 can be combined with a superelement technique, for example DMIG. Finally, it is important to consider the size of the local model. There will inevitably be boundary effect when performing a Global-Local analysis of the suggested type, and it is therefore important to make the local model big enough so that the boundary effects have faded before reaching the area of interest.

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47

Ali, Hassan O. "Near-field computation using the finite element method". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ26122.pdf.

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48

Parvini, Mehdi. "Pavement deflection analysis using stochastic finite element method". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0014/NQ42757.pdf.

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49

Durrani, Jawad Nadeem. "Dynamics of pipelines with a finite element method". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/MQ65153.pdf.

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50

Parvini, Mehdi. "Pavement deflection analysis using stochastic finite element method /". *McMaster only, 1997.

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