Dissertations / Theses on the topic 'Moment scheme of the finite element'

Гребенюк, С. М. Напружено-деформований стан просторових конструкцій на основі гомогенізації пружних сталих волокнистих композитів [Текст]: дис. … д-ра тех. наук: 01.02.04 /Гребенюк Сергій Миколайович. – Запоріжжя, 2016. – 319 с.
UK: На основі аналітичних розв’язків методом представницького об’ємного елемента отримані співвідношення для ефективних пружних сталих композита з транстропними матрицею і волокном. Побудована матриця жорсткості паралелепіпедного скінченного елемента на основі моментної схеми, яка враховує особливості просторової орієнтації волокон. Описано підхід до розв’язку геометрично нелінійної задачі за допомогою модифікованого метода Ньютона-Канторовича. Запропоновані підходи використано при створенні пакету прикладних програм. Визначено напружено-деформований стан гумовокордних віброізоляторів та автомобільної шини, а також головного обтічника ракетоносія. EN: In terms of analytical solutions by use of the presentation box unit the correlations for the effective elastic constants of the composite with the trans-tropic matrix and fiber are first obtained. It is constructed the stiffness matrix of the parallelepiped finite element on the basis of the moment scheme taking into account specific of the spatial orientation of the fibers. The approach to the solution of the geometrically non-linear problem with the help of modified Newton-Kantorovich method is described. On the basis of the approaches proposed it is developed package of the applied programs. The stress-strained state of the rubber-cord vibration isolators and the car tyre as well as the main carrier rocket fairing is determined. RU: На основе аналитических решений методом представительного объемного элемента получены соотношения для эффективных упругих постоянных композита с транстропными матрицей и волокном. Построена матрица жесткости параллелепипедного конечного элемента на основе моментной схемы, которая учитывает особенности пространственной ориентации волокон. Описан подход к решению геометрически нелинейной задачи с помощью модифицированного метода Ньютона-Канторовича. Предложенные подходы использованы при создании пакета прикладных программ. Определено напряженно-деформированное состояние резинокордных виброизоляторов и автомобильной шины, а также головного обтекателя ракетоносителя.

The present thesis deals with the successful introduction of a second-moment closure turbulence model into a computer program using the Finite Element Method to solve the Navier-Stokes equations. The implementation presented has the advantage of using an equal interpolation for all the variables. It is also very economical in terms of the amount of memory required from the computer, since a fully decoupled formulation has been adopted, along with an iterative solver which permits to store in memory only the non-zero coefficients of the linear system of equations to be solved. Specialized elements are used to avoid resolving the near-wall region of the flow. The apparent viscosity concept is derived for the finite element formulation, along with a correction factor which permits a better representation of the Reynolds stresses. The RSM is compared to the older $k - epsilon$ model in two test cases where experimental data was available. The conclusion drawn from this work is that the RSM is able to reproduce more phenomenon occurring in turbulent flows than the $k - epsilon$ model. It is thought that the $k - epsilon$ model will gradually be supplanted by more complex models, as more computing power become available.

A three-phase numerical study was undertaken to address some design issues related with special truss moment frames (STMFs). In the first phase, the design approaches for distribution of shear strength among stories were examined. Multistory STMFs sized based on elastic and inelastic behavior were evaluated from a performance point of view. A set of time history analysis was conducted to investigate performance parameters such as the interstory drift ratio and the plastic rotation at chord member ends. The results of the analysis reveal that the maximum interstory drifts are not significantly influenced by the adopted design philosophy while considerable differences are observed for plastic rotations. In the second phase, the expected shear strength at vierendeel openings was studied through three dimensional finite element modeling. The results from finite element analysis reveal that the expected shear strength formulation presented in the AISC Seismic Provisions for Structural Steel Buildings is overly conservative. Based on the analysis results, an expected shear strength formula was developed and is presented herein. In the third phase, the effects of the load share and slenderness of X-diagonals in the special segment on the performance of the system were evaluated. Lateral drift, curvature at chord member ends, axial strain at X-diagonals and base shear were the investigated parameters obtained from a set of time history analysis. The results illustrate that as the load share of X-diagonals increases, the deformations decreases. Moreover, the slenderness of X-diagonals is not significantly effective on the system performance.

This thesis is devoted to the study of some difficulties of practical implementation of finite element solution of differential equations within the context of multi-scale engineering flow problems. In particular, stabilized finite elements and issues associated with computer implementation of these schemes are discussed and a novel technique towards practical implementation of such schemes is presented. The idea behind this novel technique is to introduce elemental shape functions of the polynomial forms that acquire higher degrees and are optimized at the element level, using the least squares minimization of the residual. This technique provides a practical scheme that improves the accuracy of the finite element solution while using crude discretization. The method of residual free bubble functions is the point of our departure.

Three full-scale experimental tests were conducted to investigate the strength and stiffness of weak-axis moment end-plate connections. Each test consisted of two girders connected to a column web with four-bolt extended moment end-plates. Two tests were conducted with bare steel. One test included a composite concrete slab that confined the top extension of the end-plate.

Finite element models of the tests were created with the commercial software SAP2000. A simplified modeling procedure was developed to overcome the contact problems between the end-plates and column web, and between the bolts and holes in the end-plates and web. The simplified modeling procedure accurately predicted the experimental elastic stiffness, in the form of column web rotations, of the connections.

Yield line theory was used to investigate the plastic strength of the column web. Several yield line patterns were examined. Analytical plastic moment strengths were very conservative when compared to the observed behavior of the column web.

The experimental stiffness of the test with the concrete slab confining the top extension of the end-plate was compared to the stiffness of a similar test without a slab. The slab increased the elastic stiffness of the connection; however, after the concrete began cracking and crushing around the connection, the stiffness was greatly decreased.
Master of Science

Due to problems associated with welded moment connections uncovered after the Northridge earthquake, large bolted connections are becoming a much more attractive alternative for design in seismic regions. However, stringent design requirements established by the AISC Seismic Provisions for Structural Steel Buildings (1997) make current moment end-plate configurations and design procedures inadequate for multi-story buildings. This dissertation first examines and critiques current seismic design philosophies as applied to moment end-plate connections. Next, the finite element method is used to develop much-needed design procedures for large moment end-plate connections, and to improve the understanding of the role of geometric parameters (e.g., bolt pitch and stiffener locations) in the response of these connections. Finally, single-story and multi-story frames incorporating large moment end-plate connections with known moment-rotation characteristics are considered under seismic loading to determine the effectiveness of these systems in dissipating energy caused by the ground motion.
Ph. D.

Colletotrichum gloeosporioides is the causal agent of anthracnose disease of mangoes. Infection occurs when humidity is high and rain-dispersed spores germinate and form an appressorium on immature mangoes. The infection then becomes quiescent until the fruit is harvested. On ripe fruit infection is visible as black, sunken lesions on the surface. At the pre-harvest stage, the disease is controlled with the application of a range of fungicides, and at the post-harvest stage by hot benomyl treatment. The extensive use of benomyl, both pre- and post-harvest, has resulted in the occurrence of isolates of C. gloeosporioides resistant to this fungicide. To devise an alternative strategy of disease control, the potential for biological control of anthracnose has been investigated. Potential microbial antagonists of C. gloeosporioides were isolated from blossom, leaves and fruit of mango, and screened using a series of assay techniques. In total 650 microorganisms, including bacteria, yeasts and filamentous fungi, were isolated and tested for their inhibition of growth of C. gloeosporioides on malt extract agar. Of these 650 isolates, 121 inhibited the fungus and were further tested on their ability to inhibit spore germination in vitro. Of these, 45 isolates, all bacteria and yeasts, were inoculated onto mangoes, which were artificially inoculated with C. gloeosporioides, and assessed for their potential to reduce the development of anthracnose lesions. A further selection was made, and 7 isolates were chosen to be used in a semi-commercial trial in the Philippines. This final screening procedure yielded two potential candidates for field trials, isolate 204 (identified as Bacillus cereus) and isolate 558 (identified as Pseudomonas fiuorescens). A field trial involving pre-harvest application of the biological control agent, was conducted using isolate 558. This isolate was chosen for this purpose since in in vitro experiments it significantly reduced germination of C. gloeosporioides spores. In the field trial 558 was applied in combination with nutrients and compared to treatments which had received no treatment or which had received conventional fungicide (benomyl) application. On spraying, high numbers of 558 were recorded on the leaf surface, but no reduction in post-harvest development of disease was observed. Failure of disease control was attributed to rapid death of the bacterium on the phylloplane. Inpost-harvest trials, isolates 204 and 558 were both tested in combination with different application methods, including the addition of sticker, peptone, fruit wax or a sucrose polyester. Application of 204 did not reduce disease development. Application of 558, however, did significantly reduce anthracnose development compared to the control fruit. No additional benefit was achieved by incorporating the bacteria in peptone, fruit wax or sucrose polyester. The mode of action of isolate 558 was investigated in detail. There was no evidence for parasitism taking place, or the production of volatile compounds, in the suppression of disease development. No antibiotic compounds were detected, but isolate 558 did produce a siderophore. A sharp increase in pH was also observed in culture media in which 558 was grown. Disease control may result from a combination of these two factors.particularly efficient in terms of storage requirements and computational speed. It also takes advantage of the nature of the system of equations to be solved. Several laminar benchmark exercises with and without heat transfer are performed. These include developing and fully developed isothermal duct flow, backward facing step flow, natural convection in square cavity and jet impingement with heat transfer. Results show that the adopted equal order velocity-pressure method can predict the benchmark solutions efficiently and accurately. Spurious pressure modes are also shown to be completely absent. In modelling turbulent flows, the k-c two equation eddy viscosity model is employed. The advection part of the k and e equations are discretised by the upwind technique developed in this research. Special treatment of the source terms eliminate the possibility of producing negative values of k or e during the iterative solution sequence, which can cause convergence difficulties. By combining the Law of the Wall and the Log Law of the Wall to determine shear stresses near solid regions, the need for an excessively fine mesh in these regions is avoided.

Structural steel components erected in real buildings include a wide range of artifacts. In this case, the word artifact is used to describe both defects and fasteners that create discontinuities in the steel such as notches, nicks, welds, powder actuated fasteners, self-drilling screws, repaired defects, and others. Although artifacts occur in real structures and their presence may affect the ductility of elements subjected to large inelastic strains, there is a dearth of experimental data on the seismic behavior of structural systems with artifacts. For instance, full-scale testing of moment resisting connections is expensive which makes it economically infeasible to experimentally examine the wide range of possible artifact types, artifact locations, and structural configurations. A framework has been developed for evaluating the effect of artifacts on special moment resisting frame (SMRF) plastic hinge regions using relatively economical coupon tests. Cyclic bend tests and monotonic tension tests on flat plate coupons that include artifacts are used to calibrate fracture parameters for different low cycle fatigue models such as the Cyclic Void Growth Model (CVGM), Stress-Weighted Damage Model (SWDM) and Cyclic Damage Plasticity Model (CDPM) which are then used in conjunction with finite element (FE) models to predict fracture initiation in full-scale SMRF connections. The framework is general and can be applied to many types of artifacts and seismic structural systems. Fracture propagation has been studied also using CDPM for full-scale tests using FE finite element software LS-DYNA. Alternatively, recommendations for future work is proposed for developing a new test setup, studying artifacts sensitivity to material thickness, and a method of demonstrating equivalence for the artifacts.
Ph. D.

Thesis (DEng (Electrical and Electronic Engineering))--University of Stellenbosch, 2009.
The Finite Element Method (FEM) as applied to Computational Electromagnetics (CEM), can beused to solve a large class of Electromagnetics problems with high accuracy and good computational efficiency. For solving wide-band problems time domain solutions are often preferred; while time domain FEM methods are feasible, the Finite Difference Time Domain (FDTD) method is more commonly applied. The FDTD is popular both for its efficiency and its simplicity. The efficiency of the FDTD stems from the fact that it is both explicit (i.e. no matrices need to be solved) and second order accurate in both time and space. The FDTD has limitations when dealing with certain geometrical shapes and when electrically large structures are analysed. The former limitation is caused by stair-casing in the geometrical modelling, the latter by accumulated dispersion error throughout the mesh. The FEM can be seen as a general mathematical framework describing families of concrete numerical method implementations; in fact the FDTD can be described as a particular FETD (Finite Element Time Domain) method. To date the most commonly described FETD CEM methods make use of unstructured, conforming meshes and implicit time stepping schemes. Such meshes deal well with complex geometries while implicit time stepping is required for practical numerical stability. Compared to the FDTD, these methods have the advantages of computational efficiency when dealing with complex geometries and the conceptually straight forward extension to higher orders of accuracy. On the downside, they are much more complicated to implement and less computationally efficient when dealing with regular geometries. The FDTD and implicit FETD have been combined in an implicit/explicit hybrid. By using the implicit FETD in regions of complex geometry and the FDTD elsewhere the advantages of both are combined. However, previous work only addressed mixed first order (i.e. second order accurate) methods. For electrically large problems or when very accurate solutions are required, higher order methods are attractive. In this thesis a novel higher order implicit/explicit FETD method of arbitrary order in space is presented. A higher order explicit FETD method is implemented using Gauss-Lobatto lumping on regular Cartesian hexahedra with central differencing in time applied to a coupled Maxwell’s equation FEM formulation. This can be seen as a spatially higher order generalisation of the FDTD. A convolution-free perfectly matched layer (PML) method is adapted from the FDTD literature to provide mesh termination. A curl conforming hybrid mesh allowing the interconnection of arbitrary order tetrahedra and hexahedra without using intermediate pyramidal or prismatic elements is presented. An unconditionally stable implicit FETD method is implemented using Newmark-Beta time integration and the standard curl-curl FEM formulation. The implicit/explicit hybrid is constructed on the hybrid hexahedral/tetrahedral mesh using the equivalence between the coupled Maxwell’s formulation with central differences and the Newmark-Beta method with Beta = 0 and the element-wise implicitness method. The accuracy and efficiency of this hybrid is numerically demonstrated using several test-problems.

The neutron Electric Dipole Moment Experiment at the Spallation Neutron Source requires an overall magnetic shielding factor of order 105 to attenuate external background magnetic fields. At present, the shielding design includes an external (room-temperature) multi-layer μ-metal magnetic shield, a cryogenic (4 Kelvin) Pb superconducting shield, and a cryogenic (4 Kelvin) ferromagnetic shield composed of Metglas ribbon. This research determined how to construct a Metglas shield using minimal material that produced axial and transverse shielding factors of ~267 and ~1500. In addition, the μ-metal and Metglas shields were modeled using finite element analysis. The FEA model includes external coils and their effect on the residual magnetic fields. This study will help with the design of the shielding.

Structural engineers have used finite element methods for the design of reinforced concrete plate type structures for decades. The theory behind this method is well researched, however, there is still a lack of direction on how to use the information obtained from this type of analysis to practically design reinforced concrete structures for strength and serviceability criteria. The literature study reviews the analysis of concrete plate type structures using traditional and finite element methods and highlights the difference between linear and non-linear finite element analysis. It is apparent that when designing and detailing using a FE analysis, a great deal is left up to engineering judgement, especially in areas of the structures where peak load effects (singularities) are experienced. In this thesis these peak areas are investigated, in an effort to provide insight into the actual behaviour of the structure as opposed to the theoretical results obtained from a FE analysis. The research consists of both numerical, (linear and non-linear FE analyses) and practical experimental work performed on different types of concrete plate type structures, including concrete pad foundations and simply supported flat slabs. The response to loading, i.e: cracking characteristics, softening of the concrete, moment redistribution, variation of the strain in reinforcement across the section, and deflection is observed and discussed. The results show that the traditional simplified methods are adequate with respect to overall strength. Finite element peaks or singularities may be averaged or smoothed without compromising durability and serviceability. Suggestions on how the reinforcement obtained from linear finite element methods be detailed are given.
Dissertation (MEng)--University of Pretoria, 2013.
gm2014
Civil Engineering
unrestricted

Panel zone is one of the significant parts of beam-column connections in steel structures. Until the 1994 Northridge Earthquake, a few experimental research and parametric studies had been carried out to understand the behavior of the panel zones. However, after the Northridge Earthquake, it was observed that beam-column connections were unable to show presumed seismic performance. Therefore, current design codes needed to be revised to improve seismic performance of connections in general and panel zones in particular. In this research, panel zone deformation demands are examined using explicit three dimensional finite element models and considering different parameters. For this purpose, a frame model with two different beam-column configurations was developed in order to observe the effects of beam depth, the axial load level and the level of seismicity. The frame models were analyzed under twenty different ground motion records. Local strain demands at the panel zones as well as the global frame deformation demands are evaluated. Analysis results revealed that AISC Specification designs allowed panel zone yielding
however, panel zones designed according to FEMA 355D showed minimal yielding for both shallow and deep beam configurations. Based on the analysis results, local shear strain demands in panel zones were expressed as a function of interstory drifts and normalized panel zone thicknesses.

We consider the problem of Adaptive Control of finite-dimensional, stable, Linear Time Invariant (LTI) plants. Amongst such plants, the subclass regarding which an upper bound on the order is not known or which are known to be nonminimum phase (zeros in the unstable region) pose formidable problems in their own right. On one hand, if an upper bound on the order of the plant is not known, adaptive control usually involves some form of order estimation. On the other hand, when the plant is allowed to be either minimum phase or nonminimum phase, the adaptive control problem, as is well-known, becomes considerably-less tractable. In this study, the class of unknown plants considered is such that no information is available on the upper bound of the plant order and, further, the plant may be either minimum phase or nonminimum phase. Albeit known to be stable, such plants throw myriads of challenges in the context of adaptive control. Adaptive control involving such plants has been addressed [79] in a Model Reference Adaptive Control (MRAC) framework. There, the inputs and outputs of the unknown plant are the only quantities available by measurement in terms of which any form of modeling of the unknown plant may be made. Inputs to the reference model have been taken from certain restricted classes of bounded signals. In particular, the three classes of inputs considered are piecewise continuous bounded functions which asymptotically approach • a nonzero constant, • a sinusoid, and • a sinusoid with a nonzero shift. Moreover, the control law is such that adaptation is carried out at specific instants separated by progressively larger intervals of time. The schemes there have been proved to be e-optimal in the sense of a suitably formulated optimality criterion. If, however, the reference model inputs be extended to the class of piecewise continuous bounded functions, that would compound the complexity of the adaptive control problem. Only one attempt [78] in adaptive control in such a setting has come to our notice. The problem there has been tackled by an application of the theory of Pade Approximations to time moments of an LTI system. Based on a time moments estimation procedure, a simple adaptive scheme for Single-Input Single-Output (SISO) systems with only a cascade compensator has been reported. The first chapter is essentially meant to ensure that the problem we seek to address in the field of adaptive control indeed has scope for research. Having defined Adaptive Control, we selectively scan through the literature on LTI systems, with focus on MRAC. We look out in particular for studies involving plants of which not much is known regarding their order and systems which are possibly nonminimum phase. We found no evidence to assert that the problem of adaptive control of stable LTI systems, not necessarily minimum phase and of unknown upper bound on the order, was explored enough, save two attempts involving SISO systems. Taking absence of evidence (of in-depth study) for evidence of absence, we make a case for the problem and formally state it. We preview the thesis. We set two targets before us in Chapter 2. The first is to review one of the existing procedures attacking the problem we intend to address. Since the approach is based on the notion of time moments of an LTI system, and as we are to employ Pade Approximations as a tool, we uncover these concepts to the limited extent of our requirement. The adaptive procedure, Plant Command Modifier Scheme (PCMS) [78], for SISO plants is reported in some detail. It stands supported on an algorithm specially designed to estimate the time moments of an LTI system given no more than its input and output. Model following there has been sought to be achieved by matching the first few time moments of the reference model by the corresponding ones of the overall compensated plant. The plant time moment estimates have been taken to represent the unknown plant. The second of the goals is to analyze PCMS critically so that it may serve as a forerunner to our work. We conclude the chapter after accomplishing these goals. In Chapter 3, we devise a time moment estimator for SISO systems from a perspective which is conceptually equivalent to, yet functionally different from, that appropriated in [78]. It is a recipe to obtain estimates of time moments of a system by computing time moment estimates of system input and output signals measured up to current time. Pade approximations come by handy for this purpose. The lacunae exposed by a critical examination of PCMS in Chapter 2 guide us to progressively refine the estimator. Infirmities in the control part of PCMS too have come to light on our probing into it. A few of these will be fixed by way of fabricating two exclusively cascade compensators. We encounter some more issues, traceable to the estimator, which need redressal. Instead of directly fine-tuning the estimator itself, as is the norm, we propose the idea of 'estimating' the lopsidedness of the estimator by using it on the fully known reference model. This will enable us to effect corrections and obtain admissible estimates. Next, we explore the possibility of incorporating feedback compensation in addition to the existing cascade compensation. With output error minimization in mind, we come up with three schemes in this category. In the process, we anticipate the risk of instability due to feedback and handle it by means of an instability preventer with an inbuilt instability detector. Extensive simulations with minimum and rionminimum phase unknown plants employing the various schemes proposed are presented. A systematic study of simulation results reveals a dyad of hierarchies of progressively enhanced overall performance. One is in the sequence of the proposed schemes and the other in going for matching more and more moments. Based on our experiments we pick one of the feedback schemes as the best. Chapter 4 is conceived of as a bridge between SISO and multivariable systems. A transition from SISO to Multi-Input Multi-Output (MIMO) adaptive control is not a proposition confined to the mathematics of dimension-enhancement. A descent from the MIMO to the SISO case is expected to be relatively simple, though. So to transit as smoothly and gracefully as possible, some issues have to be placed in perspective before exploring multivariable systems. We succinctly debate on the efforts in pursuit of the exact vis-a-vis the accurate, and their implications. We then set some notations and formulate certain results which serve to unify and simplify the development in the subsequent three chapters. We list a few standard results from matrix theory which are to be of frequent use in handling multivariable systems. We derive control laws for Single-Input Multi-Output (SIMO) systems in Chapter 5. Expectedly, SIMO systems display traits of observability and uncontrollability. Results of illustrative simulations are furnished. In Chapter 6, we formulate control laws for Multi-Input Single-Output (MISO) systems. Characteristics of unobservability and controllability stand out there. We present case studies. Before actually setting foot onto MIMO systems, we venture to conjecture on what to expect there. We work out all the cascade and feedback adaptive schemes for square and nonsquare MIMO systems in Chapter 7. We show that MIMO laws when projected to MISO, SIMO and SISO cases agree with the corresponding laws in the respective cases. Thus the generality of our treatment of MIMO systems over other multivariable and scalar systems is established. We report simulations of instances depicting satisfactory performance and highlight the limitations of the schemes in tackling the family of plants of unknown upper bound on the order and possibly nonminimum phase. This forms the culmination of our exercise which took off from the reported work involving SISO systems [78]. Up to the end of the 7th chapter, we are in pursuit of solutions for the problem as general as in §1.4. For SISO systems, with input restrictions, the problem has been addressed in [79]. The laws proposed there carry out adaptation only at certain discrete instants; with respect to a suitably chosen cost, the final laws are proved to be e>optimal. In Chapter 8, aided by initial suboptimal control laws, we finally devise two algorithms with continuous-time adaptation and prove their optimality. Simulations with minimum and nonminimum phase plants reveal the effectiveness of the various laws, besides throwing light on the bootstrapping and auto-rectifying features of the algorithms. In the tail-piece, we summarize the work and wind up matters reserved for later deliberation. As we critically review the present work, we decant the take-home message. A short note on applications followed by some loud thinking as a spin-off of this report will take us to finis.

A series of full-scale beam-to-column moment connection tests were completed to determine the effects of powder actuated fasteners (PAF) and puddle welds on the seismic behavior of steel moment connections.  In seismic regions, PAF are currently prohibited in the connection region (referred to as the protected zone) due to the concern of low-cycle fatigue fracture.  There is almost no information available in the literature regarding the seismic behavior of moment connections with PAF or puddle welds.
Full-scale connection testing is the most accurate way to investigate the behavior of different moment connections with common defects and fasteners applied in the protected zone.  However, it is cost prohibitive to conduct full-scale testing programs that are sufficiently comprehensive to investigate a wide range of defect types, severity, and locations.  For this reason, it is desired to develop alternative methods of investigation.  A finite element (FE) model capable of simulating both the global deformation patterns and local buckling effects in a moment connection has been developed.  Validated FE models will allow for further evaluation through numerical simulation of additional configurations.  Furthermore, alternate, more economical, test configurations to experimentally investigate the effect of defects on steel moment connections were explored.  This report discusses the full-scale test setup, results and analysis of completed experimental testing, the development of an FE connection model, and the preliminary development of alternate test configurations.

Master of Science

Une description spatio-temporelle des grandes déformations thermomécaniques des milieux continus est développée: l'utilisation d'une telle approche quadridimensionnelle garantit la covariance générale des modèles proposés. Les équations de conservation sont écrites dans ce contexte et un modèle constitutif est dérivé pour les transformations réversibles. Nous utilisons des opérateurs de projection pour obtenir les composantes spatiales et temporelles des équations régissant 4D et pour interpréter les résultats. Nous proposons ensuite une formulation faible du problème ainsi que sa discrétisation par éléments finis, à résoudre pour les grandes déformations d'un solide. L'avantage de cette description est que l'intégration sur l'espace et le temps se fait en une seule étape. Nous discutons pourquoi le système de coordonnées convectives 4D est intéressant pour résoudre le problème. Enfin, nous illustrons la démarche par des exemples analytiques et résolvons numériquement des problèmes thermomécaniques avec une implémentation sur le logiciel FEniCS
A space-time description of the finite transformations of thermo-mechanical continua is developed: the use of such a four-dimensional approach guarantees the general covariance of the proposed models. The conservation equations are written in this context and a constitutive model is derived for reversible transformations. We use projection operators to obtain the space and time components of the 4D governing equations and to interpret the results. We next propose a weak formulation of the problem along with its finite-element discretization, to be solved for the finite transformations of a solid. The advantage of this description is that the integration on space and time is performed in one step. We discuss why the 4D convective coordinate system is of interest to solve the problem. Finally, we illustrate the approach with analytical examples and solve thermo-mechanical problems numerically with an implementation on FEniCS software

Myocardial infarctions induce a maladaptive ventricular remodeling process that independently contributes to heart failure. In order to develop effective treatments, it is necessary to understand the way and extent to which the heart undergoes remodeling over the course of healing. There have been few studies to produce any data on the in-vivo material properties of infarcts, and much less on the properties over the time course of healing. In this paper, the in-vivo passive material properties of an infarcted porcine model were estimated through a combined use of magnetic resonance imaging, catheterization, finite element modeling, and a genetic algorithm optimization scheme. The collagen fiber orientation at the epicardial and endocardial surfaces of the infarct were included in the optimization. Data from porcine hearts (N=6) were taken at various time points after infarction, specifically 1 week, 4 weeks, and 8 weeks post-MI. The optimized results shared similarities with previous studies. In particular, the infarcted region was shown to dramatically increase in stiffness at 1 week post-MI. There was also evidence of a subsequent softening of the infarcted region at later time points post infarction. Fiber orientation results varied greatly but showed a shift toward a more circumferential orientation.

Concrete-filled tubular (CFT) columns have been widely adopted in building structures owing to their superior structural performance, such as enhanced load bearing capacity, compared to hollow tubes. Circular, square and rectangular hollow sections are most commonly used in the past few decades. Elliptical hollow section (EHS) available recently is regarded as a new cross-section for the CFT columns due to its attractive appearance, optional orientation either on major axis or minor axis and improved structural efficiency. The state of the research in terms of elliptical columns, tubular joints between EHSs and connections with CFT columns, etc., are reviewed in this thesis, showing a lack of investigations on EHSs, especially on beam to elliptical column connections which are essential in framed structures. The structural behaviour of elliptical column to I-beam connections under bending is studied in this thesis to fill the research gap. Overall ten specimens with various joint assemblies were tested to failure to highlight the benefits of adopting concrete infill and stiffeners in the columns. A three-dimensional finite element model developed by using ABAQUS software is presented and verified against obtained experimental results, which shows acceptable accuracy and reliability in predicting failure modes of the connections and their moment capacities. Parametric studies were performed to access the main parameters that affecting the bending behaviour of the connections. A simple hand calculation method in terms of ultimate moment capacity is proposed according to experiments conducted for connections with concrete-filled columns.

[EN] The neutron diffusion equation is an approximation of the neutron transport equation that describes the neutron population in a nuclear reactor core. In particular, we will consider here VVER-type reactors which use the neutron diffusion equation discretized on hexagonal meshes. Most of the simulation codes of a nuclear power reactor use the multigroup neutron diffusion equation to describe the neutron distribution inside the reactor core.To study the stationary state of a reactor, the reactor criticality is forced in artificial way leading to a generalized differential eigenvalue problem, known as the Lambda modes equation, which is solved to obtain the dominant eigenvalues of the reactor and their corresponding eigenfunctions. To discretize this model a finite element method with h-p adaptivity is used. This method allows to use heterogeneous meshes, and allows different refinements such as the use of h-adaptive meshes, reducing the size of specific cells, and p-refinement, increasing the polynomial degree of the basic functions used in the expansions of the solution in the different cells. Once the solution for the steady state neutron distribution is obtained, it is used as initial condition for the time integration of the neutron diffusion equation. To simulate the behaviour of a nuclear power reactor it is necessary to be able to integrate the time-dependent neutron diffusion equation inside the reactor core. The spatial discretization of this equation is done using a finite element method that permits h-p refinements for different geometries. Transients involving the movement of the control rod banks have the problem known as the rod-cusping effect. Previous studies have usually approached the problem using a fixed mesh scheme defining averaged material properties and many techniques exist for the treatment of the rod cusping problem. The present work proposes the use of a moving mesh scheme that uses spatial meshes that change with the movement of the control rods avoiding the necessity of using equivalent material cross sections for the partially inserted cells. The performance of the moving mesh scheme is tested studying different benchmark problems. For reactor calculations, the accuracy of a diffusion theory solution is limited for for complex fuel assemblies or fine mesh calculations. To improve these results a method that incorporates higher-order approximations for the angular dependence, as the simplified spherical harmonics (SPN ) method must be employed. In this work an h-p Finite Element Method (FEM) is used to obtain the dominant Lambda mode associated with a configuration of a reactor core using the SPN approximation. The performance of the SPN (N= 1, 3, 5) approximations has been tested for different reactor benchmarks.
[ES] La ecuación de la difusión neutrónica es una aproximación de la ecuación del transporte de neutrones que describe la población de neutrones en el núcleo de un reactor nuclear. En particular, consideraremos reactores de tipo VVER y para simular su comportamiento se utilizará la ecuación de la difusión neutrónica para cuya discretización se hace uso de mallas hexagonales. La mayoría de los códigos de simulación de reactores nucleares utilizan aproximación multigrupo de energía de la ecuación de la difusión neutrónica para describir la distribución de neutrones en el interior del núcleo del reactor. Para estudiar el estado estacionario del reactor, es posible forzar la criticidad del reactor de forma artificial modificando las secciones eficaces de forma que se obtiene un problema de valores propios diferencial, conocido como el problema de los Modos Lambda, que se resuelve para obtener los valores propios dominantes del reactor y sus correspondientes funciones propias. Para discretizar este modelo se ha hecho uso de un método de elementos finitos con adaptabilidad h-p. Este método permite el uso de mallas heterogéneas, y de diferentes refinamientos como el uso mallas h-adaptativas, reduciendo el tamaño de los distintos nodos, y el p-refinado, aumentando el grado del polinomio de las funciones básicas utilizado en los desarrollos de la solución en los diferentes nodos. Se ha desarrollado un código basado en un método de elementos finitos de alto orden para resolver el problema de los Modos Lambda en un reactor con geometría hexagonal y se han obtenido los Modos dominantes para distintos problemas de referencia. Una vez que se ha obtenido la solución para la distribución de neutrones en estado estacionario, ésta se utiliza como condición inicial para la integración de la ecuación de difusión neutrónica dependiente del tiempo. Para simular el comportamiento de un reactor nuclear para un determinado transitorio, es necesario ser capaz de integrar la ecuación de la difusión neutrónica dependiente del tiempo en el interior del núcleo del reactor. La discretización espacial de esta ecuación se hace usando un método de elementos finitos de alto orden que permite refinados de tipo h-p para distintas geometrías. Los transitorios que implican el movimiento de los bancos de las barras de control tienen el problema conocido como el efecto 'rod-cusping'. Estudios anteriores, por lo general, han abordado este problema utilizando una malla fija y definiendo propiedades promedio para los materiales correspondientes a las celdas donde se tiene la barra de control parcialmente insertada. En el presente trabajo se propone el uso de un esquema de malla móvil, de forma que en mallado espacial va cambiando con el movimiento de la barra de control, evitando la necesidad de utilizar secciones eficaces equivalentes para las celdas parcialmente insertadas. El funcionamiento de este esquema de malla móvil propuesto se estudia resolviendo distintos problemas tipo. La precisión obtenida mediante de la teoría de la difusión en los cálculos de reactores es limitada cuando se tienen elementos de combustible complejos o se pretenden realizar cálculos en malla fina. Para mejorar estos resultados, es necesario disponer de un método que incorpore aproximaciones de orden superior de la ecuación del transporte de neutrones. Una posibilidad es hacer uso de las ecuaciones PN simplificadas (SPN ). En este trabajo se utiliza un método de elementos finitos h-p para obtener los modos dominantes asociados con una configuración dada del núcleo de un reactor nuclear con geometría hexagonal usando la aproximación SPN . El funcionamiento de las aproximaciones SPN (N = 1, 3, 5) se ha estudiado para distintos problemas de referencia.
[CAT] L'equació de la difusió neutrònica és una aproximació de l'equació del transport de neutrons que descriu la població de neutrons en el nucli de un reactor nuclear. En particular, considerarem reactors de tipus VVER i per a simular el seu comportament s'utilitzarà l'equació de la difusió neutrónica que es discretitza fent ús de malles hexagonals. La majoria dels codis de simulació de reactors nuclears utilitzen l'aproximació multigrup d'energia de l'equació de la difusió neutrónica per a descriure la distribució de neutrons a l'interior del nucli del reactor. Per a estudiar l'estat estacionari del reactor, és possible forçar la seua criticitat de forma artificial modificant les seccions eficaces de manera que s'obté un problema de valors propis diferencial, conegut com el problema dels Modes Lambda, que es resol per a obtenir els valors propis dominants del reactor i les seues corresponents funcions pròpies. Per a discretitzar aquest model s'ha fet ús d'un mètode d'elements finits amb adaptabilitat h-p. Aquest mètode permet l'ús de malles heterogènies, i de diferents refinaments com l'ús malles h-adaptatives, reduint la grandària dels diferents nodes, i el p-refinat, augmentant el grau del polinomi de les funcions bàsiques utilitzat en els desenvolupaments de la solució en els diferents nodes. S'ha desenvolupat un codi basat en un mètode d'elements finits d'alt ordre per a resoldre el problema dels Modes Lambda en un reactor amb geometria hexagonal i s'han obtingut els Modes dominants per a diferents problemes de referència. Una vegada que s'ha obtingut la solució per a la distribució de neutrons en estat estacionari, aquesta s'utilitza com a condició inicial per a la integració de l'equació de difusió neutrònica depenent del temps. Per a simular el comportament d'un reactor nuclear per a un determinat transitori, és necessari ser capaç d'integrar l'equació de la difusió neutrónica depenent del temps a l'interior del nucli del reactor. La discretitzación espacial d'aquesta equació es fa usant un mètode d'elements finits d'alt ordre que permet refinats de tipus h-p per a diferents geometries. Els transitoris que impliquen el moviment dels bancs de les barres de control tenen el problema conegut com l'efecte 'rod-cusping'. Estudis anteriors, en general, han abordat aquest problema utilitzant una malla fixa i definint propietats equivalents per als materials corresponents a les cel·les on es té la barra de control parcialment inserida. En el present treball es proposa l'ús d'un esquema de malla mòbil, de manera que en mallat espacial va canviant amb el moviment de la barra de control, evitant la necessitat d'utilitzar seccions eficaces equivalents per a les cel·les parcialment inserides. El funcionament de aquest esquema de malla mòbil s'estudia resolent diferents problemes tipus. La precisió obtinguda mitjançant de la teoria de la difusió en els càlculs de reactors és limitada quan es tenen elements de combustible complexos o es pretenen realitzar càlculs en malla fina. Per a millorar aquests resultats, és necessari disposar d'un mètode que incorpore aproximacions d'ordre superior de l'equació del transport de neutrons. Una possibilitat és fer ús de les equacions PN simplificades (SPN ). En aquest treball s'utilitza un mètode d'elements finits h- p per a obtenir els modes dominants associats amb una configuració donada del nucli de un reactor amb geometria hexagonal usant l'aproximació SPN . El funcionament de les aproximacions SPN (N = 1, 3, 5) s'ha estudiat per a diferents problemes de referència.
Fayez Moustafa Moawad, R. (2016). Approximation of The Neutron Diffusion Equation on Hexagonal Geometries Using a h-p finite element method [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/65353
TESIS

The objective of this research is to determine the three-dimensional stiffness matrix of a rectangular cross-section helical coil compression spring. The stiffnesses of the spring are derived using strain energy methods and Castiglianoâ s second theorem. A theoretical model is developed and presented in order to describe the various steps undertaken to calculate the springâ s stiffnesses. The resulting stiffnesses take into account the bending moments, the twisting moments, and the transverse shear forces. In addition, the springâ s geometric form which includes the effects of pitch, curvature of wire and distortion due to normal and transverse forces are taken into consideration. Similar methods utilizing Castiglianoâ s second theorem and strain energy expressions were also used to derive equations for a circular cross-section spring. Their results are compared to the existing solutions and used to validate the equations derived for the rectangular cross-section helical coil compression spring. A finite element model was generated using IDEAS (Integrated Design Engineering Analysis Software) and the stiffness matrix evaluated by applying a unit load along the springâ s axis, then calculating the corresponding changes in deformation. The linear stiffness matrix is then obtained by solving the linear system of equations in changes of load and deformation. This stiffness matrix is a six by six matrix relating the load (three forces and three moments) to the deformations (three translations and three rotations). The natural frequencies and mode shapes of a mechanical system consisting of an Additional mass and the spring are also determined. Finally, a comparison of the stiffnesses derived using the analytical methods and those obtained from the finite element analysis was made and the results presented.
Master of Science

Denna studie har till syfte att undersöka hur lastfördelningen och följaktligen dimen­sionerande tvärkrafter och moment i brobaneplattor av betong skiljer sig åt beroende på val av beräkningsmetod. Jämförelsen sker primärt för tre utvalda hand­beräknings­metoder som jämförts med beräkningar gjorda i ett beräknings­program baserat på finita element­metoder (FEM). I jämförelsen undersöks hur laster sprids i brobaneplattan enligt de olika beräknings­metoderna och vilka resulterande maximala snittkrafter som erhålls. Hur lastfördelningen sker är en komplex fråga och det är därför intressant att se vilka skillnader det blir i resultat utifrån olika beräknings­metoder. Studien skedde på ett utvalt studieobjekt, en åtta meter bred samverkansbro i Njurunda strax söder om Sundsvall. De trafiklaster som beaktats är lastmodell 1 och lastmodell 2 enligt Eurokod (CEN, 2003). De beräknings­metoder som jämförts i den här studien är dels en metod för beräkning av tvärgående konsol­moment där kantbalken bidrar mycket till den lastspridande effekten. En annan metod är för beräkning av tvärkraftsfördelning vilken generellt anses mycket gynnsam, alltså ger små tvärkrafter att dimensionera bron utifrån. Den tredje och sista handberäkningsmetoden som studerats är beräkningar av tvärgående moment i fältmitt, med hjälp av influensytediagram. Influensytediagrammen som dessa studier baseras på är fram­tagna av Adolf Pucher (Pucher, 1977) och kallas ibland för Pucherdiagram. Finita element­modeller (FE-modeller) skapades för jämförelse av resultat från hand­beräkningar. Flera olika FE-modeller skapades med varierande detaljnivå, för att kunna se hur modelleringstekniken påverkar resultatet. I alla FE-modeller har bro­bane­plattan modellerats som skalelement eftersom detta är det vanligaste sättet att modellera en bro med FEM. Skillnaderna mellan de olika FE-modellerna är framför allt hur huvudbalkarna modellerats. Även ytterligare en handberäkningsmetod tillämpades för respektive snittkraft för att ge ytterligare en referens. Referensmetoderna valdes för att vara enklare metoder som baseras på andra randvillkor än de primära handberäkningsmetoderna i den här studien. Resultatet från studien visar att de förenklingar som finns i handberäkningar kan ha signifikant inverkan på resultatet. Ett konstant förhållande mellan handberäkning och FEM, där den ena beräkningsmetoden alltid resulterade i större snittkrafter, kunde inte konstateras rakt igenom studien. För tvärgående konsolmoment gav hand­beräkningen ett större maxmoment samt att en del skillnader kunde avläsas FE-modellerna emellan. Vid beräkning av tvärkraft gav FE-beräkningen ett resultat som var nära på det dubbla av det resultat handberäkningen gav. För Pucherdiagrammen blev resultaten varierade och det fanns ingen tydlig indikation för om handberäkningar ger större eller mindre tvärgående moment än en FE-modell. Studien resulterade bland annat i ökad kunskap om att förenklingar, vid dimen­sionering av en bro med hjälp av handberäkningar, kan ha stor betydelse för resultatet. Då förenklingar vid handberäkning inte går att välja av användaren finns en fördel med FEM. Fördelen med FEM är då att förenklingar styrs av användaren och det går även att studera vilken effekt en viss förenkling ger. En annan slutsats var att betong är ett material som har ett komplext beteende och i metoder som bygger på empiriska studier kan lättare få med olika effekter som finns i en verklig brobaneplatta av betong.
The aim of this thesis is to study different design methods for determing load distribution, and design values for shear force and bending moment in concrete bridge decks. The study was performed based on three design methods for hand calculations, which have been compared to the results from finite element modelling (FEM). The load distribution has a major impact on the design of a bridge and how the results from different design methods will correlate is of a great interest. The evaluation has been performed on one case study, wich is an eight-meter wide composite girder bridge in Njurunda, situated south of Sundsvall in Sweden. The traffic loads applied for this study was load model 1 and load model 2 prescribed in Eurocode (CEN, 2003). One of the design methods investigated is a method used to determine for bending moment for a cantilever slab. A significant impact from the edge beam utilizes by the method to calculate the bending moment. The second method is a design method for shear forces recommended by The Swedish Transport Administration. The third and last design methods for hand calculation is to use influence charts by Pucher (Pucher, 1977). By using the influence chart to calculate the maximum bending moment in mid-span. Results from different models, created with FEM, were compared to the results from hand ­calculations. The bridge slab was modelled with shell elements, and the girders of the bridge were modelled in four different ways to study the impact of the level of detail in the numerical models. The results in this report show that hand calculation methods are based on significant simplifications of the structure and these may have a major impact on the results. The relation between results from hand calculation methods and results obtained with FEM was not consistent in all cases analysed. While studying the bending moment for a cantilever slab, the main conclusion was that the simplifications in the hand calculation methods resulted in significantly higher moments compared to the FE-calculations. Regarding design for shear forces, the FE analyses resulted in nearly twice as high shear forces compared to the hand calculation methods. While using the influence charts by Pucher the relation between results from hand calculations and results from FEM was not consistent. Conclusions from the study included that the simplifications in hand calcu­lations is hard to change. These simplifications can have a major influence to the results. Some simplifications will make the results more on the safe side. With FEM the user is more free to choose which simplifications that will be made, but it can sometimes be hard to see the effect simplifications have on the results. Concrete is a complex material and design methods based on empirical studies does most likely give a result that reflects the reality better than methods based on mathe­matic theories.

This master’s thesis deals with topological optimization of the impeller of a radial turbocharger turbine. It focuses on reducing the moment of inertia with unchanged aerodynamic properties. The optimization was carried out using CFD, thermal and structural analysis. The computational modeling was performed using the finite element analysis in ANSYS. The work proposes models of the impeller with the topological modification of the internal structure. Based on the values of moment of inertia, the stress and the strain the most suitable model was selected.

The design of 3D microwave devices can be improved by using computational optimization techniques combined with numerical simulations of the electromagnetic field. However, high accuracy field analysis is often computationally expensive and time consuming. One way to cut costs is to vary the accuracy level of the analysis at different stages of the optimization. This idea is based on the premise that the accuracy need not be constant throughout the optimization, and so the numerical analysis can be run more cheaply without compromising design quality.
This thesis presents a software system that minimizes the return loss of 3D microwave devices over a frequency band efficiently through accuracy control. It combines a custom gradient-based optimizer with a p-adaptive frequency-domain finite element solver. The solver computes the cost function and its gradient to a specified accuracy in a cost efficient manner. The p-adaptive solver comprises of two original components: an a-posteriori error estimator to evaluate the error in the cost function gradient, and an error indicator to identify the high error regions in the mesh. The optimizer controls the accuracy of the cost function evaluation through a link with the solver, specifying the required relative error for the gradient at each optimization step.
The combined adaption-optimization scheme was applied to 3D rectangular waveguide problems for validation: an E-plane miter bend, a U-bend, an impedance transformer and a compensated magic-T. For comparison, all the problems were also optimized using high-order finite elements at every step. Test results prove the computational efficiency of the new combined scheme at various stages of the optimization. In the early stages, when the element orders are low, the scheme is able to attain similar cost function reductions as the high-order analysis, with computational savings up to a factor of 25. Even in the late stages, when the accuracy is more stringent, the scheme manages a reduction in cumulative computation time of at least a factor of 4.

Numerical Analysis of Passive Force on Skewed BridgeAbutments with Reinforced Concrete WingwallsScott Karl SnowDepartment of Civil and Environmental Engineering, BYU Master of Science Historically bridges with skewed abutments have proven more likely to fail during earthquake loadings (Toro et al, 2013) when compared to non-skewed bridges (Apirakvorapinit et al. 2012; Elnashai et al. 2010). Previous studies including small-scale laboratory tests by Jessee (2012), large-scale field tests by Smith (2014), and numerical modeling by Shamsabadi et al. (2006) have shown that 45° skewed bridge abutments experience a reduction in peak passive force by about 65%. With numerous skewed bridges in the United States, this study has great importance to the nation's infrastructure.The finite element models produced in this study model the large-scale field-testing performed by Smith (2014), which was performed to study the significant reduction in peak passive resistance for abutments with longitudinal reinforced concrete wingwalls. The finite element models largely confirm the findings of Smith (2014). Two models were created and designed to match the large-scale field tests and were used to calibrate the soil parameters for this study. Two additional models were then created by increasing the abutment widths from 11 feet to 38 feet to simulate a two-lane bridge. The 45° skewed 11-foot abutment experienced a 38% reduction in peak passive resistance compared to the non-skewed abutment. In contrast, the 45° skewed 38-foot abutment experienced a 65% reduction in peak passive resistance compared to the non-skewed abutment. When the wingwalls are extended 10 feet into the backfill the reduction decreased to 59% due to the change in effective skew angle.The finite element models generally confirmed the findings of Smith (2014). The results of the 11- and 38-foot abutment finite element models confirmed that the wingwall on the obtuse side of the 45° skewed abutments experienced approximately 4 to 5 times the amount of horizontal soil pressure and 5 times the amount of bending moment compared to the non-skewed abutment. Increases in the pressures and bending moments are likely caused by soil confined between the obtuse side of the abutment and the wingwall.A comparison of the 11- and 38-foot 45° skewed abutment models showed a decrease in the influence of the wingwalls as the abutment widened. The wingwall on the acute side of the 38-foot abutment developed approximately 50% of the horizontal soil pressure compared to the 11-foot abutment. The heave distribution of the 11-foot abutment showed approximately 1- to 2-inches of vertical displacement over a majority of the abutment backwall versus more than half of the 38-foot abutment producing ½ an inch or less.

Dans ce travail, nous avons introduit le concept sous-jacent de PUFEM et la formulation de base lié à l'équation de Helmholtz dans un domaine borné. Le processus d'enrichissement de l'onde plane de variables PUFEM a été montré et expliqué en détail. L'idée principale est d'inclure une connaissance a priori sur le comportement local de la solution dans l'espace des éléments finis en utilisant un ensemble de fonctions d'onde qui sont des solutions aux équations aux dérivées partielles. Dans cette étude, l'utilisation des ondes planes se propageant dans différentes directions a été favorisée car elle conduit à des algorithmes de calcul efficaces. En outre, nous avons montré que le nombre de directions d'ondes planes dépend de la taille de l'élément PUFEM et la fréquence des ondes à la fois en 2D et 3D. Les approches de sélection de ces ondes planes sont également illustrés. Pour les problèmes 3D, nous avons étudié deux systèmes de distribution des directions d'ondes planes qui sont la méthode du cube discrétisé et la méthode de la force de Coulomb. Il a été montré que celle-ci permet d'obtenir des directions d'onde espacées de façon uniforme et permet d'obtenir un nombre arbitraire d'ondes planes attachées à chaque noeud de l'élément de PUFEM, ce qui rend le procédé plus souple.Dans le chapitre 3, nous avons étudié la simulation numérique des ondes se propageant dans deux dimensions en utilisant PUFEM. La principale priorité de ce chapitre est de venir avec un schéma d'intégration exacte (EIS), résultant en un algorithme d'intégration rapide pour le calcul de matrices de coefficients de système avec une grande précision. L'élément 2D PUFEM a ensuite été utilisé pour résoudre un problème de transmission acoustique impliquant des matériaux poreux. Les résultats ont été vérifiés et validés par la comparaison avec des solutions analytiques. Les comparaisons entre le régime exact d'intégration (EIS) et en quadrature de Gauss ont montré le gain substantiel offert par l'EIE en termes de temps CPU.Une 3D exacte Schéma d'intégration a été présenté dans le chapitre 4, afin d'accélérer et de calculer avec précision (jusqu'à la précision de la machine) des intégrales très oscillatoires découlant des coefficients de la matrice de PUFEM associés à l'équation 3D Helmholtz. Grâce à des tests de convergence, un critère de sélection du nombre d'ondes planes a été proposé. Il a été montré que ce nombre ne pousse que quadratiquement avec la fréquence qui donne lieu à une réduction drastique du nombre total de degrés de libertés par rapport au FEM classique. Le procédé a été vérifié pour deux exemples numériques. Dans les deux cas, le procédé est représenté à converger vers la solution exacte. Pour le problème de la cavité avec une source de monopôle située à l'intérieur, nous avons testé deux modèles numériques pour évaluer leur performance relative. Dans ce scénario, où la solution exacte est singulière, le nombre de directions d'onde doit être choisie suffisamment élevée pour faire en sorte que les résultats ont convergé.Dans le dernier chapitre, nous avons étudié les performances numériques du PUFEM pour résoudre des champs sonores intérieurs 3D et des problèmes de transmission d'ondes dans lequel des matériaux absorbants sont présents. Dans le cas particulier d'un matériau réagissant localement modélisé par une impédance de surface. Un des critères d'estimation d'erreur numérique est proposé en considérant simplement une impédance purement imaginaire qui est connu pour produire des solutions à valeur réelle. Sur la base de cette estimation d'erreur, il a été démontré que le PUFEM peut parvenir à des solutions précises tout en conservant un coût de calcul très faible, et seulement environ 2 degrés de liberté par longueur d'onde ont été jugées suffisantes. Nous avons également étendu la PUFEM pour résoudre les problèmes de transmission des ondes entre l'air et un matériau poreux modélisé comme un fluide homogène équivalent
In this work, we have introduced the underlying concept of PUFEM and the basic formulation related to the Helmholtz equation in a bounded domain. The plane wave enrichment process of PUFEM variables was shown and explained in detail. The main idea is to include a priori knowledge about the local behavior of the solution into the finite element space by using a set of wave functions that are solutions to the partial differential equations. In this study, the use of plane waves propagating in various directions was favored as it leads to efficient computing algorithms. In addition, we showed that the number of plane wave directions depends on the size of the PUFEM element and the wave frequency both in 2D and 3D. The selection approaches for these plane waves were also illustrated. For 3D problems, we have investigated two distribution schemes of plane wave directions which are the discretized cube method and the Coulomb force method. It has been shown that the latter allows to get uniformly spaced wave directions and enables us to acquire an arbitrary number of plane waves attached to each node of the PUFEM element, making the method more flexible.In Chapter 3, we investigated the numerical simulation of propagating waves in two dimensions using PUFEM. The main priority of this chapter is to come up with an Exact Integration Scheme (EIS), resulting in a fast integration algorithm for computing system coefficient matrices with high accuracy. The 2D PUFEM element was then employed to solve an acoustic transmission problem involving porous materials. Results have been verified and validated through the comparison with analytical solutions. Comparisons between the Exact Integration Scheme (EIS) and Gaussian quadrature showed the substantial gain offered by the EIS in terms of CPU time.A 3D Exact Integration Scheme was presented in Chapter 4, in order to accelerate and compute accurately (up to machine precision) of highly oscillatory integrals arising from the PUFEM matrix coefficients associated with the 3D Helmholtz equation. Through convergence tests, a criteria for selecting the number of plane waves was proposed. It was shown that this number only grows quadratically with the frequency thus giving rise to a drastic reduction in the total number of degrees of freedoms in comparison to classical FEM. The method has been verified for two numerical examples. In both cases, the method is shown to converge to the exact solution. For the cavity problem with a monopole source located inside, we tested two numerical models to assess their relative performance. In this scenario where the exact solution is singular, the number of wave directions has to be chosen sufficiently high to ensure that results have converged. In the last Chapter, we have investigated the numerical performances of the PUFEM for solving 3D interior sound fields and wave transmission problems in which absorbing materials are present. For the specific case of a locally reacting material modeled by a surface impedance. A numerical error estimation criteria is proposed by simply considering a purely imaginary impedance which is known to produce real-valued solutions. Based on this error estimate, it has been shown that the PUFEM can achieve accurate solutions while maintaining a very low computational cost, and only around 2 degrees of freedom per wavelength were found to be sufficient. We also extended the PUFEM for solving wave transmission problems between the air and a porous material modeled as an equivalent homogeneous fluid. A simple 1D problem was tested (standing wave tube) and the PUFEM solutions were found to be around 1% error which is sufficient for engineering purposes

Much of the vibration in fast moving vehicles is caused bydistributed random excitation, such as turbulent flow and roadroughness. Piping systems transporting fast flowing fluid isanother example, where distributed random excitation will causeunwanted vibration. In order to reduce these vibrations andalso the noise they cause, it is important to have accurate andcomputationally efficient prediction methods available.

The aim of this thesis is to present such a method. Thefirst step towards this end was to extend an existing spectralfinite element method (SFEM) to handle excitation of planetravelling pressure waves. Once the elementary response tothese waves is known, the response to arbitrary homogeneousrandom excitation can be found.

One example of random excitation is turbulent boundary layer(TBL) excitation. From measurements a new modified Chase modelwas developed that allowed for a satisfactory prediction ofboth the measured wall pressure field and the vibrationresponse of a turbulence excited plate. In order to model morecomplicated structures, a new spectral super element method(SSEM) was formulated. It is based on a waveguide formulation,handles all kinds of boundaries and its elements are easily putinto an assembly with conventional finite elements.

Finally, the work to model fluid-structure interaction withanother wave based method is presented. Similar to the previousmethods it seems to be computationally more efficient thanconventional finite elements.

This is a book on numerical methods for singular perturbation problems - in particular stationary convection-dominated convection-diffusion problems. More precisely it is devoted to the construction and analysis of layer-adapted meshes underlying these numerical methods. An early important contribution towards the optimization of numerical methods by means of special meshes was made by N.S. Bakhvalov in 1969. His paper spawned a lively discussion in the literature with a number of further meshes being proposed and applied to various singular perturbation problems. However, in the mid 1980s this development stalled, but was enlivend again by G.I. Shishkin's proposal of piecewise- equidistant meshes in the early 1990s. Because of their very simple structure they are often much easier to analyse than other meshes, although they give numerical approximations that are inferior to solutions on competing meshes. Shishkin meshes for numerous problems and numerical methods have been studied since and they are still very much in vogue. With this contribution we try to counter this development and lay the emphasis on more general meshes that - apart from performing better than piecewise-uniform meshes - provide a much deeper insight in the course of their analysis. In this monograph a classification and a survey are given of layer-adapted meshes for convection-diffusion problems. It tries to give a comprehensive review of state-of-the art techniques used in the convergence analysis for various numerical methods: finite differences, finite elements and finite volumes. While for finite difference schemes applied to one-dimensional problems a rather complete convergence theory for arbitrary meshes is developed, the theory is more fragmentary for other methods and problems and still requires the restriction to certain classes of meshes.

This thesis deals with the determination of the load torque during flood conditions on the hydrostatic sectoral weir in Roudnice nad Labem. Problems are solved due to a glitch in the lowering sector. The aim of this study is to determine the resulting torque, of three selected states, which occurred at the water works. The issue was solved as a plane 2D problem using AutoCAD, in which were read the relevant data. It was also used ANSYS software, which modeled the flow of water over the weir to detect pressures acting on overflow face. All calculations are then counted in Microsoft Excel. Force balance is performed on the one-meter design.

The flexural capacity of the new hollow flange steel section known as LiteSteel beam (LSB) is limited by lateral distortional buckling for intermediate spans, which is characterised by simultaneous lateral deflection, twist and web distortion. Recent research based on finite element analysis and testing has developed design rules for the member capacity of LiteSteel beams subject to this unique lateral distortional buckling. These design rules are limited to a uniform bending moment distribution. However, uniform bending moment conditions rarely exist in practice despite being considered as the worst case due to uniform yielding across the span. Loading position or load height is also known to have significant effects on the lateral buckling strength of beams. Therefore it is important to include the effects of these loading conditions in the assessment of LSB member capacities. Many steel design codes have adopted equivalent uniform moment distribution and load height factors for this purpose. But they were derived mostly based on data for conventional hot-rolled, doubly symmetric I-beams subject to lateral torsional buckling. In contrast LSBs are made of high strength steel and have a unique crosssection with specific residual stresses and geometrical imperfections along with a unique lateral distortional buckling mode. The moment distribution and load height effects for LSBs, and the suitability of the current steel design code methods to accommodate these effects for LSBs are not yet known. The research study presented in this thesis was therefore undertaken to investigate the effects of nonuniform moment distribution and load height on the lateral buckling strength of simply supported and cantilever LSBs. Finite element analyses of LSBs subject to lateral buckling formed the main component of this study. As the first step the original finite element model used to develop the current LSB design rules for uniform moment was improved to eliminate some of the modelling inaccuracies. The modified finite element model was validated using the elastic buckling analysis results from well established finite strip analysis programs. It was used to review the current LSB design curve for uniform moment distribution, based on which appropriate recommendations were made. The modified finite element model was further modified to simulate various loading and support configurations and used to investigate the effects of many commonly used moment distributions and load height for both simply supported and cantilever LSBs. The results were compared with the predictions based on the current steel code design rules. Based on these comparisons, appropriate recommendations were made on the suitability of the current steel code design methods. New design recommendations were made for LSBs subjected to non-uniform moment distributions and varying load positions. A number of LSB experiments was also undertaken to confirm the results of finite element analysis study. In summary the research reported in this thesis has developed an improved finite element model that can be used to investigate the buckling behaviour of LSBs for the purpose of developing design rules. It has increased the understanding and knowledge of simply supported and cantilever LSBs subject to non-uniform moment distributions and load height effects. Finally it has proposed suitable design rules for LSBs in the form of equations and factors within the current steel code design provisions. All of these advances have thus further enhanced the economical and safe design of LSBs.

This is a book on numerical methods for singular perturbation problems - in particular stationary convection-dominated convection-diffusion problems. More precisely it is devoted to the construction and analysis of layer-adapted meshes underlying these numerical methods. An early important contribution towards the optimization of numerical methods by means of special meshes was made by N.S. Bakhvalov in 1969. His paper spawned a lively discussion in the literature with a number of further meshes being proposed and applied to various singular perturbation problems. However, in the mid 1980s this development stalled, but was enlivend again by G.I. Shishkin's proposal of piecewise- equidistant meshes in the early 1990s. Because of their very simple structure they are often much easier to analyse than other meshes, although they give numerical approximations that are inferior to solutions on competing meshes. Shishkin meshes for numerous problems and numerical methods have been studied since and they are still very much in vogue. With this contribution we try to counter this development and lay the emphasis on more general meshes that - apart from performing better than piecewise-uniform meshes - provide a much deeper insight in the course of their analysis. In this monograph a classification and a survey are given of layer-adapted meshes for convection-diffusion problems. It tries to give a comprehensive review of state-of-the art techniques used in the convergence analysis for various numerical methods: finite differences, finite elements and finite volumes. While for finite difference schemes applied to one-dimensional problems a rather complete convergence theory for arbitrary meshes is developed, the theory is more fragmentary for other methods and problems and still requires the restriction to certain classes of meshes.

This thesis deals with the analysis of a three-phase winding of an induction engine. After the theoretical introduction concerning different types of windings, two types of their analysis and the importance of the winding factor, two methods of analysis and design tools are explained: Görges diagram and Tingley scheme. This scheme is then used for the design of all possible variants of winding for a certain number of stator slots and the theoretical shape of magnetic field is analysed. The next step is a deeper software analysis of the engines with variants of windings with different coil pitches and number of conductors per slot. Especially the finite element method is used in this part. The obtained values and their characteristics of the simulated engines are compared numerically and graphically. Then the changes of important values for different windings are described. The optimal winding according to chosen requirements is chosen.

Until recently, the hot-rolled steel members have been recognized as the most popular and widely used steel group, but in recent times, the use of cold-formed high strength steel members has rapidly increased. However, the structural behavior of light gauge high strength cold-formed steel members characterized by various buckling modes is not yet fully understood. The current cold-formed steel sections such as C- and Z-sections are commonly used because of their simple forming procedures and easy connections, but they suffer from certain buckling modes. It is therefore important that these buckling modes are either delayed or eliminated to increase the ultimate capacity of these members. This research is therefore aimed at developing a new cold-formed steel beam with two torsionally rigid rectangular hollow flanges and a slender web formed using intermittent screw fastening to enhance the flexural capacity while maintaining a minimum fabrication cost. This thesis describes a detailed investigation into the structural behavior of this new Rectangular Hollow Flange Beam (RHFB), subjected to flexural action The first phase of this research included experimental investigations using thirty full scale lateral buckling tests and twenty two section moment capacity tests using specially designed test rigs to simulate the required loading and support conditions. A detailed description of the experimental methods, RHFB failure modes including local, lateral distortional and lateral torsional buckling modes, and moment capacity results is presented. A comparison of experimental results with the predictions from the current design rules and other design methods is also given. The second phase of this research involved a methodical and comprehensive investigation aimed at widening the scope of finite element analysis to investigate the buckling and ultimate failure behaviours of RHFBs subjected to flexural actions. Accurate finite element models simulating the physical conditions of both lateral buckling and section moment capacity tests were developed. Comparison of experimental and finite element analysis results showed that the buckling and ultimate failure behaviour of RHFBs can be simulated well using appropriate finite element models. Finite element models simulating ideal simply supported boundary conditions and a uniform moment loading were also developed in order to use in a detailed parametric study. The parametric study results were used to review the current design rules and to develop new design formulae for RHFBs subjected to local, lateral distortional and lateral torsional buckling effects. Finite element analysis results indicate that the discontinuity due to screw fastening has a noticeable influence only for members in the intermediate slenderness region. Investigations into different combinations of thicknesses in the flange and web indicate that increasing the flange thickness is more effective than web thickness in enhancing the flexural capacity of RHFBs. The current steel design standards, AS 4100 (1998) and AS/NZS 4600 (1996) are found sufficient to predict the section moment capacity of RHFBs. However, the results indicate that the AS/NZS 4600 is more accurate for slender sections whereas AS 4100 is more accurate for compact sections. The finite element analysis results further indicate that the current design rules given in AS/NZS 4600 is adequate in predicting the member moment capacity of RHFBs subject to lateral torsional buckling effects. However, they were inadequate in predicting the capacities of RHFBs subject to lateral distortional buckling effects. This thesis has therefore developed a new design formula to predict the lateral distortional buckling strength of RHFBs. Overall, this thesis has demonstrated that the innovative RHFB sections can perform well as economically and structurally efficient flexural members. Structural engineers and designers should make use of the new design rules and the validated existing design rules to design the most optimum RHFB sections depending on the type of applications. Intermittent screw fastening method has also been shown to be structurally adequate that also minimises the fabrication cost. Product manufacturers and builders should be able to make use of this in their applications.

Bridge edge beam system is an increasing concern in Sweden. Because it is the mostvisible part of the structure which is subjected to harsh weather. The edge beamcontributes to the stiffness of overhang slab and helps to distribute the concentratedload. The design of edge beam is not only affected by the structural members, but it isalso affected by non-structural members.The aim of the thesis is to investigate the influence of edge beam on the structuralbehavior of reinforced concrete overhang slab. A three-dimensional (3D) non-linearfinite element model is developed by using the commercial software ABAQUS version6.1.14. The load displacement curves and failure modes were observed. The bendingmoment and shear capacity of the cantilever slab is studied.The validated model from non-linear analysis of reinforced concrete slab gives morestiffer result and leads to the high value of load capacity when comparing with theexperimental test. The presence of the edge beam in the overhang slab of length 2.4 mslightly increases the load capacity and shows ductile behavior due to the self-weightof the edge beam. The non-linear FE-analysis of overhang slab of length 10 m leads tomuch higher load capacity and gives stiffer response as compare to the overhang slabof 2.4 m. The presence of the edge beam in the overhang slab of length 10 m giveshigher load capacity and shows stiffer response when comparing with the overhangslab of length 10 m. This might be due to the self-weight of the edge beam and theoverhang slab is restrained at the right side of the slab.

My diploma thesis deals with a specific dynamic model of DC motor with the parameters obtained from the calculation and from the program using the finite element method. It shows how much accurate results can be achieved in the model, if you use only the values which can be measured, recorded and calculated on the engine. This thesis contens three parts. First part describes the structure and function of DC motor and the basic principle and the use of FEM. Next is calculation analytical and numerical parameters. The search parameters include torque, resistance and inductance of armature winding, resistance and inductance of excitation windings. The last part is dedicated to creating a dynamic model. Results from the dynamic model and measured values are compared in the conclusion of my thesis.