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Investigation of Contact between Elastic Bodies One of Which has a Thin Coating Connected with the Body through a Nonlinear Winkler Layer by the Domain Decomposition methods

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Journal of Mathematical Sciences (United States) 2021年第4期258卷 477-506页

作者： Prokopyshyn, І.І. Styahar, А.О. Pidstryhach Institute for Applied Problems in Mechanics and Mathematics National Academy of Sciences of Ukraine Lviv Ukraine University of L’Aquila L’Aquila Italy

We consider the problem of contact interaction between two elastic bodies one of which has a coating in the form of a thin Timoshenko-type shell connected with the body through a nonlinear Winkler layer. We present a weak formulation of this problem in the form of a nonlinear variational equation. We propose a class of iterative domain decomposition methods that reduce the solution of this equation to the solution, in each iteration, of independent linear variational equations corresponding to problems of elasticity for massive bodies and a problem of the Timoshenko theory of shells for the coating with Robin boundary conditions imposed on the contact boundaries. The conditions of weak convergence of these methods are established. We analyze the numerical efficiency of the obtained algorithms with the use of finite-element approximations. © 2021, Springer Science+Business Media, LLC, part of Springer Nature.

关键词： contact problems of elasticity domain decomposition methods finite-element methods nonlinear variational equations thin coatings Timoshenko shells Winkler layers

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The optimisation of the mesh in first-order systems least-squares methods

The optimisation of the mesh in first-order systems least-sq...

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5th International Congress on Industrial and Applied Mathematics

作者： Tourigny, Y Univ Bristol Sch Math Bristol BS8 1TW Avon England

We describe an algorithm for optimising the mesh in the least-squares finite element discretisation of first-order systems of partial differential equations. The key feature of the method is that the optimisation process is based entirely on the solution of local PDE problems. We apply the algorithm to the Stokes equations for the flow of a viscous incompressible fluid, and to a convection diffusion equation where convection dominates.

关键词： least-squares finite element adaptivity finite-element methods STOKES EQUATIONS LINEAR ELASTICITY ALGORITHM

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A Novel Octagonal Wound Core for Distribution Transformers Validated by Electromagnetic Field Analysis and Comparison With Conventional Wound Core

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IEEE TRANSACTIONS ON MAGNETICS 2010年第5期46卷 1251-1258页

作者： Hernandez, Ivan Olivares-Galvan, Juan C. Georgilakis, Pavlos S. Canedo, Jose M. NYU Power Elect Syst Polytech Inst Dept Elect & Comp Engn Brooklyn NY 11201 USA CINVESTAV Unidad Guadalajara Dept Sistemas Elect Potencia Zapopan 45015 Jal Mexico Univ Autonoma Metropolitana Azcapotzalco Dept Energia Ciudad De Mexico 02200 DF Mexico Natl Tech Univ Athens Sch Elect & Comp Engn GR-15780 Athens Greece

This paper analyzes a novel configuration of transformer core, called octagonal wound core (OWC), and shows the minimization of the excitation current and the reduction of the eddy-current losses. The OWC is compared with the conventional wound core (CWC) configuration. The comparison is based on two-dimensional and three-dimensional finite-element method (FEM) simulations, taking into account the nonlinear properties of the magnetic material of the core. The results show that the OWC reduces the excitation current and the eddy-current losses when compared with CWC. Moreover, several combinations of grades of the grain-oriented silicon steel (GOSS) were investigated so as to further reduce the eddy-current losses and the excitation current.

关键词： Eddy currents electromagnetic field finite-element methods laminations octagonal wound cores rolling direction transformer core wound core

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Higher order interpolatory vector bases on pyramidal elements

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 1999年第5期47卷 775-782页

作者： Graglia, RD Gheorma, IL Politecn Torino Dipartimento Elettr I-10129 Turin Italy

In the numerical solution of three dimensional (3-D) electromagnetic field problems, the regions of interest can be discretized by elements having tetrahedral, brick or prismatic shape. However, such different shape elements cannot be linked to form a conformal mesh;to this purpose pyramidal elements are required, In this paper, we define interpolatory higher order curl- and divergence-conforming vector basis functions on pyramidal elements, with extension to curved pyramids, and discuss their completeness properties. A general procedure to obtain vector bases of arbitrary polynomial order is given and bases up to second order are explicitly reported. These new elements ensure the continuity of the proper vector components across adjacent elements of equal order but different shape. Results to confirm the faster convergence of higher order functions on pyramids are presented.

关键词： electromagnetic fields finite-element methods higher order vector elements method of moments numerical analysis pyramidal elements

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Analytical interpretation and quantification of rotational losses in stator cores of induction motors

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IEEE TRANSACTIONS ON MAGNETICS 2007年第10期43卷 3861-3867页

作者： Diaz, Guzman Gonzalez-Moran, Cristina Arboleya, Pablo Gomez-Aleixandre, Javier Univ Oviedo Dept Elect Engn Gijon 33204 Spain

We propose an approach to allocate and delimit a region in which the rotational losses are of most importance in the stator core of induction motors. The delimitation is based on the analysis of points at which the minimum flux density is not null. The analysis of flux paths and values of flux density over a number of motors allows a model of flux density to be proposed for the chosen rotational region. We conducted the process by post-processing finite-element results. A comparison with bench test results shows that the approach can confine the effects of rotational losses within a region allocated in the tooth roots without significant loss of accuracy. We give analytical expressions based on geometrical data. The approach provides a quick method to evaluate the rotational losses by analytical means, bypassing the use of numerical methods at those design stages at which is preferable to reduce the accuracy in favor of computational speed.

关键词： finite-element methods induction motors magnetic losses

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VOLMAX: A solid-model-based, transient volumetric Maxwell solver using hybrid grids

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IEEE ANTENNAS AND PROPAGATION MAGAZINE 1997年第1期39卷 20-33页

作者： Riley, DJ Turner, CD Laboratory of Chromatography DEPg.Fac.Quimica Universidad Nacional Autonoma de Mexico Circuito interior Cd Universitaria/CP 04510 Mexico D.F.Mexico

This paper provides an overview of the finite-volume algorithm, the dissipative time-integration scheme, boundary condition implementation, grid generation, and a time-step definition suitable for sub-time cycling. To examine the accuracy of VOLMAX operating in either a purely unstructured or a hybrid-grid mode, the resonances of a rectangular cavity, the input admittance of a \"thick\" wire antenna, and three simple microstrip applications (microstrip line, patch antenna and low pass filter) with well-known FDTD solutions are examined. The latter three examples demonstrate the accuracy that can be obtained by launching microstrip-guided waves on cubical hexahedral (FDTD) grids and through a dense, unstructured linear tetrahedral region.

关键词： transient analysis FDTD methods finite-element methods finite-volume methods time-domain analysis numerical analysis

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Process Innovations to Prevent Glass Substrate Fracture From RDL Stress and Singulation Defects

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IEEE TRANSACTIONS ON DEVICE AND MATERIALS RELIABILITY 2016年第4期16卷 622-630页

作者： McCann, Scott Singh, Bhupender Smet, Vanessa Sundaram, Venkatesh Tummala, Rao R. Sitaraman, Suresh K. Georgia Inst Technol Atlanta GA 30332 USA

Glass is an ideal material for package substrates due to the excellent electrical properties, tailorable coefficient of thermal expansion, high mechanical rigidity, availability in large and thin panel form, and smooth surface for fine line fabrication. Glass does have challenges, arising mainly from the brittle nature of glass, and glass substrates with copper and polymer re-distribution layers can suffer brittle fracture after dicing processes. This paper demonstrates three methods to prevent cracking induced by redistribution layer (RDL) stress and dicing defect in glass substrates for RDL build-up up to 90 mu m polymer and 40 mu m copper. These methods are edge coating, two-step dicing, and laser ablation dicing. Edge coating is a protective layer of polymer located on the diced edge of the glass substrate. After dicing, edge coating puts the glass in compression and prevents moisture from reaching the glass and, in turn, prevents the glass cracking from RDL stresses and dicing defects. In two-step dicing, the first step is used to ablate the RDL using a laser and the second step is used for blade dicing within the ablated region to singulate the glass. The resulting structure from such a dicing process reduces stress at the free glass edge, ensuring that the glass does not crack during dicing. Two-step dicing also allows for thicker RDL build-ups while ensuring no glass cracking occurs from dicing defects. Laser ablation dicing uses a CO2 laser to singulate the glass panel into individual substrates instead of blade dicing, which reduces the dicing defect size and creates a heat affected zone. Use of laser ablation dicing allows for thicker RDL build-ups with minimal process change when compared to blade dicing.

关键词： Glass substrate fracture mechanics finite-element methods

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Trefftz finite elements for electromagnetics

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 2002年第5期50卷 1328-1339页

作者： Olegovich, Y Innoveda Inc Camarillo CA 93010 USA

It is shown that the method of minimum autonomous blocks (MAB) of Nikol'skii and Nikol'skaia can be reformulated as the Trefftz finite-element method. Solutions of Maxwell's equations in form of plane waves are used to represent fields inside a finite element. Their projections on a set of basis functions on the surface of the element are used to obtain a descriptor of the element in form of an admittance matrix. It is shown that a point-matching projection procedure gives the frequency-domain transmission-line-matrix formulation and Galerkin-type projection leads to the MAB formulation. Admittance matrix representation of the descriptors of the elements makes it possible to use a finite-element-type global matrix assembling procedure and a sparse matrix solver.

关键词： finite-element methods transmission-line-matrix methods

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Evaluating Singular, Near-Singular, and Non-Singular Integrals on Curvilinear elements

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ELECTROMAGNETICS 2014年第3-4期34卷 307-327页

作者： Wilton, Donald R. Vipiana, Francesca Johnson, William A. Univ Houston Dept Elect & Comp Engn Houston TX 77204 USA Politecn Torino Dept Elect & Telecommun Antenna & EMC Lab LACE Turin Italy

Recent progress in developing accurate quadrature rules for singular integrals is potentially very useful in higher-order electromagnetic modeling. It is often not so clear, however, how methods developed for linear elements can be applied to curvilinear elements. To this end, a detailed implementation of schemes is presented for handling numerical quadrature for modeling curvilinear elements in both integral and differential equation formulations. It is shown that the introduction of a tangent element not only incorporates fundamental geometry information about the surface and is useful in describing bases defined on the element, but it also facilitates the handling of quadrature rules, especially for singular or near-singular integrals. Detailed treatment of the use of singularity cancelation methods on curvilinear elements is given, and it is shown how singularity cancelation quadrature rules derived on linear elements apply to curvilinear elements.

关键词： differential equations integral equations finite-element methods moment methods numerical integration

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Characterization of flux rotation and of the ensuing core losses in the stator of induction motors

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IEEE TRANSACTIONS ON ENERGY CONVERSION 2008年第1期23卷 34-41页

作者： Diaz, Guzman Gonzalez-Moran, Cristina Arboleya, Pablo Gomez-Aleixandre, Javier Univ Oviedo Asturias 33204 Spain

A literature survey reveals that the study of rotational power losses in stator cores has been conventionally performed by means of finite-element analysis. This paper proposes an alternative characterization of rotational power losses in the tooth roots-a region that has been long known as a seat of flux rotation-relating some geometric dimensions to the values of flux density of interest to compute the rotational losses over the region. A simplified computation of maximum and minimum flux densities is proposed based on the trajectories of flux at singular time intervals. This enables the calculation using analytical expressions. For that reason, the proposed approach improves the power losses analysis in early design stages, showing the impact of projected geometries on the total loss estimate. Moreover, it consequently provides a tool to include the rotational losses estimate within optimization-oriented iterative searches.

关键词： finite-element methods induction motors magnetic losses

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