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 ...
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We describe an algorithm for optimising the mesh in the least-squares finiteelement discretisation of first-order systems of partial differential equations. The key feature of the method is that the optimisation proc...
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We describe an algorithm for optimising the mesh in the least-squares finiteelement 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.
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 ...
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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.
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 e...
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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.
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 mi...
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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.
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...
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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.
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 smoot...
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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.
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 wave...
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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 finiteelement. 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.
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 e...
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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.
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 rotat...
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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.
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