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1
Content available Boundary integral solution for a class of fourth-order two-point boundary value problems
Al-Gahtani H. J.
Journal of Applied Mathematics and Computational Mechanics
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2016
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Vol. 15, nr 3
5--13
EN
In this paper, a boundary integral method is proposed for the solution of a class of fourth-order two-boundary value problems described by the equation yiv+P(x, y, y’, y’’, y’’’) = 0, x ∈ ( 0,L), where P is a polynomial function of its arguments. The differential equation is cast in an integral form and the weighted residual technique is used to generate the corresponding boundary integral equations. The boundary integral equations are then, solved by expressing the dependent variable, y, in terms of a power series. The proposed method is tested through four examples to show the applicability of the method to solve a wide range of fourth-order differential equations including the nonlinear ones.
2
Content available remote Plasmon excitation in periodic multilayers: modeling by boundary integral equations
Zidek A, Vlcek J, Krcek J
Optica Applicata
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2012
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Vol. 42, nr 4
683--697
EN
Optical diffraction is one of the few exploited applications of boundary integral equations. In this paper, a numerical model based on boundary integral equations (BIE) is applied to a periodic multilayer. We present possible implementations of a derived algorithm that enables solution, e.g., for over-coated profiles. We give our attention to optical systems producing plasmon waves, for which we study the influence of several structural parameters on the diffraction response. The results are compared with the classical rigorous coupled waves method (RCWM) method, and, the case of non-smooth interface is discussed.
3
Content available Wedge functions applied to 2D magnetostatic problems
Huijer E., Karaki S.H.
Archives of Electrical Engineering
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2011
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Vol. 60, nr 4
519-529
EN
In this paper the application of so called wedge functions is presented to solve two-dimensional simple geometries of magnetostatic and electrostatic problems, e.g. rectangles of varying aspect ratio and with different values of the magnetic permeability μ. Such problems require the use of surface charge density, or segment source, functions of the form ρs = σa-1, where the power parameters, a, have special fractional values. A methodology is presented to determine these special values of a and use them in segment sources on simple geometries, i.e. rectangles of varying aspect ratio, and with different values of the magnetic permeability μ. Wedge solutions are obtained by coupling the strength coefficients of source segments of the same power around an edge. These surface source functions have been used in the analysis of conducting and infinite permeability structures. Here we apply such functions in a boundary integral analysis method to problems having regions of finite permeability.
4
Content available Boundary-integral model of permanent magnet of a tube segment as shape
Pawluk K., Sulima R.
Archives of Electrical Engineering
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2011
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Vol. 60, nr 4
413-432
EN
The magnetic field due to a permanent magnet of a tube-side segment as shape and of radial-oriented magnetization is considered. Such a sheet modelling a single pole of the magnet is used to express the suitable contribution to magnetic quantities. A boundary-integral approach is applied that is based on a virtual scalar quantity attributed to the magnet pole. Such an approach leads to express analytically the scalar magnetic potential and the magnetic flux density by means of the elliptic integrals. Numerical examples of the computed fields are given. The general idea of the presented approach is mainly directed towards designing the magnetic field within the air gap of electric machines with permanent magnets as an excitation source. Other technical structures with permanent magnets may be a subject of this approach as well.
5
Content available remote Metoda elementów skończonych dla początkujących
Witkowski J.
Prace Naukowe Akademii im. Jana Długosza w Częstochowie. Edukacja Techniczna i Informatyczna
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2009
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T. 4
9-201
EN
The paper presents approximate methods of solving differentia equations, dealing mostly with practical aspects FEM such as principles of formulating finite elements and super-elements, transforming their mechanical and thermo-mechanical properties. The paper presents also numerical algorithms of FEM including non-linear problems. All examples of application refer to machine design. The finite elements in a set included in the paper relate to the same problems.
6
Content available remote Permanent magnet field calculated by the boundary-integral approach
Pawluk K.
Archives of Electrical Engineering
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2008
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Vol. 57, nr 3-4
257-276
EN
Analytical or quasi-analytical algorithms of the boundary-integral approach to determine the magnetic field of permanent magnets are given. The method is based on a virtual scalar quantity attributed to the magnet pole face. Orthorhombic and cylindrical magnets are considered. The inverse trigonometric and natural logarithm functions appear in the algorithms for orthorhombic magnets and the integrals of Lipschitz-Hankel type having their elliptic-integral equivalence are used to form the algorithms for cylindrical magnets. If the homogeneous magnetisation cannot be assumed for the magnet the procedure of the axial or radial discretization is proposed with the corresponding equations. Some choice of computing results achieved by the author's test programs are presented.
PL
W artykule zaprezentowano podejście całkowo-brzegowe do obliczanie pola magnetycznego magnesów trwałych. Metoda opiera się na fikcyjnej wielkości skalarnej, którą przyporządkowuje się powierzchniom biegunowym magnesu. Rozpatrzono magnesy prostopadtościenne i cylindryczne. W algorytmach dotyczących magnesów prostopadlościennych występują odwrotne funkcje trygonometryczne i logarytmy naturalne, a w przypadku magnesów cylindrycznych mamy do czynienia z całkami Lipschitza-Hankela, które mają swoje odpowiedniki w całkach eliptycznych. Wobec magnesów, co do których nie można założyć równomiernego namagnesowania, zaproponowano prostą dyskretyzację, osiową lub promieniową i podano odpowiednie równania iteracyjne. Zaprezentowano wyniki kilku obliczeń komputerowych wykonanych przez autora za pomocą specjalnych programów testowych.
7
Content available remote Permanent magnet within a ferromagnetic structure - boundary-integral model and its experimental verification
Pawluk K., Życki Z.
Archives of Electrical Engineering
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2006
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Vol. 55, nr 3-4
273-288
EN
A permanent magnet fixed (with two small air-gap distances) between two ferromagnetic walls was considered as a basic boundary-integral conceptual model that may be useful to analyse the magnetic field in electric machines with magneto-static excitation. Analytical algorithms based on the boundary-integral approach of the magneto-static field are presented. An original magnetic structure was designed and assembled. Experimental tests verifying the main idea of the boundary-integral model were performed on the structure.
PL
Rozpatrzono matematyczny model calkowo-brzegowy magnesu trwałego usytuowanego w magnetowodzie ferromagnetycznym, z zachowaniem dwóch małych szczelin powietrznych. Model ten jest ukierunkowany na analizę pola magnetycznego w maszynach elektrycznych ze wzbudzeniem magnetostatycznym. Podano analityczne algorytmy wynikające z całkowo-brzegowej metody obliczania pola wzbudzanego magnesem trwałym. W celu eksperymentalnego zweryfikowania podejścia calkowo-brzegowego przeprowadzono szereg pomiarów na specjalnie wykonanej strukturze z magnesami trwałymi.
8
Content available remote Boundary integral method for an oscillatory Stokes flow past a solid particle
Kohr M., Pop I.
International Journal of Applied Mechanics and Engineering
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2003
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Vol. 8, no 4
603-620
EN
In this paper, we present a boundary integral method in order to determine the oscillatory Stokes flow due to translational or rotational oscillations of a solid particle in an unbounded viscous incompressible fluid. As an application of this method, we study both cases of small-and high-frequency oscillations. Finally, we give some numerical results in the case of transverse oscillations of a prolate spheroid.
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