The method of inner boundary conditions and its applications. A new approach to the numerical solution of boundary integral equations

AbstractIn this paper we consider linear systems with dense-matrices which arise from numerical solution of boundary integral equations. Such matrices can be well-approximated with ℋ

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Hypersingular Boundary Integral Equations: A New Approach to Their Numerical Treatment

Boundary Integral Methods ◽

10.1007/978-3-642-85463-7_20 ◽

1991 ◽

pp. 211-220 ◽

Cited By ~ 11

Author(s):

M. Guiggiani ◽

G. Krishnasamy ◽

F. J. Rizzo ◽

T. J. Rudolphi

Keyword(s):

Integral Equations ◽

Boundary Integral Equations ◽

Boundary Integral ◽

Numerical Treatment ◽

New Approach

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Boundary Integral Equations for an Anisotropic Bimaterial with Thermally Imperfect Interface and Internal Inhomogeneities

Acta Mechanica et Automatica ◽

10.1515/ama-2016-0012 ◽

2016 ◽

Vol 10 (1) ◽

pp. 66-74 ◽

Cited By ~ 1

Author(s):

Heorhiy Sulym ◽

Iaroslav Pasternak ◽

Mykhailo Tomashivskyy

Keyword(s):

Integral Equations ◽

Boundary Integral Equations ◽

Imperfect Interface ◽

Boundary Integral ◽

Bimaterial Interface ◽

Intensity Factors ◽

New Approach ◽

Adhesive Layers ◽

Type Integral ◽

Anisotropic Bimaterial

Abstract This paper studies a thermoelastic anisotropic bimaterial with thermally imperfect interface and internal inhomogeneities. Based on the complex variable calculus and the extended Stroh formalism a new approach is proposed for obtaining the Somigliana type integral formulae and corresponding boundary integral equations for a thermoelastic bimaterial consisting of two half-spaces with different thermal and mechanical properties. The half-spaces are bonded together with mechanically perfect and thermally imperfect interface, which model interfacial adhesive layers present in bimaterial solids. Obtained integral equations are introduced into the modified boundary element method that allows solving arbitrary 2D thermoelacticity problems for anisotropic bimaterial solids with imperfect thin thermo-resistant inter-facial layer, which half-spaces contain cracks and thin inclusions. Presented numerical examples show the effect of thermal resistance of the bimaterial interface on the stress intensity factors at thin inhomogeneities.

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Vibration of a Simply Supported L-Shaped Plate

Journal of Vibration and Acoustics ◽

10.1115/1.2889746 ◽

1997 ◽

Vol 119 (3) ◽

pp. 464-467 ◽

Cited By ~ 2

Author(s):

R. Solecki

Keyword(s):

Boundary Conditions ◽

Integral Equations ◽

Natural Vibration ◽

Boundary Integral Equations ◽

Rectangular Domain ◽

Boundary Integral ◽

Theoretical Development ◽

Natural Vibrations ◽

Simply Supported ◽

Discontinuous Functions

Recently Solecki (1996) has shown that a differential equation for vibration of a rectangular plate with a cutout can be reduced to boundary integral equations. This was accomplished by filling the cutout with a “patch” made of the same material as the rest of the plate and separated from it by an infinitesimal gap. Thanks to this procedure it was possible to apply finite Fourier transformation of discontinuous functions in a rectangular domain. Subsequent application of the available boundary conditions led to a system of boundary integral equations. A plate simply supported along the perimeter, and fixed along the cutout (an L-shaped plate), was analyzed as an example. The general solution obtained by Solecki (1996) serves here to determine the frequencies of natural vibration of a L-shaped plate simply supported all around its perimeter. This problem is, however, more complicated than the previous example: to satisfy the boundary conditions an infinite series depending on discontinuous functions must be differentiated. The theoretical development is illustrated by numerical values of the frequencies of the natural vibrations of a square plate with a square cutout. The results are compared with the results obtained using finite elements method.

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