• Journal of the Korean Institute of Telematics and Electronics D
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• v.35D no.6
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• pp.8-14
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• 1998

The derivation of the dual integral equation in the spectral domain, which has total fields of the interfaces as unknowns, is investigated. It is analytically shown that the derivation of the dual integral equation is equivalent to deriving the Helmholtz-Kirchhoff integral equation from the Wiener-Hopf integral equation.

• Proceedings of the KIEE Conference
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• 1985.07a
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• pp.344-347
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• 1985

Hew dual integral equation for electromagnetic field scattered by an arbitrary dielectric wedge is formulated. In order to check the validity and physical meaning of the formulated equation, it is applied to the well-known case which is the diffraction by a perfectly conducting wedge.

• Journal of the Korean Institute of Telematics and Electronics D
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• v.35D no.12
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• pp.21-29
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• 1998

Dual integral equation in the spectral domain is derived for an arbitrary angled perfect conducting wedge with E-polarized plane wave incidence. Analytic integration of the dual integral equation in the spectral domain with the exact boundary fields of the perfect conducting wedge, the well known series solution, gives the exact asymptotic solution. The validity of the integration is assured by showing that analytic integration gives the null fields in the complementary region.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.2
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• pp.243-253
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• 1999

The dual reciprocity boundary element method (DRBEM) is used to solve the Graetz problem of laminar flow inside circular duct. In this method the domain integral tenn of boundary integral equation resulting from source term of governing equation is transformed into equivalent boundary-only integrals by using the radial basis interpolation function, and therefore complicate domain discretization procedure Is completely removed. Velocity profile is obtained by solving the momentum equation first and then, using this velocities as Input data, energy equation Is solved to get the temperature profile by advancing from duct entrance through the axial direction marching scheme. DRBEM solution is tested for the uniform temperature and heat flux boundary condition cases. Local Nusselt number, mixed mean temperature and temperature profile inside duct at each dimensionless axial location are obtained and compared with exact solutions for the accuracy test Solutions arc in good agreement at the entry region as well as fully developed region of circular duct, and their accuracy are verified from error analysis.

• Journal of the Korean Institute of Telematics and Electronics D
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• v.36D no.1
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• pp.22-28
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• 1999

An exact asymptotic solution for a perfect conducting wedge with H-polarized plane wave incidence is analytically derived by substituting the exact boundary fields of the perfeet conducting wedge, the well known series solution, into the dual integral exquation in the spectral domain. The validity of the derivation is assured by showing that the analytic integration gives the null fields in the complementary region. The merits taking the dual integral equation for derivation of an asymptotic solution for a perfect conduction wedge is discussed.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.3
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• pp.901-909
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• 1996

A model is constructed to evaluate the stress intensity factors(SIFs) for composites with an interlaminar crack subjected to as arbitrary crack surface loading. A mixed boundary value problem is formulated by Fourier integral transform method and a Fredholm integral equation of the second kind is derived. The integral equation is solved numerically and the mode I and II SIFs are evaluated for various shear modulus ratios between each layer, crack length to layer thickness, each term of crack surface polynomial loading and the number of layers. The mode I and II SIFs for the E- glass/epoxy composites as well as the hybrid composites are also evaluated.

• Structural Engineering and Mechanics
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• v.57 no.2
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• pp.327-355
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• 2016

A new analytical derivation of the elastodynamic point load solutions for an isotropic multi-layered half-space is presented by means of the precise integration method (PIM) and the approach of dual vector. The time-harmonic external load is prescribed either on the external boundary or in the interior of the solid medium. Starting with the axisymmetric governing motion equations in a cylindrical coordinate system, a second order ordinary differential matrix equation can be gained by making use of the Hankel integral transform. Employing the technique of dual vector, the second order ordinary differential matrix equation can be simplified into a first-order one. The approach of PIM is implemented to obtain the solutions of the ordinary differential matrix equation in the Hankel integral transform domain. The PIM is a highly accurate algorithm to solve sets of first-order ordinary differential equations and any desired accuracy of the dynamic point load solutions can be achieved. The numerical simulation is based on algebraic matrix operation. As a result, the computational effort is reduced to a great extent and the computation is unconditionally stable. Selected numerical trials are given to validate the accuracy and applicability of the proposed approach. More examples are discussed to portray the dependence of the load-displacement response on the isotropic parameters of the multi-layered media, the depth of external load and the frequency of excitation.

• Composites Research
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• v.15 no.4
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• pp.37-42
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• 2002

We consider the problem of determining the singular stresses and electric fields in a functionally graded piezoelectric ceramic strip containing a Griffith eccentric crack under anti-plane shear loading with the theory of linear piezoelectricity. Fourier transforms are used to reduce the problem to the solution of two pairs of dual integral equations, which are then expressed to a Fredholm integral equation of the second kind. Numerical values on the stress intensity factor and the energy release rate are obtained.

• Structural Engineering and Mechanics
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• v.27 no.5
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• pp.609-623
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• 2007

The problem of a semi-infinite magneto-electro-elastically impermeable mode-III crack in a magneto-electro-elastic material is considered under the action of impact loads. For the case when a pair of concentrated anti-plane shear impacts, electric displacement and magnetic induction impacts are exerted symmetrically on the upper and lower surfaces of the crack, the magneto-electro-elastic field ahead of the crack tip is determined in explicit form. The dynamic intensity factors and dynamic energy density factor are obtained. The method adopted is to reduce the mixed initial-boundary value problem, by using the Laplace and Fourier transforms, into three simultaneous dual integral equations, one of which is converted into an Abel's integral equation and the others into a singular integral equation with Cauchy kernel. Based on the obtained fundamental solutions of point impact loads, the solutions of two kinds of different loading cases are evaluated by integration. For some particular cases, the present results reduce to the previous results.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2010.04a
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• pp.459-464
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• 2010

The dynamic propagation of an interface crack between two dissimilar functionally graded layers under anti-plane shear is analyzed using the integral transform method. The properties of the functionally graded layers vary continuously along the thickness. A constant velocity Yoffe-type moving crack is considered. Fourier transform is used to reduce the problem to a dual integral equation, which is then expressed to a Fredholm integral equation of the second kind. Numerical values on the dynamic energy release rate (DERR) are presented. Followings are helpful to increase of the resistance of the interface crack propagation of FGM: a) increase of the gradient of material properties; b) increase of the material properties from the interface to the upper and lower free surface; c) increase of the thickness of FGM layer. The DERR increases or decreases with increase of the crack moving velocity.