• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권3호
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• pp.257-268
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• 2010

We investigate the existence of the following Dirichlet boundary value problem $({\mid}u'\mid^{p-2}u')'\;+\;(p\;-\;1)[\alpha{\mid}u^+\mid^{p-2}u^+\;-\;\beta{\mid}u^-\mid^{p-2}u^-]$ = (p - 1)h(t), u(0) = u(T) = 0, where p > 1, $\alpha$ > 0, $\beta$ > 0 and ${\alpha}^{-\frac{1}{p}}\;+\;{\beta}^{-\frac{1}{p}}\;=\;2$, $T\;=\;{\pi}_p/{\alpha}^{\frac{1}{p}}$, ${\pi}_p\;=\; \frac{2{\pi}}{p\;sin(\pi/p)}$ and $h\;{\in}\;L^{\infty}$(0,T). The results of this paper generalize some early results obtained in [8] and [9]. Moreover, the method used in this paper is elementary and new.

• Structural Engineering and Mechanics
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• 제18권6호
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• pp.759-768
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• 2004

The torsion of a penny-shaped crack in a transversely isotropic strip is investigated in this paper. The shear moduli are functionally graded in such a way that the mathematics is tractable. Hankel transform is used to reduce the problem to solving a Fredholm integral equation. The crack tip stress field is obtained by taking the asymptotic behavior of Bessel function into account. The effects of material property parameters and geometry criterion on the stress intensity factor are investigated. Numerical results show that increasing the shear moduli's gradient and/or increasing the shear modulus in a direction perpendicular to the crack surface can suppress crack initiation and growth, and that the stress intensity factor varies little with the increasing of the strip's height.

• 대한수학회논문집
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• 제28권3호
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• pp.487-500
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• 2013

In this paper we provide a brief introduction to the continuity of approximate point spectrum on the algebra B(X), using basic properties of Fredholm operators and the SVEP condition. Also, we give an example showing that in general it not holds that if the spectrum is continuous an operator T, then for each ${\lambda}{\in}{\sigma}_{s-F}(T){\setminus}\overline{{\rho}^{\pm}_{s-F}(T)}$ and ${\in}$ > 0, the ball $B({\lambda},{\in})$ contains a component of ${\sigma}_{s-F}(T)$, contrary to what has been announced in [J. B. Conway and B. B. Morrel, Operators that are points of spectral continuity II, Integral Equations Operator Theory 4 (1981), 459-503] page 462.

• Journal of Mechanical Science and Technology
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• 제18권3호
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• pp.419-431
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• 2004

The dynamic response of a cracked functionally graded piezoelectric material (FGPM) under transient anti-plane shear mechanical and in-plane electrical loads is investigated in the present paper. It is assumed that the electroelastic material properties of the FGPM vary smoothly in the form of an exponential function along the thickness of the strip. The analysis is conducted on the basis of the unified (or natural) crack boundary condition which is related to the ellipsoidal crack parameters. By using the Laplace and Fourier transforms, the problem is reduced to the solutions of Fredholm integral equations of the second kind. Numerical results for the stress intensity factor and crack sliding displacement are presented to show the influences of the elliptic crack parameters, the electric field, FGPM gradation, crack length, and electromechanical coupling coefficient.

• Journal of Mechanical Science and Technology
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• 제15권1호
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• pp.61-65
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• 2001

Using the theory of linear piezoelectricity, the problem of two layered strip with a piezoelectric ceramic bonded to an elastic material containing a finite interface crack is considered. The out-of-plane mechanical and in-plane electrical loadings are simultaneously applied to the strip. Fourier transforms are used to reduce the problem to a pair of dual integral equations, which is then expressed in terms of a Fredholm integral equation of the second kind. The stress intensity factor is determined, and numerical analyses for several materials are performed and discussed.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 춘계학술대회논문집A
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• pp.304-309
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• 2001

In this paper, we consider the dynamic electromechanical behavior of an eccentric Yoffe permeable crack in a piezoelectric ceramic strip sandwiched between two elastic materials under the combined anti-plane mechanical shear and in-plane electrical loadings. 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. The initial crack propagation orientation for PZT-5H piezoceramics is predicted by maximum energy release rate criterion.

• Journal of Mechanical Science and Technology
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• 제15권1호
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• pp.21-25
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• 2001

We consider the problem of determining the singular stresses and electric fields in a piezoelectric ceramic strip containing a Griffith eccentric crack off the center line 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, and the influences of the electric fields for piezoelectric ceramics are discussed.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제9권1호
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• pp.63-77
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• 2005

The Dirichlet-Neumann problem for the dissipative Helmholtz equation in a connected plane region bounded by closed curves and containing cuts is studied. The Neumann condition is given on the closed curves, while the Dirichlet condition is specified on the cuts. The existence of a classical solution is proved by potential theory. The integral representation of the unique classical solution is obtained. The problem is reduced to the Fredholm equation of the second kind and index zero, which is uniquely solvable. Our results hold for both interior and exterior domains.

• Structural Engineering and Mechanics
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• 제6권4호
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• pp.457-466
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• 1998

The dynamic response of an elastic torsion shaft of revolution is analysed by the Line-Loaded Integral Equation Method (LLIEM). A "Dynamic Point Ring Couple" (DPRC) is used as a fictitious fundamental load and is distributed in an elastic space along the axis of the shaft outside the shaft occupation. According to the boundary condition, our problem is reduced to a 1-D Fredholm integral equation of the first kind, which is simpler for solving than that of a 2-D singular integral equation of the same kind obtanied by Boundary Element Method (BEM), for steady periodically varied loading. Numerical example of a shaft with quadratic generator under sinusoidal type of torque is given. Formulas for stresses and dangerous frequency are mentioned.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2004년도 춘계학술대회
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• pp.1749-1754
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• 2004

In order to measure non-intrusively velocity profile in liquid metal flow, a modified electromagnetic flowmeter was designed, which was based on electromagnetic tomography technique. Under the assumption that flow is fully-developed, axisymmetric and rectilinear, the velocity profile was reconstructed after the flowmeter equation, the first kind of Fredholm integration equation, was linearized. In reconstruction process Tikhonov regularization method with regularization parameter was used. The reconstructed velocity profile had the nearly same as turbulent flow profile which was approximately represented as log law. In addition, flowmeter output for a fixed magnet rotation angle was linearly proportional to flow rate. When magnet rotation angle was $54^{\circ}$, axisymmetric weight function was nearly uniform so that the flowmeter gives a constant signal for any fully-developed, axisymmetric and rectilinear profile with a constant flow rate.