• 대한기계학회논문집A
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• 제21권3호
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• pp.447-456
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• 1997

Stress intensity factor of semi-infinite parallel crack propagation with constant velocity in dissimilar orthotropic strip under out-of-plane clamped desplacement is investigated. Using Fourier integral transforms the boundary value problem is derived by a pair of dual integral equation and finally reduced to a single Wiener-Hopf equation. By applying Wiener-Hopf technique the equation is solved. Applying this result the asymptotic stress fields near the crack tip are determined, from which the stress intensity factor is obtained in closed form. The more the ratio of anisotropy or the ratio of bi-material shear modulus increase in the main material including the crack, the more the stress intensity factor increases. Discontinuity in the stress intensity factor is found as the parallel crack approaches the interface. In special case, the results of isotropic materials agree well with those by the previous researchers.

• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.185-200
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• 2004

A stochastic optimal LQR control problem under some integral quadratic (IQ) constraints is studied, with cross terms in both the cost and the constraint functionals, allowing all the control weighting matrices being indefinite. Sufficient conditions for the well-posedness of this problem are given. When these conditions are satisfied, the optimal control is explicitly derived via dual theory.

• Journal of Mechanical Science and Technology
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• 제17권6호
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• pp.854-859
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• 2003

In this paper, we examine the singular stresses and electric fields in a functionally graded piezoelectric ceramic strip containing an eccentric crack off the center line under anti-plane shear loading with the theory of linear piezoelectricity. It is assumed that the properties of the functionally graded piezoelectric ceramic strip vary continuously along the thickness. 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.

• 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.

• 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.

• 대한기계학회논문집A
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• 제26권10호
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• pp.2172-2179
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• 2002

In this paper, we examine the dynamic electromechanical behavior of an edge crack in a piezoelectric ceramic layer bonded between two elastic layers under the combined anti-plane mechanical shear and in-plane electric transient loadings. We adopted both the permeable and impermeable crack boundary conditions. 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 dynamic energy release rate are presented to show the dependences upon the geometry, material combination, electromechanical coupling coefficient and electric field.

• 대한기계학회논문집
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• 제15권5호
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• pp.1611-1619
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• 1991

본 연구에서는 Hilton과 Sih의 경우를 확장 적용하여 Fig. 1(b)와 같이 탄성 층 내부에 존재하는 중앙균열선단의 응력확대계수 산출을 위하여 균열부위를 제외하고 는 섬유층과 레진층이 완전히 접착되었다고 가정한 모델을 다음과 같이 설정하였다. 중앙균열을 내재하고 있는 복합재료의 역학적 거동을 해석하기 위하여, 접착레진을 주 로하는 층(resin rich layer)을 중심으로 하여 상하 각1개의 섬유 (fiber)층과 균질한 특성을 갖는 복합재료의 층으로 단순화 하였으며, 이러한 단순화는 적층재에서의 균열 주위의 국부응력을 해석하기 위한 것으로서 복합재료는 레진층이나 섬유층에 비하여 매우 두꺼우므로 반무한체로 이상화 하였다. 선형탄성 이론에 의하여 혼합 경계조건 문제(mixed boundary value problem)로 부터 제2종 Fredholm적분방정식(fredholm int- egral equation of a second kind)을 유도하였으며 수치해석적인 방법에 의하여 응력 확대계수를 구하였다.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1986년도 하계학술대회논문집
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• pp.591-594
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• 1986

An asymptotic solution of electro-magnetic waves diffracted by a dielectric wedge of the angle larger than $180^{\circ}$ is obtained in case of the incidence of a E-polarized plane wave. Based on the dual integral equation in the spectral domain, physical optics approximation is supplemented by correction currents distributed along the interfaces. Those currents are expanded in a series of Bessel functions, known as Neumann's expansion of which fractional order is chosen to satisfy the static edge condition as the limiting value of dynamic case. Numerical results of edge diffraction patterns and field patterns are presented for some typical cases.

• 대한전자공학회논문지
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• 제25권8호
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• pp.874-883
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• 1988

A complete form of physical optics solution to the diffraction of electromagnetic waves by a dielectric wedge with arbitrary dielectric constant and general wedge angle is obtained for an incident plane wave with any angle. Based on the formulation of dual integral equation in the spectral domain, the physical optics solution is constructed by sum of geometrical optics term including multiple reflection inside the wedge and the edge diffracted field, of which diffraction functions are represented in a quite simple form as series of cotangent functions weighted by the Fresnel reflection coefficients. Since diffraction patterns of physical optics are discontinous at dielectric interfaces, Part II and III of these three companion papers will be concerned with correction to the error of the physical optics approximation.

• Structural Engineering and Mechanics
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• 제58권4호
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• pp.613-625
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• 2016

Contact interaction of a beam (flexible element) with an elastic half-plane is considered, when a soft inhomogeneous (functionally graded) interlayer is present between them. The beam is bent under the action of a distributed load applied to the surface and a reaction of the elastic interlayer and the half-space. Solution of the contact problem is obtained for different values of thickness and parameters of inhomogeneity of the layer. The interlayer is assumed to be significantly softer than the underlying half-plane; case of 100 times difference in Young's moduli is considered as an example. The influence of the interlayer thickness and gradient of elastic properties on the distribution of the contact stresses under the beam is studied.