• 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.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.305-320
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• 2012

In this paper, we study a class of integral boundary value problems for fractional differential equations. By using some fixed point theorems, the results of existence of at least three positive solutions for the boundary value problems are obtained.

• Journal of Mechanical Science and Technology
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• v.14 no.8
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• pp.845-850
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• 2000

We consider the problem of determining the singular stresses and electric fields in a piezoelectric ceramic strip containing a Griffith crack under in-plane normal loading within the framework of linear piezoelectricity. The potential theory method and Fourier transforms are used to reduce the problem to the solution of dual integral equations, which are then expressed to a Fredholm integral equation of the second kind. Numerical values on the field intensity factors are obtained, and the influences of the electric fields for PZT-6B piezoelectric ceramic are discussed.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.5
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• pp.838-848
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• 1992

The objective of the study is to provide a theoretical tools for analyzing the fracture of leyered composites with a center crack. It is assumed that the composite is composed of successive accumulation of the fiber layer and resin layer with the fiber layer being perfectly bonded to the resin layer except the region of a center crack. In-plane shear loading (Mode II) and the anti-plane shear loading (Mode III) are considered separately. Boundary value problems are formulated by using a plane theory of elasticity and governing equations are reduced to a Fredholm integral equation of a second kind. The equation is solved numerically and the stress intensity factors are obtained. The normalized Mode II and Mode III stress intensity factors are evaluated for various combinations of material properties and for various geometrical parametes.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.1
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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.

• Journal of Mechanical Science and Technology
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• v.17 no.6
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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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• v.15 no.1
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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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• v.15 no.1
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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.

• International Journal of Naval Architecture and Ocean Engineering
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• v.6 no.1
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• pp.175-185
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• 2014

This study presents the prediction of propagated wave profiles using the wave information at a fixed point. The fixed points can be fixed in either space or time. Wave information based on the linear wave theory can be expressed by Fredholm integral equation of the first kinds. The discretized matrix equation is usually an ill-conditioned system. Tikhonov regularization was applied to the ill-conditioned system to overcome instability of the system. The regularization parameter is calculated by using the L-curve method. The numerical results are compared with the experimental results. The analysis of the numerical computation shows that the Tikhonov regularization method is useful.

• Bulletin of the Society of Naval Architects of Korea
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• v.19 no.1
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• pp.23-32
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• 1982

Herein the motion of a freely-floating sphere in a water of finite depth is analysed within the framework of a linear potential theory. A velocity potential describing fluid motion is generated by distributing pulsating sources and dipoles on the immersed surface of the sphere, without introducing an inner flow model. The potential becomes the solution of an integral equation of Fredholm's second type. In the light of the vertical axisymmetry of the flow, surface integrals reduce to line integrals, which are approximated by summation of the products of the integrand and the length of segments along the contour. Following this computational scheme the diffraction potential and the radiation potential are determined from the same algorithm of solving a set of simultaneous linear equations. Upon knowing values of the potentials hydrodynamic forces such as added mass, hydrodynamic damping and wave exciting forces are evaluated by the integrating pressure over the immersed surface of the sphere. It is found in the case of finite water depth that the hydrodynamic forces are much different from the corresponding ones in deep water. Accordingly motion response of the sphere in a water of finite depth displays a particular behavior both in a amplitude and phase.