• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.41-52
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• 1998

A volume integral equation method and a mixed volume and boundary integral equation method are presented for the solution of plane elastostatic problems in solids containing orthotropic inclusions and voids. The detailed analysis of the displacement and stress fields are developed for orthotropic cylindrical and elliptic-cylindrical inclusions and voids. The accuracy and effectiveness of the new methods are examined through comparison with results obtained from analytical and boundary integral equation methods. Through the analysis of plane elastostatic problems in unbounded isotropic matrix containing orthotropic inclusions and voids, it is established that these new methods are very accurate and effective for solving plane elastostatic and elastodynamic problems in unbounded solids containing general anisotropic inclusions and voids or cracks.

• Structural Engineering and Mechanics
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• v.19 no.4
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• pp.425-440
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• 2005

In this paper, the behavior of a crack between two half-planes of functionally graded materials subjected to arbitrary tractions is resolved using a somewhat different approach, named the Schmidt method. To make the analysis tractable, it is assumed that the Poisson's ratios of the mediums are constants and the shear modulus vary exponentially with coordinate parallel to the crack. By use of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations in which the unknown variables are the jumps of the displacements across the crack surfaces. To solve the dual integral equations, the jumps of the displacements across the crack surfaces are expanded in a series of Jacobi polynomials. This process is quite different from those adopted in previous works. Numerical examples are provided to show the effect of the crack length and the parameters describing the functionally graded materials upon the stress intensity factor of the crack. It can be shown that the results of the present paper are the same as ones of the same problem that was solved by the singular integral equation method. As a special case, when the material properties are not continuous through the crack line, an approximate solution of the interface crack problem is also given under the assumption that the effect of the crack surface interference very near the crack tips is negligible. It is found that the stress singularities of the present interface crack solution are the same as ones of the ordinary crack in homogenous materials.

• Proceedings of the IEEK Conference
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• 1998.10a
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• pp.375-378
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• 1998

Scattering of TE waves by a periodic conducting surface with dielectric cover is considered. A method for the aalysis of scattering from periodic structures based on the numerical solution of the integral equations is further developed. Using periodicity (Floquet's theorem), the range of the integral equations is reduced to a single period where the kernels are the Green's functions for periodic arrays. The numerical solution of the intergral equations is obtained using the method of moments. From numerical results for the reflected power the effects of surface profile shape, period-to-depth ratio, and cover permittivity on the scattering behaviors are examined.

• East Asian mathematical journal
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• v.27 no.3
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• pp.319-337
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• 2011

We approximate a locally unique solution of a nonlinear equation in a Banach space setting using an inexact two-step Newton-type method. It turn out that under our new idea of recurrent functions, our semilocal analysis provides tighter error bounds than before, and in many interesting cases, weaker sufficient convergence conditions. Applications including the solution of nonlinear Chandrasekhar-type integral equations appearing in radiative transfer and two point boundary value problems are also provided in this study.

• Journal of the Korean Institute of Telematics and Electronics
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• v.22 no.5
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• pp.83-86
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• 1985

An alternative technique (or the numerical solution of Fredholm integral equations of second kind is presented. The approximate solution is obtained by fitting the data in mixed form at knots in the region of the problem. To decrease the error in the numerical solution, cubic B-spline functions which are twice continuously differentiable at knots are employed as basis function. For a given example, the results of this technique are compared with those of Moment method employing pulse functions for basis function and delta functions for test function and found to br in good agreement.

• Proceedings of the KIEE Conference
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• 1998.07a
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• pp.113-115
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• 1998

This paper presents the indirect boundary integral equation method(BIEM) to analyze 3D moving conductor problem. Instead of an artificial upwind algothm, the proposed method uses a fundamental Green's function which is a particular solution of diffusion equation. Therefore, this method yields a stable and accurate solution regardless of the Peclet number. The indirect BIEM is compared with 3D upwind FEM for a numerical model which has analytic solutions.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.12
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• pp.1759-1771
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• 2017

In this paper, an improved continuous integral variable structure systems(ICIVSS) with the prescribed control performance is designed for simple regulation controls of uncertain general linear systems. An integral sliding surface with an integral state having a special initial condition is adopted for removing the reaching phase and predetermining the ideal sliding trajectory from a given initial state to the origin in the state space. The ideal sliding dynamics of the integral sliding surface is analytically obtained and the solution of the ideal sliding dynamics can predetermine the ideal sliding trajectory(integral sliding surface) from the given initial state to the origin. Provided that the value of the integral sliding surface is bounded by certain value by means of the continuous input, the norm of the state error to the ideal sliding trajectory is analyzed and obtained in Theorem 1. A corresponding discontinuous control input with the exponential stability is proposed to generate the perfect sliding mode on the every point of the pre-selected sliding surface. For practical applications, the discontinuity of the VSS control input is approximated to be continuous based on the proposed modified fixed boundary layer method. The bounded stability by the continuous input is investigated in Theorem 3. With combining the results of Theorem 1 and Theorem 3, as the prescribed control performance, the pre specification on the error to the ideal sliding trajectory is possible by means of the boundary layer continuous input with the integral sliding surface. The suggested algorithm with the continuous input can provide the effective method to increase the control accuracy within the boundary layer by means of the increase of the $G_1$ gain. Through an illustrative design example and simulation study, the usefulness of the main results is verified.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.36 no.1
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• pp.59-71
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• 2012

A volume integral equation method (VIEM) is introduced for the solution of elastostatic problems in unbounded isotropic elastic solids containing multiple interacting isotropic or anisotropic diamond-shaped inclusions subject to remote uniaxial tension. The method is applied to two-dimensional problems involving long parallel diamond-shaped cylindrical inclusions. A detailed analysis of the stress field at the interface between the matrix and the central inclusion is carried out for square and hexagonal packing of the inclusions. The effects of the number of isotropic or anisotropic diamond-shaped inclusions and of the various fiber volume fractions for the circular inclusions circumscribing its respective diamond-shaped inclusion on the stress field at the interface between the matrix and the central inclusion are also investigated in detail. The accuracy and efficiency of the method are examined through comparison with results obtained using the finite element method.

• 제어로봇시스템학회:학술대회논문집
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• 1990.10b
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• pp.1145-1149
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• 1990

This paper proposes a numerical method for redundant manipulators using predetermined optimal resolution. In order to obtain optimal joint trajectories, it is desirable to formulate redundancy resolution as an optimization problem having an integral cost criterion. We predetermine the trajectories of redundant joints in terms of the Nth partial sum of the Fourier series, which lead to the solution in the desirable homotopy class. Then optimal coefficients of the Fourier series, which yield the optimal solution within the predetermined class, are searched by the Powell's method. The proposed method is applied to a 3-link planar manipulator for cyclic tasks in Cartesian space. As the results, we can obtain the optimal solution in the desirable homotopy class without topological liftings of the solution. To show the validity of the proposed method, we analyze both optimal and extremal solutions by the Fast Fourier Transform (FFT) and discuss joint trajectories on the phase plane.

• International Journal of Precision Engineering and Manufacturing
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• v.2 no.3
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• pp.11-18
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• 2001

A simple and convenient method of analysis for obtaining the individual stress intensity factors in a three-dimensional mixed mode crack is proposed. The procedures presented here are based on the path independence of J integral and mutual or two-state conservation integral, which involves two elastic fields. The problem is reduced to the determination of mixed mode stress intensity factor solutions in terms of conservation integrals involving known auxiliary solutions. Some numerical examples are presented to investigate the effectiveness and applicability of the method for a three-dimensional penny-shaped crack problem under mixed mode. This procedure is applicable to a three-dimensional mixed mode curved crack.