• Journal of the Korean Institute of Telematics and Electronics A
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• v.31A no.12
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• pp.142-151
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• 1994

This paper proposes new algorithms to solve canonical piecewise-linear equations with linear partitions and illustrates their efficiency through the analysis of resistive network. The basic idea of the proposed algorithm is to find the best next guess, closest to the actual solution, at each Newton-Raphson (N-R) iteration by comparing the images of nest guess candidates and that of the actual solution. The proposed algorithm can reduce the number of the N-R iterations rquired for convergence greatly, compared to the actual solution, at each Newton-Raphson (N-R) iteration by comparing the images of next guess candidates and that of the actual solution. The proposed algorithm can reduce the number of the N-R iterations required for convergence greatly, compared to the Katzenelson algorithm. When applied to analyzing test circuits, the proposed algorithm required 8 to 20 times fewer N-R iterations and 5 to 10 times less CPU time than the Katzenelson algorithm, depending on the size of the circuits. The experimental results also exhibit that the efficiency of the proposed algorithm over the Katzenelson algorithm increases as the number of the piecewise-linear regions for the representation of the circuit.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.4
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• pp.642-651
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• 1988

The present paper develops finite element procedures to calculate displacements, strains and stresses in initially stressed elastic solids subjected to static or time-dependent loading conditions. As a point of departure, we employ Hamilton's principle to obtain nonlinear equations of motion characterizing the displacement in a solid. The equations of motion reduce to linear equations of motion if incremental stresses are assumed to be infinitesimal. In the case of linear problem, finite element solutions are obtained by Newmark's direct integration method and by modal analysis. An analytic solution is referred to compare with the linear finite element solution. In the case of nonlinear problem, finite element solutions are obtained by Newton-Raphson iteration method and compared with the linear solution. Finally, the effect of the order of Gauss-Legendre numerical integration on the nonlinear finite element solution, has been investigated.

• KIEE International Transactions on Electrophysics and Applications
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• v.3C no.5
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• pp.199-206
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• 2003

Numerical solutions to complex characteristic equations are quite often required to solve electromagnetic wave problems. In general, two traditional complex root search algorithms, the Newton-Raphson method and the Muller method, are used to produce such solutions. However, when utilizing these two methods, the choice of the initial iteration value is very sensitive, otherwise, the iteration can fail to converge into a solution. Thus, as an alternative approach, where the selection of the initial iteration value is more relaxed and the computation speed is high, Davidenko's method is used to determine accurate complex propagation constants for leaky circular symmetric modes in circular dielectric rod waveguides. Based on a precise determination of the complex propagation constants, the leaky mode characteristics of several lower-order circular symmetric modes are then numerically analyzed. In addition, no modification of the characteristic equation is required for the application of Davidenko's method.

• Proceedings of the KIEE Conference
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• 1998.07c
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• pp.918-922
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• 1998

With the development of industry, the qualitical advancement of power is needed. Since it is placed in the end step of power system, the fault at the distribution system causes some users blackout directly. So if the fault occurs, quick restoration is very important subject and, for the reason, induction of the distribution automation system is now being progressed briskly. For the quick restoration of the faulted distribution system, the load shedding of the blackout-area must be followed, and the other problems like the shedded load, faulted voltage and the rest may cause other accident. Accordingly load shedding must be based on the precise calculation technique during the distribution system load flow(dist flow) calculation. In these days because of its superior convergence characteristic the Newton-Raphson method is most widely used. The number of buses in the distribution system amounts to thousands, and if the fault occurs at the distribution system, the speed for the dist flow calculation is to be improved to apply to the On-Line system. However, Newton-Raphson method takes much time relatively because it must calculate the Jacobian matrix and inverse matrix at every iteration, and in the case of huge load, the equation is hard to converge. In this thesis. matrix equation is used to make algebraical expression and then to solve load flow equation and to modify above defects. Then the complex matrix is divided into real part and imaginary part to keep sparcity. As a result time needed for calculation diminished. Application of mentioned algorithm to 302 bus, 700 bus, 1004 bus system led to almost identical result got by Newton-Raphson method and showed constant convergence characteristic. The effect of time reduction showed 88.2%, 86.4%, 85.1% at each case of 302 bus, 700 bus system 86.4%, and 1004 bus system.

• Journal of the Chungcheong Mathematical Society
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• v.8 no.1
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• pp.1-10
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• 1995

For analyzing systems of multi-variate nonlinear equations, the linearized modelling techniques are elaborated. The technique applies Newton-Raphson iteration, partial differentiation and matrix operation providing solvable solutions to complicated problems. Practical application examples are given in; determining the zero point of functions, determining maximum (or minimum) point of functions, nonlinear regression analysis, and solving complex co-efficient polynomials. Merits and demerits of linearized modelling techniques are also discussed.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1997.10a
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• pp.28-31
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• 1997

Buckling analysis of thin compressed beam has been carried out. Pre-buckling and post-buckling are simulated by finite element method incorporating with the incremental nonlinear theory and the Newton-Raphson solution technique. In order to find the bifurcation point, the determinent of the stiffness matrix is calculated at every iteration procedure. For post-buckling analysis, a small perturbed initial guess is given along the eigenvector direction at the bifurcation point. Nonlinear elastic buckling and elastic-plastic buckling of cantilever beam are analyzed. The buckling load and buckled shape of the two models are compared.

• Coupled systems mechanics
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• v.6 no.4
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• pp.399-415
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• 2017

This paper deals with the nonlinear static deflections of functionally graded (FG) porous under thermal effect. Material properties vary in both position-dependent and temperature-dependent. The considered nonlinear problem is solved by using Total Lagrangian finite element method within two-dimensional (2-D) continuum model in the Newton-Raphson iteration method. In numerical examples, the effects of material distribution, porosity parameters, temperature rising on the nonlinear large deflections of FG beams are presented and discussed with porosity effects. Also, the effects of the different porosity models on the FG beams are investigated in temperature rising.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.3
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• pp.799-808
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• 1991

본 연구에서는 연속체 역학의 에너지 원리에서 출발하여, 동적 비선형 해석을 위한 유한요소 식들을 유도하고, 이를 이용하여 특이 경계조건을 갖는 고체의 대변위 동적 선형 현상과 비선형 현상에 관하여 연구하고자 한다.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2002.05a
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• pp.161-166
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• 2002

Low-tension cables have been increasingly used in recent years due to deep-sea developments and the advent of synthetic cables. In the case of low-tension cables, large displacements may happen due to relatively small restoring forces of tension and thus the effects of fluid and geometric non-linearities become predominant. In this study, three-dimensional (3-D) dynamic behavior of a towed low-tension cable with non-uniform characteristics is numerically analyzed by considering fluid and geometric non-linearities and bending stiffness. A Fortran program is developed by employing a finite difference method. In the algorithm, an implicit time integration and Newton-Raphson iteration are adopted. For the calculation of huge size of matrices, block tri-diagonal matrix method is applied, which is much faster than the well-known Gauss-Jordan method in two point boundary value problems. Some case studies are carried out and the results of numerical simulations are compared with a in-house program of WHOI Cable with good agreements.

• Composites Research
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• v.25 no.6
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• pp.217-223
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• 2012

This study investigates a geometrical nonlinear dynamic behaviors of laminated skew plates made of advanced composite materials (ACM). Based on the first-order shear deformation plate theory (FSDT), the Newmark method and Newton-Raphson iteration are used for the nonlinear dynamic solution. The effects of cutout sizes, skew angles and lay up sequences on the nonlinear dynamic response for various parameters are studied using a nonlinear dynamic finite element program developed for this study. The several numerical results were in good agreement with those reported by other investigators for square composite plates with or without central cutouts, and the new results reported in this paper show the significant interactions between the cutout, skew angles and layup sequence in the laminate. Key observation points are discussed and a brief design guideline of skew laminates is given.