• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.04a
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• pp.71-78
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• 1997

The high precision analysis by the p-version of the finite element method are fairly well established as highly efficient method for linear elastic problems, especially in the presence of stress singularity. It has been noted that the merits of p-version are accuracy, modeling simplicity, robustness, and savings in user's and CPU time. However, little has been done to exploit their benefits in elasto-plastic analysis. In this paper, the p-version finite element model is proposed for the materially nonlinear analysis that is based on the incremental theory of plasticity, the associated flow rule, and von-Mises yield criteria. To obtain the solution of nonlinear equation, the Newton-Raphson method and initial stiffness method, etc are used. Several numerical examples are tested with the help of the square plates with cutout, the thick-walled cylinder under internal pressure, and the center cracked plate under tensile loading. Those results are compared with the there cal solutions and the numerical solutions of ADINA software.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1990.04a
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• pp.18-23
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• 1990

The paper is concerned with the elasto-plastic and geometrically nonlinear analysis of shell structures using an improved degenerated shell element. In the formulation of the improved degenerated shell element, an enhanced interpolation of transverse shear strains in the natural coordinate system is used to overcome the shear locking problems; the reduced integration technique in in-plane strains is applied to avoid membrane locking behavior; selective addition the nonconforming displacement modes improve the element performances. This element is free of serious locking problems and undesirable compatible or commutable spurious kinematic deformation modes and passes the patch tests. An incremental total Lagrangian formulation is presented which allows the calculation of arbitrarily large displacements and rotations. The resulting nonlinear equations are solved by the Newton-Raphson solution scheme. The versatility and accuracy of this improved degenerated shell element are demonstrated by solving several numerical examples.

• The Journal of the Acoustical Society of Korea
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• v.18 no.2E
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• pp.18-23
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• 1999

This paper proposes a method of separately determining three intrinsic mechanical parameters of an unknown object in the framework of ultrasound inverse scattering tomography. Those parameters are the speed of sound, density, and absorption whose values are given as the solution of an inhomogeneous Helmholtz wave equation. The separate reconstruction method is mathematically formulated, the integral equations are discretized using the sinc basis functions, and the Newton-Raphson method is adopted as a numerical solver in a measurement configuration where the object is insonified by an incident plane wave over 360˚ and the scattered field is measured by detectors arranged in a rectangular fashion around it. Two distinct frequencies are used to separate each parameter of three Gaussian objects that are either located at the same position or separately from each other. Computer simulation results show that the separate reconstruction method is able to separately reconstruct the three mechanical parameters. The absorption parameter turns out to be a little difficult to reconstruct as compared with the other two parameters.

• Structural Engineering and Mechanics
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• v.36 no.5
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• pp.529-544
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• 2010

Nonlinear equations of structures are generally solved numerically by the iterative solution of linear equations. However, this iterative procedure diverges when the tangent stiffness is ill-conditioned which occurs near limit points. In other words, a major challenge with simple iterative methods is failure caused by a singular or near singular Jacobian matrix. In this paper, using the Newton-Raphson algorithm based on Davidenko's equations, the iterations can traverse the limit point without difficulty. It is argued that the propose algorithm may be both more computationally efficient and more robust compared to the other algorithm when tracing path through severe nonlinearities such as those associated with structural collapse. Two frames are analyzed using the proposed algorithm and the results are compared with the previous methods. The ability of the proposed method, particularly for tracing the limit points, is demonstrated by those numerical examples.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.32 no.10
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• pp.335-340
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• 1983

The analysis of static power converter circuit using state-space method is presented. Semiconductors are modeled in two-state resistors depending on their ON or OFF states. Then the modes of circuit are determined according to the conducting states of semiconductors and different describing matrices are given automatically for each mode. Newton-Raphson algorithm is used as an iterative method for obtaining steady-state solution and an adjoint network is introduced for the efficient and accurate evaluation of the Jacobi matrix in the algorithm. Using the porogram exploited from the above algorithm, it is shown through examples that the results are in good agreement with the analytic solutions and computation time is considerably reduced for obtaining the steady-state solutions.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.34 no.7
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• pp.267-275
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• 1985

The finite element method for calculating single phase transformer inductance is presented in this paper. There are three basic definitions of saturated transormer inductance. The set of nonlinear finite element equations is solved by the Newton-Raphson method which assures nearly quadratic convergence of the iteration process. The effect of perturbation of currents of this transformer is used to calculate the saturated winding inductance. This approach is used to calculate the apparent, effective and incremental inductance of single phase transformer. The apparent inductance is in good agreement with resting result. The approach enabled one to study the variation of winding inductance according to the saturation levels in the core at any operating point.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.38 no.1
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• pp.1-9
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• 1989

In this paper, an efficient method of a hybrid stepping motor is proposed using permeance method. To be specific, hybrid stepping motor is modelled firstly as an equivalent nonlinear magnetic circuit including the saturation effects of iron parts, and then the static holding torque of the motor is calculated as a function of each design factor via Newton-Raphson's method. To show the validities of the proposed method, a prototype of hybrid stepping motor for 5 1/4 inches FDD header drive is made and tested in laboratory. As a result, the experimental data for the static holding torque is shown to be within 10% error compared with that of the simulated results.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.39 no.1
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• pp.22-28
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• 1990

This paper is a study on the reduction of computation time in case of nonlinear magnetic field analysis by finite element method and Newton-Raphson method. For the purpose, the nonlinear convergence equation is computed by the conjugate gradient method which is known to be applicable to symmetric positive definite matrix equations only. As the results, we can not prove mathematically that the system Jacobian is positive definite, but when we applied this method, the diverging case did not occur. And the computation time is reduced by 25-55% and 15-45% in comparison with the case of direct and successive over-relaxation method, respectively. Therefore, we proved the utility of conjugate gradient method.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.48 no.10
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• pp.523-529
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• 1999

In the case of the large power transformer, the grain-oriented material is usually used. So, to obtain more accurate results, anisotropy and non-linearity of the material must be considered. The Newton-Raphson(NR) method is generally used for analyzing these non-linear properties, but it consumes so much time, especially when the number of nodes is large or the shape of the model is complex. The transmission line modeling (TLM) method is successfully adopted to the analysis of non-linear properties with FEM, but it has not been adopted to the analysis of the anisotropic material. In this paper, the formulation of the TLM method considering anisotropy is developed and the adoption to the 3-phase transformer is presented.

• KIEE International Transactions on Power Engineering
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• v.4A no.4
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• pp.192-200
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• 2004

This paper evaluates FACTS control on the available transfer capability (ATC) enhancement. Technical merits of FACTS technology on boosting ATC are analyzed. More effective control means for line flow and bus voltage require the application of FACTS. In this paper, the power flow calculation method for the power systems with FACTS is based on the current injection model (CIM) and the Newton-Raphson method. An integrated scheme for ATC calculation, which considers the dynamic characteristic of the power system, is suggested. The study is applied to the IEEE 57-bus power system to demonstrate the effectiveness of FACTS control on ATC enhancement.