• Computational Structural Engineering
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• v.11 no.1
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• pp.205-216
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• 1998

A solution method is presented to solve the eigenvalue problem arising in the dynamic analysis of nonclassicary damped structural systems with multiple eigenvalues. The proposed method is obtained by applying the modified Newton-Raphson technique and the orthonormal condition of the eigenvectors to the linear eigenproblem through matrix augmentation of the quadratic eigenvalue problem. In the iteration methods such as the inverse iteration method and the subspace iteration method, singularity may be occurred during the factorizing process when the shift value is close to an eigenvalue of the system. However, even though the shift value is an eigenvalue of the system, the proposed method provides nonsingularity, and that is analytically proved. Since the modified Newton-Raphson technique is adopted to the proposed method, initial values are need. Because the Lanczos method effectively produces better initial values than other methods, the results of the Lanczos method are taken as the initial values of the proposed method. Two numerical examples are presented to demonstrate the effectiveness of the proposed method and the results are compared with those of the well-known subspace iteration method and the Lanczos method.

• The Korean Journal of Applied Statistics
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• v.6 no.2
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• pp.319-328
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• 1993

The actual convergence rate of Newton-Raphson iteration method at each step is studied under the regularity conditions for the limiting distribution: The convergence rate of it is accelerated with good starting values. Hence we can decide a number of iterations according to our purposes.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.347-350
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• 2004

In this paper, the acceleration is studied for the rigid-plastic FEM of metal forming simulation. In the FEM, the direct iteration and Newton-Raphson iteration are applied to obtain the initial solution and accurate solution respectively. In general, the acceleration scheme for the direct iteration is not used. In this paper, an Aitken accelerator is applied to the direct iteration. In the modified Newton-Raphson iteration, the step length or the deceleration coefficient is used for the fast and robust convergence. The step length can be determined by using the accelerator. The numerical experiments have been performed for the comparisons. The faster convergence is obtained with the acceleration in the direct and Newton-Raphson iterations.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.18 no.4 s.70
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• pp.385-393
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• 2005

This paper established the dynamic model of a flexible Timoshenko beam capable of geometrical nonlinearities subject to large overall motions by using the finite element method. Equations of motion are derived by using Hamilton principle and are formulated in terms of finite elements in which the nonlinear constraint equations are adjoined to the system using Lagrange multipliers. The Newmark direct integration method and the Newton-Raphson iteration are employed here for the numerical study which is to demonstrate the efficiency of the proposed formulation.

• 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.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.29 no.3
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• pp.237-244
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• 2016

This paper presents a nonlinear Moving Least Squares(MLS) difference method for material nonlinearity problem. The MLS difference method, which employs strong formulation involving the fast derivative approximation, discretizes governing partial differential equation based on a node model. However, the conventional MLS difference method cannot explicitly handle constitutive equation since it solves solid mechanics problems by using the Navier's equation that unifies unknowns into one variable, displacement. In this study, a double derivative approximation is devised to treat the constitutive equation of inelastic material in the framework of strong formulation; in fact, it manipulates the first order derivative approximation two times. The equilibrium equation described by the divergence of stress tensor is directly discretized and is linearized by the Newton method; as a result, an iterative procedure is developed to find convergent solution. Stresses and internal variables are calculated and updated by the return mapping algorithm. Effectiveness and stability of the iterative procedure is improved by using algorithmic tangent modulus. The consistency of the double derivative approximation was shown by the reproducing property test. Also, accuracy and stability of the procedure were verified by analyzing inelastic beam under incremental tensile loading.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.34 no.10
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• pp.1-6
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• 2006

This paper predicts the stall characteristics of three-dimensional wings. An iterative decambering approach is introduced into the nonplanar lifting surface method to take into consideration the stall characteristics of wings. An iterative decambering approach uses known airfoil lift curve and moment curve to predict the stall characteristics of wings. The multi-dimensional Newton iteration is used to take into consideration the coupling between the different sections of wings. Present results are compared with experiments and other numerical results. Computed results are in good agreement with other data. This scheme can be used for any wing with the twist or control surface and for wing-wing configurations such as wing-tail configuration or canard-wing configuration.

• Journal of the Society of Naval Architects of Korea
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• v.45 no.4
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• pp.389-395
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• 2008

It is very well known that the natural frequency of an oscillating body on the free surface is determinable only after the added mass is given. However, it is hard to find analytical investigations in which actually the natural frequency is obtained. Difficulties arise from the fact that in order to determine the natural frequency we need to compute the added mass at least for a range of frequencies, and to solve an equation where the frequency is a variable. In this study, first, a formula is obtained for the added mass, and then an equation for finding the natural frequency is defined and solved by Newton's iteration. It is confirmed that the formula shows a good agreement with the results given by Ursell(1949), and the value of natural frequency is reduced by 21.5% compared to the pre-natural frequency, which is obtained without considering the effect of added mass.

• Geophysics and Geophysical Exploration
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• v.17 no.2
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• pp.95-103
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• 2014

This paper presents a practical inversion method for recovering a three-dimensional (3D) resistivity model and static shifts simultaneously. Although this method is based on a Gauss-Newton approach that requires a sensitivity matrix, the computer time can be greatly reduced by implementing a simple and effective procedure for updating the sensitivity matrix using the Broyden's algorithm. In this research, we examine the approximate inversion procedure and the weighting factor ${\beta}$ for static shifts through inversion experiments using synthetic MT data. In methods using the full sensitivity matrix constructed only once in the iteration process, a procedure using the full sensitivity in the earlier stage is useful to produce the smallest rms data misfit. The choice of ${\beta}$ is not critical below some threshold value. Synthetic examples demonstrate that the method proposed in this paper is effective in reconstructing a 3D resistivity structure from static-shifted MT data.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.35 no.5
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• pp.375-380
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• 2007

The nonlinear aerodynamic analysis of wing with control surface is performed using the frequency-domain panel method. To take into consideration the nonlinear aerodynamic characteristics of wing an iterative decambering approach is introduced. The iterative decambering approach uses the known aerodynamic characteristics of airfoil to calculate the aerodynamic characteristics of wing. The multi-dimensional Newton iteration is used to account for the coupling between the different sections of wing. The present method is verified by showing that it produces results that are in good agreement with experiments. The present method will be useful for the analysis of aircraft in the conceptual design because the present method can calculate promptly the nonlinear aerodynamic characteristics of wing with a few computing resources.