• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.7 no.3
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• pp.141-154
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• 1987

The algorithm proposed utilizes the tow-levels technique. In the first level which consists of teeatment only the applied load and design stress as the random variables whose parent distribution has the normal distribution, the cross-sectional areas of the truss members such that the their probabilities of failure have the preseribed failure probabilites are optimized by transforming the nonlinear problem into SUMT, and solving it utilizing modified Newton-Raphson method. In the second level, the geometric shape of truss structure is optimized by utilizing the unidirectional search technique of Powell method which makes it possible to minimize only the objective function. The algorithm proposed is numerically tested for the several truss structures with various shapes and loading conditions. The numerical analysis shows that the rate of decreasing the weight of truss structures is dependent on the prescribed failure probability of the each member of truss structure and the covariance of the applied load and design stress.

• Advances in nano research
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• v.13 no.4
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• pp.393-406
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• 2022

In the present article, functionally graded small-scaled plates based on modified strain gradient theory (MSGT) are studied for analyzing the nonlinear bending and post-buckling responses. Von-Karman's assumptions are applied to incorporate geometric nonlinearity and the first-order shear deformation theory is used to model the plates. Modified strain gradient theory includes three length scale parameters and is reduced to the modified couple stress theory (MCST) and the classical theory (CT) if two or all three length scale parameters become zero, respectively. The Ritz method with Legendre polynomials are used to approximate the unknown displacement fields. The solution is found by the minimization of the total potential energy and the well-known Newton-Raphson technique is used to solve the nonlinear system of equations. In addition, numerical results for the functionally graded small-scaled plates are obtained and the effects of different boundary conditions, material gradient index, thickness to length scale parameter and length to thickness ratio of the plates on nonlinear bending and post-buckling responses are investigated and discussed.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.3
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• pp.481-490
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• 2002

The purpose of this paper is to evaluate the efficiency of various solution techniques and propose new efficient solution techniques for space trusses. Solution techniques used in this study are three load control methods (Newton-Raphson Method, modified Newton-Raphson Method, Secant-Newton Method), two load-displacement control methods(Arc-length Method, Work Increment Control Method) and three combined load-displacement control methods(Combined Arc-length Method I , Combined Arc-length MethodⅡ, Combined Work Increment Control Method). To evaluate the efficiency of these solution techniques, we must examine accuracy of their solutions, convergences and computing times of numerical examples. The combined load-displacement control methods are the most efficient in the geometric nonlinear solution techniques and in tracing post-buckling behavior of space truss. The combined work increment control method is the most efficient in tracing the buckling load of spate trusses with high degrees of freedom.

• Journal of Hydrospace Technology
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• v.2 no.2
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• pp.24-35
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• 1996

This paper describes parameter identification techniques formulated for the estimation of maneuvering coefficients of a submerged body. The first part of this paper is concerned with the identifiability of the system parameters. The relationship between a stochastic linear time-invariant system and the equivalent dynamic system is investigated. The second is concerned with the development of the numerically stable identification technique. Two identification techniques are tested; one is the ma7mum likelihood (ML) methods using the Holder & Mead simplex search method and using the modified Newton-Raphson method, and the other is the modified extended Kalman filter (MEKF) method with a square-root algorithm, which can improve the numerical accuracy of the extended Kalman filter. As a results, it is said that the equations of motion for a submerged body have higher probability to generate simultaneous drift phenomenon compared to general state equations and only the ML method using the Holder & Mead simplex search method and the MEKF method with a square-root algorithm gives acceptable results.

• Journal of the Society of Disaster Information
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• v.16 no.4
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• pp.832-841
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• 2020

Purpose: This study attempts at analyzing mechanical response of functionally graded material (FGM) plates in bending. An accurate and effective numerical approach based on isogeometric analysis (IGA) combined with higher-order shear deformation plate theory to predict the nonlinear flexural behavior is developed. Method: A higher-order shear deformation theory(HSDT) which accounts for the geometric nonlinearity in the von Karman sense is presented and used to derive the equilibrium and governing equations for FGM plate in bending. The nonlinear equations are solved by the modified Newton-Raphson iterative technique. Result: The volume fraction, plate length-to-thickness ratio and boundary condition have signifiant effects on the nonlinear flexural behavior of FGM plates. Conclusion: The proposed IGA method can be used as an accurate and effective numerical tool for analyzing the mechanical responses of FGM plates in flexure.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.6 no.2
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• pp.1-15
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• 1986

The algorithm Proposed utilizes the two-levels technique. In the first level which consists of two phases, the cross-sectional area of the truss member is optimized by transforming the nonlinear problem into SUMT, and solving SUMT utilizing the modified Newton-Rahson method. In the second level, the geometric shape is optimized utilizing the unindirectional search technique of the Powell method which make it possible to minimize only the objective function. The algorithm Proposed in this study is numerically tested for several truss structures with various shapes, loading conditions and design criteria, and compared with the results of the other algorithms to examine its applicability and stability. The numerical comparisons show that the two-Levels algorithm Proposed in this study is safely applicable to any design criteria, and the convergency rate is relathely fast and stable compared with other iteration methods for the geometric optimization of truss structures.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.2
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• pp.523-536
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• 1991

This dissertation analyzes the running mechanism of flexible and thin tape above rotating head through the numerical simulation and the experiment. The scope of analysis is confined to the phenomena of two dimensional elasto hydrodynamic lubrication between the protruded bump on a rotating cylinder and the running tape. This model is based on the elastic deformation equation of plate and shell and Reynolds equation. Finite difference method is employed as a numerical technique to calculate (1) the distribution of pressure between the running tape and rotating bump and (2) the vertical deformation of elastic thin tape over he rotating bump under hydrodynamic pressure. In numerical analyses, the effects of bump size on flying characteristics of the tape were evaluated and examined considering the influence of tension and stiffness of tape.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.906-909
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• 2005

In this study, the dynamic flying characteristics of the worn head sliders are investigated theoretically due to the change in head geometry caused by head and disk contact. The film shapes can be approximated as taper- truncated cycloidal-flat film. Two-dimensional time dependent modified Reynolds equation included molecular slip effect are formulated with neglected the roughness effect. The motion of head slider was assumed to have two degree of freedom in this work. Finite difference approximation with Newton Raphson iterative technique and the fourth order Runge-Kutta method were implemented to obtain the transient response of the slider head with various change in head geometry numerically and compared with the transient response of the IBM3380 type head slider. The simulation results show the film shape has affects significantly on the static and dynamic characteristic of slider head in magnetic storage systems.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.10a
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• pp.431-438
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• 1998

An efficient solution method is presented to solve the eigenvalue problem arising in tile dynamic analysis of non-proportionally damped structural systems with multiple or close eigenvalues. The proposed method is obtained by applying the modified Newton-Raphson technique and the orthonormal condition of the eigenvectors to the quadratic eigenvalue problem. Even if the shift value is an eigenvalue of the system, the proposed method guarantees nonsingularity, which is analytically proved. The initial values of the proposed method can be taken as the intermediate results of iteration methods or results of approximate methods. Two numerical examples are also 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.