• Journal of Mechanical Science and Technology
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• v.18 no.9
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• pp.1519-1528
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• 2004

Atmospheric Re-Entry guidance is divided as longitudinal and lateral. This paper proposes a longitudinal reference trajectory and control law using the inverse dynamics method with pseudospectral Legendre method. Application of this method into Re-Entry problem forces a power of calculation time-reduction due to unnecessary of integration or any iteration as well as sufficient accuracy convergence. The used guidance scheme is time-to-go.

• Structural Engineering and Mechanics
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• v.65 no.4
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• pp.359-368
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• 2018

Dynamic analysis of complex and large structures may be costly from a numerical point of view. For coupled vibroacoustic finite element models, the importance of reducing the size becomes obvious because the fluid degrees of freedom must be added to the structural ones. In this paper, a component mode synthesis method is proposed for large vibroacoustic interaction problems. This method couples fluid subdomains and dynamical substructuring of Craig and Bampton type. The acoustic formulation is written in terms of the velocity potential, which implies several advantages: coupled algebraic systems remain symmetric, and a potential formulation allows a direct extension of Craig and Bampton's method to acoustics. Those properties make the proposed method easy to implement in an existing finite element code because the local numerical treatment of substructures and fluid subdomains is undifferentiated. Test cases are then presented for axisymmetric geometries. Numerical results tend to prove the validity and the efficiency of the proposed method.

• Journal of the Korean Society for Railway
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• v.5 no.3
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• pp.174-180
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• 2002

In multibody dynamics, DAE(Differential Algebraic Equations) that combine differential equations of motion and kinematic constraint equations should be solved. To solve these equations, either coordinate partitioning method or constraint stabilization method is commonly used. The most typical coordinate partitioning methods are LU decomposition, QR decomposition, and SVD(singular value decomposition). The objective of this research is to suggest a hybrid coordinate partitioning method in the dynamic analysis of multibody systems containing singular configurations. Two coordinate partitioning methods, i.e. LU decomposition and QR decomposition for constrained multibody systems, are combined for a new hybrid coordinate partitioning method. The proposed hybrid method reduces the simulation time while keeping accuracy of the solution.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.25 no.10
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• pp.653-659
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• 2015

A new formulation of the non-dimensional dynamic influence function method, which is a type of the meshless method, is introduced to extract highly accurate eigenvalues of clamped plates with arbitrary shape. Originally, the final system matrix equation of the method, which was introduced by the author in 1999, does not have a form of algebraic eigenvalue problem unlike FEM. As the result, the non-dimensional dynamic influence function method requires an inefficient process to extract eigenvalues. To overcome this weak point, a new approach for clamped plates is proposed in the paper and the validity and accuracy is shown in verification examples.

• Honam Mathematical Journal
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• v.43 no.3
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• pp.373-383
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• 2021

In this study, a numerical method deals with the Chebyshev wavelet collocation and Adomian decomposition methods are proposed for solving Korteweg-de Vries equation. Integration of the Chebyshev wavelets operational matrices is derived. This problem is reduced to a system of non-linear algebraic equations by using their operational matrix. Thus, it becomes easier to solve KdV problem. The error estimation for the Chebyshev wavelet collocation method and ADM is investigated. The proposed method's validity and accuracy are demonstrated by numerical results. When the exact and approximate solutions are compared, for non-linear or linear partial differential equations, the Chebyshev wavelet collocation method is shown to be acceptable, efficient and accurate.

• Coupled systems mechanics
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• v.7 no.6
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• pp.755-774
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• 2018

The Ritz method is known as very successful strategy for discretizing continuous problems, but it has never been used for solving systems of algebraic equations. The Iterated Ritz Method (IRM) is a novel iterative solver based on the discretized Ritz procedure applied at each iteration step. With an appropriate choice of coordinate vectors, the method may be efficient in linear, nonlinear and optimization problems. Additionally, some iterative methods can be explained as special cases of this approach, which helps to understand advantages and limitations of these methods and gives motivation for their improvement in sense of IRM. In this paper, some ideas for generation of efficient coordinate vectors are presented. The algorithm was developed and tested independently and then implemented into the open source program FEAP. Method has been successfully applied to displacement based (even ill-conditioned) models of structural engineering practice. With this original approach, a new iterative solution strategy has been opened.

• Structural Engineering and Mechanics
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• v.72 no.4
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• pp.491-502
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• 2019

This paper explores the analytical buckling solution of rectangular thin plates by the finite integral transform method. Although several analytical and numerical developments have been made, a benchmark analytical solution is still very few due to the mathematical complexity of solving high order partial differential equations. In solution procedure, the governing high order partial differential equation with specified boundary conditions is converted into a system of linear algebraic equations and the analytical solution is obtained classically. The primary advantage of the present method is its simplicity and generality and does not need to pre-determine the deflection function which makes the solving procedure much reasonable. Another advantage of the method is that the analytical solutions obtained converge rapidly due to utilization of the sum functions. The application of the method is extensive and can also handle moderately thick and thick elastic plates as well as bending and vibration problems. The present results are validated by extensive numerical comparison with the FEA using (ABAQUS) software and the existing analytical solutions which show satisfactory agreement.

• Journal of the Optical Society of Korea
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• v.7 no.4
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• pp.258-263
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• 2003

Simple algebraic expressions are derived to approximate the optimal input RMS pulse width and the resulting output RMS pulse width in single-mode fibers. The results are compared with the previously published methods and with numerical results by the split-step Fourier method. In addition, for a transform-limited Gaussian input pulse, it is shown that there is no optimum input pulse width to minimize the output spectrum width. Finally, with fiber nonlinearity, it is shown mathematically that there is not an optimum input pulse width to minimize the product,${\sigma}_t{\sigma}_{\omega}$, which is inversely proportional to the transmission capacity of WDM systems.

• Journal of the Korean Statistical Society
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• v.30 no.3
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• pp.435-451
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• 2001

We describe a hierarchical bayesian model to analyze multinomial nonignorable nonresponse data. Using a Dirichlet and beta prior to model the cell probabilities, We develop a complete hierarchical bayesian analysis for multinomial proportions without making any algebraic approximation. Inference is sampling based and Markove chain Monte Carlo methods are used to perform the computations. We apply our method to the dta on body mass index(BMI) and show the model works reasonably well.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.04a
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• pp.9-16
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• 2004

This paper deals with the development of computational schemes for the dynamic analysis of flexible and nonlinear multibody systems. Different from the existing method, this paper introduces the quaternion algebra to develop the equation of the conservation of energy. Simultaneously, Rodrigues parameters are used to express the finite rotation for the proposed scheme. The proposed energy scheme is derived such that it provides unconditionally stable conditions for the nonlinear problems. Several examples of dynamic systems are presented which illustrate the efficiency and accuracy of the developed energy schemes.