• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.267-284
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• 2014

The multiresolution analysis for Legendre multiwavelets are given, anti-derivatives of Legendre multiwavelets are used for the numerical solution of differential equations, a special form of multilevel augmentation method algorithm is proposed to solve the disrete linear system efficiently, convergence rate of the Galerkin methods is given and numerical examples are presented.

• Journal of Power Electronics
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• v.14 no.2
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• pp.282-291
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• 2014

This paper presents a detailed theoretical analysis and performance assessment of the capacitor voltage balancing strategies for staircase modulated modular multilevel converters (MMC) in terms of the algorithm structures, voltage balancing effect, and switching frequency. A constant-frequency redundancy selection (CFRS) method with minimal switching loss is proposed and the function realization of specific modules of the algorithm is given. This method is simple and efficient in both switching frequency and regulation capacity. Laboratory results show very good agreement with the theoretical analysis and numerical simulations.

• Tribology and Lubricants
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• v.29 no.4
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• pp.228-234
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• 2013

This paper presents analysis of elastohydrodynamic lubrication (EHL) of ball bearings, in which surface roughness is considered. A lot of time is required to obtain a solution in the case of EHL analysis where surface roughness is considered, because the analysis requires a variety of analytic nodes. To save time, we use the full approximation scheme (FAS) among multilevel methods. We analyze the results of EHL and contact analyses in terms of pressure. We also compare the results for smooth and rough surfaces with respect to film thickness. We confirm that the film pressure decreases as compared to contact pressure because of the presence of lubricants between the ball and the raceway. Furthermore, in the case when surface roughness is considered, the film pressure increases because of contact asperities. Therefore, surface roughness should be considered when designing ball bearings.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 1999.11a
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• pp.323-330
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• 1999

The conventional analysis for the numerical computation of fluid film thickness with elastic deformation of contact region. is performed by Newton-Rephson method for its 18st convergence characteristics. However, both high load and relatively low sliding velocity frequently make it impossible for Newton-Rahpson method to get both converged and stable solutions. In particular, this method cannot provide converged Solution under the condition of high load above 1.0 GPa which frequently occurs in line contact of EHL problem. Multigird multi-level method for the solver of non-linear partial differential equation including solid deformation is preferred to Newton-Rshpson method for better convergence and stability and is applied to line contact EHL behavior in this study.

• Proceedings of the Korea Concrete Institute Conference
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• 2010.05a
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• pp.11-12
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• 2010

PSC girder with holed web have several benefits. Most of all placing tendon anchorage in the holes can make prestressing forces be loaded stepwise. In addition it can reduce the self-weight of the beams and increase the span length of beams. And holed web might minimize the interference of view. In this study, a 50-meter long full scale multilevel post-tensioned PSC girder was fabricated and modal test was carried out. In order to obtain precise frequency response, vibration exciter was placed at the middle of the girder and excited with several frequencies. Natural frequency and damping ratio were evaluated from FFT and PSD using the obtained frequency response and compared with numerical analysis result.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.9 no.1
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• pp.33-40
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• 1989

In the design of reinforced concrete framed structures, which consist of various design variables, the objective and the constraint functions are formulated in complicated forms. Usually iterative methods have been used to optimize the design variables. In this paper, multilevel formulation is adopted, and design variables are selected in reduced numbers at each level, to reduce the iterative cycle and to accelerate the convergence rate. At level 1, elastic analysis is performed to get the upper and lower bounds of the redistributed design moments due to inelastic behavior of the frame. Then the design moments are taken as design variables and optimized at level 2, and the sizing variables are optimized at level 3. The optimization of redistributed moments is performed using the design sensitivity obtained at the level 2, and force approximation technique is used to reflect the variation of design variables in the lower level to the upper level. The design variables are selected in reduced numbers at each level, and the optimization formulation is simplified effectively. A cost function is taken as the objective function, and the constraints of the stress of the structures are derived from BSI CP 110 following limit state theory. Numerical examples are included to prove the effectiveness of the developed algorithm.

• Journal of Korean Society of Steel Construction
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• v.12 no.1 s.44
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• pp.93-102
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• 2000

Substructuring-based hierarchical approach for design analysis and optimization of structural frames is presented in this study. The conceptual framework of this method is in the hierarchical modeling for design processes as well as structural systems and the methodology combining substructuring analysis and multilevel optimization. Mathematical models for analysis and synthesis are established on the common basis of substructuring systems. Modularized behavioral analysis, design sensitivity analysis and optimization are linked and integrated on the mathematical and structural basis of substructuring. Substructures are coordinated with the active constraints for system level and the weight ratio criteria. Numerical examples for test frames show the validity and effectiveness of the present approach.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.12 no.3
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• pp.397-406
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• 1999

A new solution procedure for approximate reanalysis, using the staged hybrid methods with substructuring, is proposed in this study. Displacements are calculated with two step mixed procedures. First step is to introduce the conservative approximation, which is a hybrid form of the linear and reciprocal approximation, as local approximation. In the next step, it is combined with the global approximation by reduced basis approach. Stresses are evaluated from the displacements by matrix transformation. The quality of reanalyzed quantities can be greatly improved through these staged hybrid approximations, specially for large changes in the design. Overall procedures are based on substructuring scheme. Several numerical examples illustrate the validity and effectiveness of the proposed methods.

• Journal of Korean Society of Steel Construction
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• v.16 no.1 s.68
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• pp.123-134
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• 2004

In this research, a multilevel decomposition technique to enhance the efficiency of the configuration optimization of truss structures was proposed. On the first level, the nonlinear programming problem was formulated considering cross-sectional areas as design variables, weight, or volume as objective function and behavior under multiloading condition as design constraint. Said nonlinear programming problem was transformed into a sequential linear programming problem. which was effective in calculation through the approximation of member forces using behavior space approach. Such approach has proven to be efficient in sensitivity analysis and different form existing shape optimization studies. The modified method of feasible direction (MMFD) was used for the optimization process. On the second level, by treating only shape design variables, the optimum problem was transformed into and unconstrained optimal design problem. A unidirectional search technique was used. As numerical examples, some truss structures were applied to illustrate the applicability. and validity of the formulated algorithm.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.9 no.6
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• pp.735-745
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• 1998

The method of moments has been widely used in the analysis of TM scattering problems. Recently, significant advances in the development of fast and efficient techniques for solving large problems have been reported. In such methods, iterative matrix solvers are preferred by virtue of their speed and low memory requirements. But for near resonant and strong multiple scattering problems, e.g., involving an aircraft engine inlet, a large number of iterations is required for convergence. In this paper, an efficient approximate inverse based preconditioner is used to reduce this number of iterations. By using the matrix partitioning method, the computational is used to reduce this number of iterations. By using the matrix partitioning method, the computational cost for obtaining the approximate inverse is reduced to O(N). We apply this preconditioner to an O(NlogN) algorithm, the multilevel fast multipole algorithm, for the aircraft engine inlet problem. The numerical results show the efficiency of this preconditioner.