• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.2
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• pp.139-148
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• 2012

The MLS(Moving Least Squares) Difference Method is a numerical scheme that combines the MLS method of Meshfree method and Taylor expansion involving not numerical quadrature or mesh structure but only nodes. This paper presents an dynamic algorithm of MLS difference method for solving transient solid mechanics problems. The developed algorithm performs time integration by using Newmark method and directly discretizes strong forms. It is very convenient to increase the order of Taylor polynomial because derivative approximations are obtained by the Taylor series expanded by MLS method without real differentiation. The accuracy and efficiency of the dynamic algorithm are verified through numerical experiments. Numerical results converge very well to the closed-form solutions and show less oscillation and periodic error than FEM(Finite Element Method).

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.1038-1043
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• 2003

There are many industrial applications including thin-body structures such as fins. For the numerical modeling of radiation of sound from thin bodies, the conventional boundary element method (BEM) using the Helmholtz integral equation fails to yield a reliable solution. Therefore, many researchers have tried to solve the thin-body acoustic problems. In the area of the design sensitivity analysis (DSA) and optimization methods, however, there has been just a few study reported. Especially fur the thin-body acoustics, however, no further study in the DSA and optimization fields has been reported. In this research, the normal derivative integral equation is adopted as an analysis formulation in the thin-body acoustics, and then used for the sizing DSA and optimization. Since the gradient-based method is used for the optimization, it is important to have accurate gradients (design sensitivities) of the objective function and constraints with respect to the design variables. The DSA formulations are derived through chain-ruled derivatives using the finite element method (FEM) and BEM by using the direct differentiation and continuum variation concepts. The proposed approaches are implemented and validated using a numerical example.

• Journal of the Korean Mathematical Society
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• v.40 no.5
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• pp.901-920
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• 2003

The notion of infinitely near singular points, classical in the case of plane curves, has been generalized to higher dimensions in my earlier articles ([5], [6], [7]). There, some basic techniques were developed, notably the three technical theorems which were Differentiation Theorem, Numerical Exponent Theorem and Ambient Reduction Theorem [7]. In this paper, using those results, we will prove the Finite Presentation Theorem, which the auther believes is the first of the most important milestones in the general theory of infinitely near singular points. The presentation is in terms of a finitely generated graded algebra which describes the total aggregate of the trees of infinitely near singular points. The totality is a priori very complex and intricate, including all possible successions of permissible blowing-ups toward the reduction of singularities. The theorem will be proven for singular data on an ambient algebraic shceme, regular and of finite type over any perfect field of any characteristics. Very interesting but not yet apparent connections are expected with many such works as ([1], [8]).

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2005.04a
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• pp.335-342
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• 2005

Using higher order Mindlin plates and piezoelectric materials, eigenvalue problems are considered. Since piezoelectric crystal resonators produce a proper amount of electric signal for a thickness-shear frequency, the objective is to decouple the thickness-shear mode from the others. Design variables are the bulk material densities corresponding to the mass of masking plates for electrodes. The design sensitivity expressions for the thickness-shear frequency and mode shape vector are derived using direct differentiation method(DDM). Using the developed design sensitivity analysis (DSA) method, we formulate a topology optimization problem whose objective function is to maximize the thickness-shear component of strain energy density at the thickness-shear mode. Constraints are the allowable volume and area of masking plate. Numerical examples show that the optimal design yields an improved mode shape and thickness-shear energy.

• Proceedings of the KIEE Conference
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• 1991.07a
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• pp.93-96
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• 1991

This paper describes a new algorithm based on design sensitivity analysis for optimal shape design of electrostatic devices. The design sensitivity, the variation of the object function with respect to the design variables, is derived by using implicit differentiation and direct boundary element methods. The proposed algorithm is applied to the optimal shape design of a concentric cable and the rod electrode enclosed by earthed case, It is shown, from the numerical results, that the algorithm is very usefull for the optimal shape design of the electrostatic devices.

• Journal of Korea Multimedia Society
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• v.10 no.12
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• pp.1622-1631
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• 2007

To realize the wireless packet scheduler which efficiently considers both the effect of adaptive modulation and coding (AMC) scheme due to variable wireless communication channel information from physical layer and the QoS differentiation of multimedia services from internet protocol (IP) layer, this paper proposes a new downlink AMC-based priority queuing (APQ) scheduler which combines AMC scheme and service priority method in multimedia services at the same time. The result of numerical analysis shows that the proposed APQ algorithm plays a role in increasing the number of services satisfying the mean waiting time requirements per each service in multimedia services because the APQ scheme allows the mean waiting time of each service to be reduced much more than existing packet scheduler having only user selection processor.

• Structural Engineering and Mechanics
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• v.4 no.4
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• pp.425-436
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• 1996

An application of the perturbation method to optimum structural design with random parameters is presented. It is formulated on the basis of the first-order stochastic finite element perturbation method. It also takes into full account the stress, displacement and eigenvalue constraints, together with the rates of change of the random variables. A method for calculating the sensitivity coefficients in regard to the governing equation and the first-order perturbed equation has been derived, by using a direct differentiation approach. A gradient-based nonlinear programming technique is used to solve the problem. The numerical results are specifically noted, where the stiffness parameter and external load are treated as random variables.

• Transactions on Control, Automation and Systems Engineering
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• v.1 no.1
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• pp.22-31
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• 1999

In this paper, a robust observer design method for nonlinear multi input multi-output(MINO) plants is presented. This method enables the extension of the time delay observer (TDO) for nonlinear SISO plants in the phase variable form to MIMO plants. The designed TDO reconstructs the states of the plant expressed in the generalized observability canonical form (GOBCF), yet requiring neither the transformation of a plant, nor the real time computation coordinates, the observer turned out to be computationally efficient and easy to design for nonlinear MIMO plants. In a simulation of a two-link manipulator with flexible joints, the control performances using TDO appeared to be similar to those using actual states and superior to those using numerical differentiation. Finally, in an experiment with a robot, it was confirmed that the TDO reconstructs the states reliability and TDO can be effectively used in a real closed-loop system.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.8
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• pp.1822-1831
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• 1995

A general formulation of the design optimization problem with the random parameters is presented here. The formulation is based on the stochastic finite element second-order perturbation method ; it takes into full account of the stress and displacement constraints together with the rates of change of the random variables. A method of direct differentiation for calculating the sensitivity coefficients in regard to the governing equation and the second-order perturbed equation is derived. A gradient-based nonlinear programming technique is used to solve the problem. The numerical results are specifically noted, where the stiffness parameter and external load are treated as random variables.

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.332-335
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• 1995

A simple and effective method for improving Euclidean norm condition number for chemical processing system is presented. The singular value sensitivities of Freudenberg et al. (1982) is used to estimate the behavior of singular values of process transfer function matrix when design parameter is changed, then the condition number can be calculated straightforwardly. The method requires explicit dependencies of each transfer function matrix elements on design parameters. These dependencies can be obtained either by symbolic differentiation in the form of explicit function of design parameters, or by numerical perturbation studies for units with large and complicated models. Gerschgorin-type lower bound for minimum singular value is introduced to detect the large divergencies near singular point due to linearity of sensitivities. The case studies are performed to show the efficiency of the proposed method.