• Journal of Mechanical Science and Technology
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• v.17 no.10
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• pp.1496-1506
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• 2003

The SIMP (solid isotropic material with penalization) approach is perhaps the most popular density variable relaxation method in topology optimization. This method has been very successful in many applications, but the optimization solution convergence can be improved when new variables, not the direct density variables, are used as the design variables. In this work, we newly propose S-shape functions mapping the original density variables nonlinearly to new design variables. The main role of S-shape function is to push intermediate densities to either lower or upper bounds. In particular, this method works well with nonlinear mathematical programming methods. A method of feasible directions is chosen as a nonlinear mathematical programming method in order to show the effects of the S-shape scaling function on the solution convergence.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.10
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• pp.946-949
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• 2007

This paper discusses the lateral vibration of a beam with boundary condition of one end fixed and the other end free. The uniform beam has a solution by summation of some simple exponential functions. But if its shape is not uniform, its solution could be by Bessel's function or mathematical solution could not exist. Even if the solution of Bessel's function exists, as Bessel function is a series function, we must get the solution by numerical method. Author had proposed the solution of the matrix method by Ritz's method and a new mode shape function, and had earned the good results for a wedge beam. Hereby a vibration analysis for the tapered beam with circle cross section was executed, and so good results were showed.

• Journal of Advanced Marine Engineering and Technology
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• v.29 no.8
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• pp.877-882
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• 2005

This paper discusses the lateral vibration of a bar which has its tip free. The uniform bar has a solution by summation of some simple exponential functions But if its shape is not uniform, its solution could be by Bessel's function, or mathematical solution could not be existed. Enen if the solution of Bessel's function exists. as Bessel function is a series function. we must got the solution by numerical method Hereby the author Proposes the ununiform beam solution of the matrix method by Ritz's method. and Proposes a new deflection shape function.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.984-987
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• 2003

This paper discusses the lateral vibration of a bar which has its tip free. The uniform bar has a solution by summation of some simple exponential functions. But if its shape is not uniform, its solution could be by Bessel's function, or mathematical solution could not be existed. Even if the solution of Bessel's function exists. as Bessel function is a series function, we must get the solution by numerical method, Hereof the author proposes the solution of the matrix method by Ritz's method, and proposes a new deflection shape

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.275-278
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• 1995

In this paper, we consider a dynamic shape control problem with an example of controlling a flexible beam shape. Mathematical formulations are obtained by employing the Green's function approach. Necessary conditions for optimality are derived by considering the quadratic performance criteria. Numerical results for both of the dynamic and the static cases are obtained and compared.

• Communications for Statistical Applications and Methods
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• v.15 no.4
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• pp.543-549
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• 2008

Inspired by using a robust loss function in the support vector machine regression to control training error and the idea of robust template matching with M-estimator, Chen (2004) applies M-estimator techniques to gaussian radial basis functions and form a new class of robust kernels for the support vector machines. We are specially interested in the shape of the Huber's M-estimator in this context and propose a way to find the shape parameter of the Huber's M-estimating function. For simplicity, only the two-class classification problem is considered.

• Journal of Institute of Control, Robotics and Systems
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• v.13 no.8
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• pp.790-797
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• 2007

This paper proposes a new measure of cost function ruggedness in local optimization with DEAS. DEAS is a computational optimization method developed since 2002 and has been applied to various engineering fields with success. Since DEAS is a recent optimization method which is rarely introduced in Korean, this paper first provides a brief overview and description of DEAS. In minimizing cost function with this non-gradient method, information on function shape measured automatically will enhance search capability. Considering the search strategies of DEAS are well designed with binary matrix structures, analysis of search behaviors will produce beneficial shape information. This paper deals with a simple quadratic function contained with various magnitudes of noise, and DEAS finds local minimum yielding ruggedness measure of given cost function. The proposed shape information will be directly used in improving DEAS performance in future work.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.04a
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• pp.279-287
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• 2003

This paper deals with a comparative study on coupling of Element-free Galerkin(EFG) method and Infinite Element(IE) by IE's shape function. In this study, mapped infinite elements(mapped IE) and decay function infinite elements(decay IE) are coupled with the EFG method. A coupling procedure of EFG-Mapped IE is much easier to be integrated than a coupled EFG-Decay IE. A coupled EFG-IE method used well-defined functions to preserve the continuity and linear consistency on the interface of the EFG region and IE region. Several benchmark problems are solved to verify the effectiveness and accuracy of the coupling algorithms by IE's shape function. The numerical results show that the developed algorithms work well for the elastic problems with infinite boundaries.

• Journal of computational fluids engineering
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• v.14 no.2
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• pp.1-8
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• 2009

The purposes of present work are to analyze the convective heat transfer with three-dimensional Reynolds-averaged Navier-Stokes analysis, and to optimize shape of the mixing vane taken tolerance into consideration by using the analysis results. Response surface method is employed as an optimization technique. The objective function is defined as a combination of heat transfer rate and inverse of pressure drop. Two bend angles of mixing vane are selected as design variables. Thermal-hydraulic performances have been discussed and optimum shape has been obtained as a function of weighting factor in the objective function. The results show that the optimized geometry improves the heat transfer performance far downstream of the mixing vane.

• Proceedings of the KSR Conference
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• 2008.06a
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• pp.2218-2223
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• 2008

A nose shape is strongly related with the aerodynamic performances of train. Therefore shape definition and aerodynamic performance analysis are important for train nose shape design. In this study, a new design method was suggested for train nose shape design by configuration function. To this end, the nose shape was classified by box type and each box shape is defined. After that the 3-D shape of train was defined as several mathematical functions by combination of each box shape. Also it was shown that the wind shield of driver's seat and complex curves of surface can be expressed using superposition of functions. This methodology can be used for grid generation of numerical analysis, and applied to aerodynamic optimization design of nose shape.