• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.7 s.250
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• pp.787-793
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• 2006

Recently kriging model has been widely used in the DACE (Design and Analysis of Computer Experiment) because of prominent predictability of nonlinear response. Since DACE has no random or measurement errors contrast to physical experiment, space filling experimental design that distributes uniformly design points over whole design space should be employed as a sampling method. In this paper, we examine the maximum entropy experimental design that reveals the space filling strategy in which defines the maximum entropy based on Gaussian or exponential. The influence of these two correlation functions on space filling design and their model parameters are investigated. Based on the exploration of numerous numerical tests, enhanced maximum entropy design based on exponential correlation function is suggested.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2000.04a
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• pp.143-148
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• 2000

In this article, we presents multi-objective design optimization of laminated composite beam using Fuzzy programming method. At first, the two design objectives are minimizing the structural weight and maximizing the buckling load respectively. Fuzzy multi-optimization problem can be formulated based on results of single optimizations. Due to different relative importance of design objectives, membership functions are constructed by adding exponential parameters for different objective's weights. Finite element analysis of composite beam for buckling behavior are carried by Natural mode method proposed by J.Argyris and computational time of analysis can be reduced. With this scheme, a designer can conveniently obtain a compromise optimal solution of a multi-objective optimization problem only by providing some exponential parameters corresponding to the importance of the objective functions.

• Industrial Engineering and Management Systems
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• v.16 no.1
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• pp.52-63
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• 2017

The inventory level of concurrent spare parts (CSP) has a significant impact on the availability of a weapon system. A failure rate function might be of particular importance in deciding the CSP inventory level. We developed a CSP optimization model which provides a compromise between purchase costs and shortage costs on the basis of the Weibull and the exponential failure rate functions, assuming that a failure occurs according to the (non-) homogeneous Poisson process. Computational experiments using the data obtained from the Korean Navy identified that, throughout the initial provisioning period, the optimization model using the exponential failure rate tended to overestimate the optimal CSP level, leading to higher purchase costs than the one using the Weibull failure rate. A Pareto optimality was conducted to find an optimal combination of these two failure rate functions as input parameters to the model, and this provides a practical solution for logistics managers.

• The Pure and Applied Mathematics
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• v.15 no.4
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• pp.387-392
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• 2008

In this note, an alternative proof and extensions are provided for the following conclusions in [6, Theorem 1 and Theorem 3]: The functions $\frac1{x^2}-\frac{e^{-x}}{(1-e^{-x})^2}\;and\;\frac1{t}-\frac1{e^t-1}$ are decreasing in (0, ${\infty}$) and the function $\frac{t}{e^{at}-e^{(a-1)t}}$ for a $a{\in}\mathbb{R}\;and\;t\;{\in}\;(0,\;{\infty})$ is logarithmically concave.

• Journal of the Korean School Mathematics Society
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• v.15 no.2
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• pp.299-316
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• 2012

In this paper, we examine high school in order to know their ability for understanding about fundamental functions, such as polynomial, trigonometric, logarithm and exponential functions which have learned from high school. The result of this study shows as follows. More than half students are not able to draw shape of given functions, except polynomial. More students do not fully understand about function properties such as domain, codomain, range, maximum and minimum value.

• Wind and Structures
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• v.13 no.3
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• pp.235-256
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• 2010

The aeroelastic stability of bridge decks equipped with multiple tuned mass dampers is studied. The problem is attacked in the time domain, by representing self-excited loads with the aid of aerodynamic indicial functions approximated by truncated series of exponential filters. This approach allows to reduce the aeroelastic stability analysis in the form of a direct eigenvalue problem, by introducing an additional state variable for each exponential term adopted in the approximation of indicial functions. A general probabilistic framework for the optimal robust design of multiple tuned mass dampers is proposed, in which all possible sources of uncertainties can be accounted for. For the purposes of this study, the method is also simplified in a form which requires a lower computational effort and it is then applied to a general case study in order to analyze the control effectiveness of regular and irregular multiple tuned mass dampers. A special care is devoted to mistuning effects caused by random variations of the target frequency. Regular multiple tuned mass dampers are seen to improve both control effectiveness and robustness with respect to single tuned mass dampers. However, those devices exhibit an asymmetric behavior with respect to frequency mistuning, which may weaken their feasibility for technical applications. In order to overcome this drawback, an irregular multiple tuned mass damper is conceived which is based on unequal mass distribution. The optimal design of this device is finally pursued via a full domain search, which evidences a remarkable robustness against frequency mistuning, in the sense of the simplified design approach.

• Steel and Composite Structures
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• v.47 no.5
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• pp.569-585
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• 2023

This paper proposes an efficient approach for the structural topology optimization of bi-directional functionally graded structures by incorporating popular radial basis functions (RBFs) into an implicit level set (ILS) method. Compared to traditional element density-based methods, a level set (LS) description of material boundaries produces a smoother boundary description of the design. The paper develops RBF implicit modeling with multiquadric (MQ) splines, thin-plate spline (TPS), exponential spline (ES), and Gaussians (GS) to define the ILS function with high accuracy and smoothness. The optimization problem is formulated by considering RBF-based nodal densities as design variables and minimizing the compliance objective function. A LS-RBF optimization method is proposed to transform a Hamilton-Jacobi partial differential equation (PDE) into a system of coupled non-linear ordinary differential equations (ODEs) over the entire design domain using a collocation formulation of the method of lines design variables. The paper presents detailed mathematical expressions for BiDFG beams topology optimization with two different material models: continuum functionally graded (CFG) and mechanical functionally graded (MFG). Several numerical examples are presented to verify the method's efficiency, reliability, and success in accuracy, convergence speed, and insensitivity to initial designs in the topology optimization of two-dimensional (2D) structures. Overall, the paper presents a novel and efficient approach to topology optimization that can handle bi-directional functionally graded structures with complex geometries.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.34 no.1
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• pp.91-98
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• 2016

In order to apply Kriging methods for geostatistics of spatial data, an estimation of spatial coherency functions is required priorly based on the spatial distance between measurement points. In the study, the typical coherency functions, such as semi-variogram, homeogram, and covariance function, were estimated using the national geoid model. The test area consisting of 2°×2° and the Unified Control Points (UCPs) within the area were chosen as sampling measurements of the geoid. Based on the distance between the control points, a total of 100 sampling points were grouped into distinct pairs and assigned into a bin. Empirical values, which were calculated with each of the spatial coherency functions, resulted out as a wave model of a semi-variogram for the best quality of fit. Both of homeogram and covariance functions were better fitted into the exponential model. In the future, the methods of various Kriging and the functions of estimated spatial coherency need to be studied to verify the prediction accuracy and to calculate the Mean Squared Prediction Error (MSPE).

• Research in Mathematical Education
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• v.7 no.3
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• pp.191-209
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• 2003

In this paper, we present a new environment of learning and teaching of trigonometric, exponential and logarithmic functions, the most difficult parts for students to learn among functions, through sound and music, students like the most. First, by using sound and music, we try to arouse student's interest. Second, we let students see and hear properties of transcendental functions so that students can understand and remember them easily. Finally we encourage students to compose their favorite song using transcendental functions so that they can experience the practicality of transcendental functions.

• Geomechanics and Engineering
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• v.6 no.1
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• pp.47-63
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• 2014

In this paper, asymmetric drainage boundaries modeled by exponential functions which can simulate intermediate drainage from pervious to impervious boundary is proposed for the one-dimensional consolidation problem, and the solution for the new boundary conditions was derived. The new boundary conditions satisfy the initial and the steady state conditions, and the solution for the new boundary conditions can be degraded to the conventional solution by Terzaghi. Convergence study on the infinite series solution showed that only one term in the series is needed to meet the precision requirement for larger degree of consolidation, and that more terms in the series for smaller degree of consolidation. Comparisons between the present solution with those by Terzaghi and Gray are also provided.