• Advances in nano research
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• 제4권4호
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• pp.251-264
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• 2016

In this paper, a simple and refined nonlocal hyperbolic higher-order beam theory is proposed for bending and vibration response of nanoscale beams. The present formulation incorporates the nonlocal scale parameter which can capture the small scale effect, and it considers both shear deformation and thickness stretching effects by a hyperbolic variation of all displacements across the thickness without employing shear correction factor. The highlight of this formulation is that, in addition to modeling the displacement field with only two unknowns, the thickness stretching effect (${\varepsilon}_z{\neq}0$) is also included in the present model. By utilizing the Hamilton's principle and the nonlocal differential constitutive relations of Eringen, the equations of motion of the nanoscale beam are reformulated. Verification studies demonstrate that the developed theory is not only more accurate than the refined nonlocal beam theory, but also comparable with the higher-order shear deformation theories which contain more number of unknowns. The theoretical formulation proposed herein may serve as a reference for nonlocal theories as applied to the static and dynamic responses of complex-nanobeam-system such as complex carbon nanotube system.

• 한국수학사학회지
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• 제32권3호
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• pp.109-134
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• 2019

In order to improve the educational situation in which the natural number e and the natural logarithm are dealt with somewhat perfunctorily, this study explores the genetic process in which the natural logarithm and its base e occurred, and has an educational discussion based on that analysed process. Specifically, the study inquires into how the natural logarithm happened in relation to the quadrature of the hyperbolic curves through analysis and thought experimentation in mathematics history. Particularly, it sheds light on the role of e and the naturalness of the natural logarithm in terms of the introduction of the real number exponent. Also, this study discusses what the findings suggest educationally.

• Bulletin of the Korean Chemical Society
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• 제13권4호
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• pp.413-419
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• 1992

The theoretical equation for the relaxation spectrum of nonlinear viscoelastic polymeric material was derived from the Ree-Eyring and Maxwell non-Newtonian model. This model consists of infinite number of hyperbolic sine law Maxwell elements coupled in parallel plus a spring without a dashpot. Infinite number of nonlinear viscoelastic Maxwell elements can be used by specifying distribution of relaxation times, hole volumes, molecular weights, crystallite size and conformational size, etc. The experimentals of stress relaxation were carried out using the tensile tester with the solvent chamber. The relaxation spectra of nylon 6 filament fibers in various electrolytic solutions were obtained by applying the experimental stress relaxation curves to the theoretical equation of relaxation spectrum. The determination of relaxation spectra was performed from computer calculation.

• Steel and Composite Structures
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• 제18권4호
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• pp.1063-1081
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• 2015

In this paper, a new nonlocal hyperbolic refined plate model is presented for free vibration properties of functionally graded (FG) plates. This nonlocal nano-plate model incorporates the length scale parameter which can capture the small scale effect. The displacement field of the present theory is chosen based on a hyperbolic variation in the in-plane displacements through the thickness of the nano-plate. By dividing the transverse displacement into the bending and shear parts, the number of unknowns and equations of motion of the present theory is reduced, significantly facilitating structural analysis. The material properties are assumed to vary only in the thickness direction and the effective properties for the FG nano-plate are computed using Mori-Tanaka homogenization scheme. The governing equations of motion are derived based on the nonlocal differential constitutive relations of Eringen in conjunction with the refined four variable plate theory via Hamilton's principle. Analytical solution for the simply supported FG nano-plates is obtained to verify the theory by comparing its results with other available solutions in the open literature. The effects of nonlocal parameter, the plate thickness, the plate aspect ratio, and various material compositions on the dynamic response of the FG nano-plate are discussed.

• Earthquakes and Structures
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• 제14권2호
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• pp.103-115
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• 2018

In this work, a simple but accurate hyperbolic plate theory for the free vibration analysis of functionally graded material (FGM) sandwich plates is developed. The significant feature of this formulation is that, in addition to including the shear deformation effect, it deals with only 3 unknowns as the classical plate theory (CPT), instead of 5 as in the well-known first shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). A shear correction factor is, therefore, not required. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM face sheet and the homogeneous core and the sandwich with the homogeneous face sheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton's principle. The closed form solutions are obtained by using the Navier technique. The fundamental frequencies are found by solving the eigenvalue problems. Numerical results of the present theory are compared with the CPT, FSDT, order shear deformation theories (HSDTs), and 3D solutions. Verification studies show that the proposed theory is not only accurate and simple in solving the free vibration behaviour of FGM sandwich plates, but also comparable with the higher-order shear deformation theories which contain more number of unknowns.

• 한국광학회지
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• 제17권5호
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• pp.412-419
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• 2006

초정밀 비구면 기공기로 제작한 구경 300 mm이고 f-수가 1.98인 알루미늄 쌍곡면 거울의 형상을 측정하기 위하여 자동무수차점 널(null) 렌즈 광학계를 설계하고 제작하였으며, 이를 이용하여 이 대구경 쌍곡면 거울의 형상을 측정하였다. 이때 널 렌즈간 정렬은 구조적으로 안정하고 부피가 작은 경통고정식을 선택하였고, 널 렌즈 및 경통의 제작 허용오차는 요구되는 측정 정밀도를 만족하도록 공차분석기법을 통하여 계산하고 제작하였다.

• 한국농공학회논문집
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• 제63권1호
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• pp.103-116
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• 2021

Analysis of runoff is substantial for effective water management in the watershed. Runoff occurs by reaction of a watershed to the rainfall and has non-linearity and uncertainty due to the complex relation of weather and watershed factors. ANN (Artificial Neural Network), which learns from the data, is one of the machine learning technique known as a proper model to interpret non-linear data. The performance of ANN is affected by the ANN's structure, the number of hidden layer nodes, learning rate, and activation function. Especially, the activation function has a role to deliver the information entered and decides the way of making output. Therefore, It is important to apply appropriate activation functions according to the problem to solve. In this paper, ANN models were constructed to estimate runoff with different activation functions and each model was compared and evaluated. Sigmoid, Hyperbolic tangent, ReLU (Rectified Linear Unit), ELU (Exponential Linear Unit) functions were applied to the hidden layer, and Identity, ReLU, Softplus functions applied to the output layer. The statistical parameters including coefficient of determination, NSE (Nash and Sutcliffe Efficiency), NSEln (modified NSE), and PBIAS (Percent BIAS) were utilized to evaluate the ANN models. From the result, applications of Hyperbolic tangent function and ELU function to the hidden layer and Identity function to the output layer show competent performance rather than other functions which demonstrated the function selection in the ANN structure can affect the performance of ANN.

• 한국지반신소재학회논문집
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• 제17권4호
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• pp.21-28
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• 2018

대심도 연약지반을 개량하여 상부에 개설되는 도로 등 각종 시설물의 안전을 확보하기 위해서는 공용개시 후 잔류 침하량에 대한 명확한 이해를 바탕으로 한 합리적인 설계관리기준의 설정과 예측 값 산정이 매우 중요하다. 그러나 지난 수십 년 동안 낙동강 하구 일원 등 대심도 연약지반상의 지반개량을 통해 조성된 부지에서는 설계단계에서 예측한 잔류 침하량을 크게 상회하는 침하가 발생하여 많은 시설물의 파손과 아울러 사회적인 논란을 야기되고 있음에도 이에 대한 연구는 거의 전무한 실정이다. 본 논문에서는 공용하중 개시 이후 장기간에 걸쳐 발생하는 잔류 침하에 대한 기초적이며 실무적인 연구를 위해, 대심도 연약지반개량을 통해 조성된 부지에서 약 10년에 걸쳐 측정한 침하계측결과를 이용하여 장기 침하거동 양상을 분석하였다. 그 결과 계측된 잔류침하량은 점성토층의 두께의 차이로 지점별로 차이가 있으나 침하양상은 모든 계측결과가 유사하였으며, 쌍곡선 함수식을 이용한 장래 잔류침하 예측결과와는 매우 좋은 일치를 보였다. 또한, 하부 미개량층에서 발생한 침하량이 전체침하량의 대부분(62-76%)을 차지하는 것으로 확인되어 개량층을 대상으로 허용침하량을 규정하고 있는 국내의 현실에 좀 더 신중한 고민이 필요한 것으로 나타났다.

• 대한수학회지
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• 제45권4호
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• pp.965-976
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• 2008

In this article, we constructively prove that on a surface S with genus g$\geq$2, there exit maximal geodesic laminations with 7g-7,...,9g-9 leaves. Thus, S can have ideal cell-decompositions (i.e., S can be (ideally) triangulated by maximal geodesic laminations) with 7g-7,...,9g-9 (ideal) 1-cells. Once there is a triangulation for a compact surface, the Euler characteristic for the surface can be calculated as the alternating sum F-E+V, where F, E, and V denote the number of faces, edges, and vertices, respectively. We also prove that the same formula holds for the ideal cell decompositions.

• Journal of the Korean Data and Information Science Society
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• 제27권6호
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• pp.1661-1671
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• 2016

Risk analysis is a systematic study of uncertainties and risks we encounter in business, engineering, public policy, and many other areas. Value at Risk (VaR) is one of the most widely used risk measurements in risk management. In this paper, the Korean Composite Stock Price Index data has been utilized to model the VaR employing the classical ARMA (1,1)-GARCH (1,1) models with normal, t, generalized hyperbolic, and generalized pareto distributed errors. The aim of this paper is to compare the performance of each model in estimating the VaR. The performance of models were compared in terms of the number of VaR violations and Kupiec exceedance test. The GARCH-GPD likelihood ratio unconditional test statistic has been found to have the smallest value among the models.