• 한국방재학회 논문집
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• 제8권2호
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• pp.39-43
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• 2008

Determination of strain associated with shear modulus and damping ratio during torsional test is complicated. This is due to nonuniform stress-strain variation occurring linearly with radius in a soil specimen in torsion. A conventional equivalent radius approach proposed by Chen and Stokoe appears to be adequate for evaluating strain associated with shear modulus at low to intermediate strain levels. This approach is less accurate for damping measurement, particularly at high strain. Modified equivalent radius approach was used to account for the nonuniform stress-strain effect more precisely. The modified equivalent radius approach was applied for hyperbolic, modified hyperbolic, and Ramberg-Osgood models. The results illustrate the usefulness of the modified equivalent radius approach and suggest that using a single value of equivalent radius ratio to calculate strains is not appropriate.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제6권2호
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• pp.87-93
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• 1999

A holomorphic function f on D = {z : │z│ ＜ 1} is called uniformly locally univalent if there exists a positive constant $\rho$ such that f is univalent in every hyperbolic disk of hyperbolic radius $\rho$. We establish a characterization of uniformly locally univalent functions and investigate uniform local univalence of holomorphic universal covering projections.

• 한국방재학회 논문집
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• 제8권2호
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• pp.97-103
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• 2008

Determination of stress-strain relationship in torsional tests is complicated due to nonuniform stress-strain variation occurring linearly with the radius in a soil specimen in torsion. The equivalent radius approach is adequate when calculating strain at low to intermediate strains, however, the approach is less accurate when performing the test at higher strain levels. The modified equivalent radius approach was developed to account for the problem more precisely. This approach was extended to generate the plots of equivalent radius ratio versus strain using modified hyperbolic and Ramberg-Osgood models. Results showed the effects of soil nonlinearity on the equivalent radius ratio curves were observed. Curve fitting was also performed to find the stress-strain relationship by fitting the theoretical torque-rotation relationship to measured torque-rotation relationship.

• 한국지진공학회논문집
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• 제12권1호
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• pp.43-55
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• 2008

비틂시험에서 전단탄성계수와 감쇠비에 상응하는 변형률 산정의 복잡성은 여러 방법에 의하여 해결되어 왔다. 특히, 수정 등가반경법은 공진주/비틂전단 시험의 모든 변형률 영역에서 변형률에 따른 등가반경비 곡선을 보다 효과적으로 나타내는데 적합하다. 감쇠비 산정시 수정 등가반경법을 쌍곡선 모델, 수정 쌍곡선 모델, 램버그오스굿 모델등에 적용시켜 보았다. 연구결과는 감쇠비 산정시 재래식 등가반경법에 의한 하나의 등가반경 수치를 사용하는 것은 적절치 않다는 것을 보여주었다. 이력감쇠뿐 아니라 미소변형률 영역에서의 흙의 감쇠 현상을 고려하기 위하여 새로운 모델이 개발되었고, 이러한 두 가지 복합감쇠에 상응하는 변형률 산정시 부가적 조정이 필요한지 검토해 보았다.

• 한국광학회지
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• 제12권5호
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• pp.352-355
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• 2001

고해상도 원격관측용 카메라로 설계된 비축 3반사 광학계의 제1거울인 쌍곡면 형상 측정을 위한 null 렌즈를 설계하였다. Null 렌즈는 autostigmatic 방식과 mixed 방식으로 설계하였으며, 렌즈의 곡률반경, 두께등의 변수에 대한 상대적 민감도를 비교 분석하여 보다 측정이 용이한 null 렌즈를 제시하였다.

• 대한수학회지
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• 제33권3호
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• pp.587-599
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• 1996

We assume throughout the paper that f(z) is a conformal function in the ipen unit disk $D = {z : $\mid$z$\mid$ < 1}$. In the rest of paper, conformal means analytic and locally univalent.

• Structural Engineering and Mechanics
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• 제84권6호
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• pp.707-722
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• 2022

In this study, a new refined hyperbolic shear deformation theory (RHSDT) is developed using an equivalent single-layer shell displacement model for the static bending and free vibration response of cross-ply laminated composite spherical shells. It is based on a new kinematic in which the transverse displacement is approximated as a sum of the bending and shear components, leading to a reduction of the number of unknown functions and governing equations. The proposed theory uses the hyperbolic shape function to account for an appropriate distribution of the transverse shear strains through the thickness and satisfies the boundary conditions on the shell surfaces without requiring any shear correction factors. The shell governing equations for this study are derived in terms of displacement from Hamilton's principle and solved via a Navier-type analytical procedure. The validity and high accuracy of the present theory are ascertained by comparing the obtained numerical results of displacements, stresses, and natural frequencies with their counterparts generated by some higher-order shear deformation theories. Further, a parametric study examines in detail the effect of both geometrical parameters (i.e., side-to-thickness ratio and curvature-radius-to-side ratio), on the bending and free vibration response of simply supported laminated spherical shells, which can be very useful for many modern engineering applications and their optimization design.

• 한국공간구조학회논문집
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• 제16권3호
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• pp.67-78
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• 2016

Determining of the shape in the process of design for natural draught cooling tower is very important, because the shape of hyperbolic shell is respond sensitively to dynamic behavior of the whole cooling tower against wind load. In engineering practice, the geometric parameters have been determining based on the natural frequency. This study analyses influence of the tower shell geometric parameters on the structural behavior. For three representative models were selected, they were analyzed based on evaluation of damage by means of nonlinear FE-method. As a result, a hyperbolic rotational shell with the small radius overall was the lowest damage index induced by sufficient capacity of the stress redistribution and thus a wind-insensitive structure.

• Structural Engineering and Mechanics
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• 제82권5호
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• pp.629-641
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• 2022

This study deals with the spinning impact on flap-wise vibration characteristics of nonlocal functionally graded (FG) cylindrical beam based on the Hyperbolic shear deformation beam theory. The nonlocal strain gradient theory is used to investigate the small-scale impact on the nonlocal motion equation as well as corresponding nonlocal boundary conditions. Based on the mathematical simulation and according to the Hamilton principle, the computerized modeling of a rotating functionally graded nanotube is generated, and then, via a numerical approach, the obtained mathematical equations are solved. The calculated outcomes are helpful to the production of Nano-electro-mechanical-systems (NEMS) by investigating some designed parameters such as rotating speed, hub radius, length-scale parameters, volume fraction parameters, etc.

• 호남수학학술지
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• 제34권1호
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• pp.103-111
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• 2012

Wetzel[5] proved if ${\Gamma}$ is a closed curve of length L in $E^n$, then ${\Gamma}$ lies in some ball of radius [L/4]. In this paper, we generalize Wetzel's result to the non-Euclidean plane with much stronger version. That is to develop a lower bound of length of a triangle inscribed in a circle in non-Euclidean plane in terms of a chord of the circle.